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									                BEAMST User Manual
                                   Version 12




ANSYS, Inc.
Southpointe
275 Technology Drive
Canonsburg, PA 15317
ansysinfo@ansys.com
http://www.ansys.com
(T) 724-746-3304
(F) 724-514-9494




             © Copyright 2009. Century Dynamics Limited. All Rights Reserved.
                     Century Dynamics is a subsidiary of ANSYS, Inc.
                Unauthorised use, distribution or duplication is prohibited.

                         ANSYS, Inc. is certified to ISO 9001:2008
                                                Revision Information

 The information in this guide applies to all ANSYS, Inc. products released on or after this date, until
superseded by a newer version of this guide. This guide replaces individual product installation guides
                                        from previous releases.

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  © 2009 SAS IP, Inc. All rights reserved. Unauthorized use, distribution or duplication is prohibited.

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                                                  Published in the U.S.A.




Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.
                            BEAMST User Manual
                                Update Sheet for Version 12
                                        April 2009


Modifications:

The following modifications have been incorporated:

Section               Page(s)                 Update/Addition          Explanation

All                   All                     Update                   Conversion to Microsoft® Word format

1.1                   1-1                     Update                  Delete reference to legacy program APCA

1.1                   1-2                     Update                  Delete references to legacy programs
                                                                      BEAMVIEW, PICASO

2.6                   2-4                     Update                  Delete reference to legacy program APCA

2.9                   2-10                    Update                  Delete reference to legacy program PICASO

3.4                   3-47                    Update                   Clarify use of GAPD command


4.2.4.3               4-51                    Update                  Correct equations for I section

4.2.5.3               4-78                    Update                  Correct equations for I section

5.4.4.2               5-61                    Update                  Correct equations for Chord Design Factor

App A.11              A-9                     Update                  Delete references to legacy program PICASO

App A.14              A-12                    Addition                Add ANSYS command

App B.4               B-1                     Update                  Delete reference to legacy program PICASO

App E                 E-1                     Update                  Delete references to legacy program PICASO

App E.1               E-1, E-2                Update                  Delete references to legacy program PICASO

App E.3               E-11 – E-14             Update                  Delete Section E.3 (Presenting BEAMST
                                                                      Results in PICASO)




Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.
                                                      TABLE OF CONTENTS


1.    Introduction ........................................................................................................................ 1-1
 1.1 General Description ......................................................................................................... 1-1
 1.2 About this Manual ............................................................................................................ 1-2
2.    Facilities in BEAMST ........................................................................................................ 2-4
 2.1 Selection of Members and Joints ..................................................................................... 2-4
 2.2 Section Properties for BEAMST...................................................................................... 2-4
 2.3 Beam Local Axes Considerations .................................................................................... 2-5
 2.4 Section Orientation........................................................................................................... 2-6
 2.5 Member Stress Evaluation ............................................................................................... 2-6
 2.6 Loadcase Combinations, Origin and Classification ......................................................... 2-7
 2.7 Code Checking in BEAMST............................................................................................ 2-8
 2.8 Output Reports ................................................................................................................. 2-9
   2.8.1 Data Echo Report ......................................................................................................... 2-10
   2.8.2 Command Summary Report ........................................................................................ 2-10
   2.8.3 Input Data Cross Check Report ................................................................................... 2-11
   2.8.4 Member Reports .......................................................................................................... 2-11
    2.8.4.1 Member Property Report ................................................................................... 2-11
    2.8.4.2 Member Force Report ........................................................................................ 2-12
    2.8.4.3 Member Stress Report........................................................................................ 2-12
   2.8.5 Unity Check Report ..................................................................................................... 2-13
   2.8.6 Summary Reports ........................................................................................................ 2-13
 2.9 Saving Results for Graphical Display ............................................................................ 2-14
3.    Input Data ........................................................................................................................... 3-1
 3.1 Command Structures ........................................................................................................ 3-1
   3.1.1 Command Syntax........................................................................................................... 3-1
   3.1.2 Data Types ..................................................................................................................... 3-2
   3.1.3 Special Symbols............................................................................................................. 3-3
   3.1.4 The NOT Command Modifier ....................................................................................... 3-4
 3.2 BEAMST Command Sets ................................................................................................ 3-6
 3.3 Priority of Data Assignments ......................................................................................... 3-24
 3.4 BEAMST Commands .................................................................................................... 3-26
 ABNO Command .................................................................................................................... 3-26
 AISC Header Command .......................................................................................................... 3-27
 API Header Command............................................................................................................. 3-28
 BRIG Command ...................................................................................................................... 3-30
 BS59 Command ....................................................................................................................... 3-31
 CASE Command ..................................................................................................................... 3-32
 CB Command .......................................................................................................................... 3-33
 CHOR Command .................................................................................................................... 3-34
 CMBV Command .................................................................................................................... 3-36
 CMY/CMZ Command ............................................................................................................. 3-38
 COMB Command .................................................................................................................... 3-39
 DESI Command ....................................................................................................................... 3-40
 DS449 Header Command ........................................................................................................ 3-43


Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.
BEAMST User Manual                                                                                                        Contents

 EFFE Command ...................................................................................................................... 3-44
 ELEM Command ..................................................................................................................... 3-45
 ELEV Command ..................................................................................................................... 3-46
 END Command ....................................................................................................................... 3-47
 EXTR Command ..................................................................................................................... 3-48
 GAPD Command ..................................................................................................................... 3-49
 GRAV Command .................................................................................................................... 3-50
 GROU Command .................................................................................................................... 3-51
 HYDR Command .................................................................................................................... 3-52
 JOIN Command ....................................................................................................................... 3-53
 LIMIT Command .................................................................................................................... 3-54
 MCOF Command .................................................................................................................... 3-55
 MFAC Command .................................................................................................................... 3-57
 MLTF Command ..................................................................................................................... 3-58
 MOVE Command .................................................................................................................... 3-59
 NPD Command........................................................................................................................ 3-61
 PHI Command ......................................................................................................................... 3-62
 POST Command ...................................................................................................................... 3-64
 PRIN Command ...................................................................................................................... 3-65
 PROF Command...................................................................................................................... 3-68
 QUAK Command .................................................................................................................... 3-71
 RENU Command ..................................................................................................................... 3-72
 SAFE Command ...................................................................................................................... 3-73
 SEAR Command ..................................................................................................................... 3-74
 SECO Command ..................................................................................................................... 3-76
 SECT Command ...................................................................................................................... 3-77
 SELE Command ...................................................................................................................... 3-78
 SIMP Command ...................................................................................................................... 3-79
 SPEC Command ...................................................................................................................... 3-80
 STUB Command ..................................................................................................................... 3-81
 TITLE Command .................................................................................................................... 3-83
 TYPE Command...................................................................................................................... 3-84
 ULCF Command ..................................................................................................................... 3-86
 UNBR Command .................................................................................................................... 3-87
 UNIT Command ...................................................................................................................... 3-88
 WAVE Command.................................................................................................................... 3-89
 YIEL Command ...................................................................................................................... 3-90
4.    AISC Code Checks ............................................................................................................. 4-1
 4.1 AISC Working Stress Design Allowable Check (AISC WSD ALLO) ........................... 4-2
   4.1.1 Overview........................................................................................................................ 4-2
   4.1.2 AISC WSD Allowable Unity Check Report ................................................................. 4-6
   4.1.3 Nomenclature ............................................................................................................... 4-13
    4.1.3.1 Dimensional ....................................................................................................... 4-13
    4.1.3.2 Acting Stresses ................................................................................................... 4-14
    4.1.3.3 Allowable Stresses ............................................................................................. 4-14
   4.1.4 AISC WSD Allowable Stresses and Unity Checks ..................................................... 4-15
    4.1.4.1 Allowable Stress Increase .................................................................................. 4-15
    4.1.4.2 Axial Tension Checks ........................................................................................ 4-15
    4.1.4.3 Axial Compression Checks ................................................................................ 4-16
    4.1.4.4 Bending Checks ................................................................................................. 4-20



Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.                                 ii
BEAMST User Manual                                                                                                      Contents

    4.1.4.5 Shear Checks ...................................................................................................... 4-25
    4.1.4.6 Unity Checks ...................................................................................................... 4-27
    4.1.4.7 Combined Stress Unity Checks ......................................................................... 4-28
    4.1.4.8 Combined Axial and Bending Yield Unity Check ............................................ 4-29
    4.1.4.9 Cb - Bending Coefficient .................................................................................... 4-30
    4.1.4.10 Cmy , Cmz - Amplification Reduction Factors..................................................... 4-32
  4.1.5 Spectral Loadcases and ‘Automatic Signed Expansion Procedures’ .......................... 4-34
    4.1.5.1 Torsional Effects ................................................................................................ 4-34
    4.1.5.2 Axial Unity Check and the Axial Component of Combined Stress Buckle and
    Yield Unity Checks ............................................................................................................. 4-34
    4.1.5.3 Local Axes Shear Unity Checks and Maximum Shear Unity Check for Tubular
    Sections 4-34
    4.1.5.4 Local Axes Pure Bending Unity Checks and Bending Components of Combined
    Stresses Yield Unity Check ................................................................................................ 4-35
    4.1.5.5 Unity Check Report for Shear, Pure Bending and Yield Unity Checks ............ 4-36
    4.1.5.6 Combined Stress Buckle Unity Check ............................................................... 4-36
 4.2 AISC Load and Resistance Factor Design Member Check ........................................... 4-39
  4.2.1 Overview...................................................................................................................... 4-39
  4.2.2 AISC LRFD Unity Check Report ................................................................................ 4-42
  4.2.3 Nomenclature ............................................................................................................... 4-48
    4.2.3.1 Definition of Symbols ........................................................................................ 4-48
    4.2.3.2 Dimensional ....................................................................................................... 4-49
    4.2.3.3 Acting Forces and Stresses ................................................................................ 4-49
    4.2.3.4 Strengths and Utilisations .................................................................................. 4-50
    4.2.3.5 Parameters .......................................................................................................... 4-50
  4.2.4 AISC LRFD MEMBER CHECKS .............................................................................. 4-51
    4.2.4.1 AISC LRFD Partial Coefficients ....................................................................... 4-51
    4.2.4.2 Nominal Axial Tension Strength ....................................................................... 4-51
    4.2.4.3 Nominal Axial Compressive Strength ............................................................... 4-52
    4.2.4.3    Nominal Axial Compressive Strength continued ............................................. 4-57
    4.2.4.4 Bending Strength ............................................................................................... 4-58
    4.2.4.5 Major Axis Bending Strength ............................................................................ 4-58
    4.2.4.6 Slender Web ....................................................................................................... 4-62
    4.2.4.7 Minor Axis Bending Strength ............................................................................ 4-64
    4.2.4.8 Bending Strength Box and RHS ........................................................................ 4-65
    4.2.4.9 Bending Strength Tubes ..................................................................................... 4-68
    4.2.4.10 Shear .................................................................................................................. 4-69
    4.2.4.11 Unity Checks ...................................................................................................... 4-71
    4.2.4.12 Combined Stress Unity Checks ......................................................................... 4-72
    4.2.4.13 Cb - Bending Coefficient .................................................................................... 4-74
    4.2.4.14 Cmy , Cmz - Amplification Reduction Factors..................................................... 4-76
  4.2.5 AISC LRFD MEMBER CHECKS - 3rd Edition ........................................................ 4-78
    4.2.5.1 AISC LRFD Partial Coefficients ....................................................................... 4-78
    4.2.5.2 Nominal Axial Tension Strength ....................................................................... 4-78
    4.2.5.3 Nominal Axial Compressive Strength ............................................................... 4-79
    4.2.5.4 Bending Strength ............................................................................................... 4-85
    4.2.5.5 Major Axis Bending Strength ............................................................................ 4-85
    4.2.5.6 Slender Web ....................................................................................................... 4-89
    4.2.5.7 Minor Axis Bending Strength ............................................................................ 4-91
    4.2.5.8 Bending Strength Box and RHS ........................................................................ 4-92



Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.                              iii
BEAMST User Manual                                                                                                        Contents

    4.2.5.9 Bending Strength Tubes ..................................................................................... 4-95
    4.2.5.10 Shear .................................................................................................................. 4-96
    4.2.5.11 Unity Checks ...................................................................................................... 4-98
    4.2.5.12 Combined Stress Unity Checks ......................................................................... 4-99
    4.2.5.13 Cb - Bending Coefficient .................................................................................. 4-101
    4.2.5.14 Cmy , Cmz - Amplification Reduction Factors................................................... 4-103
5.    API Code Check ................................................................................................................. 5-1
 5.1 API Working Stress Design Allowable Member Stress Check (API WSD ALLO) ....... 5-2
   5.1.1 Overview........................................................................................................................ 5-2
   5.1.2 API Allowable Unity Check Report .............................................................................. 5-6
   5.1.3 Nomenclature ............................................................................................................... 5-11
    5.1.3.1 Dimensional ....................................................................................................... 5-11
    5.1.3.2 Acting Section Forces and Stresses ................................................................... 5-11
    5.1.3.3 Allowable Stresses and Unity Checks ............................................................... 5-12
    5.1.3.4 Parameters .......................................................................................................... 5-12
   5.1.4 API Allowable Stresses and Unity Checks .................................................................. 5-13
    5.1.4.1 API Allowable Stress Increase........................................................................... 5-13
    5.1.4.2 Tension............................................................................................................... 5-14
    5.1.4.3 Compression ...................................................................................................... 5-14
    5.1.4.4 Bending .............................................................................................................. 5-15
    5.1.4.5 Shear .................................................................................................................. 5-16
    5.1.4.6 Unity Checks ...................................................................................................... 5-16
    5.1.4.7 Combined Stresses ............................................................................................. 5-17
   5.1.5 Spectral Loadcases....................................................................................................... 5-19
    5.1.5.1 Torsional Effects ................................................................................................ 5-19
    5.1.5.2 Axial Unity Check and the Axial Component of Combined Stress Buckle and
    Yield Unity Checks ............................................................................................................. 5-19
    5.1.5.3 Local Axes Shear Unity Checks and Maximum Shear Unity Check for Tubular
    Sections 5-19
    5.1.5.4 Local Axes Pure Bending Unity Checks and Bending Components of Combined
    Stresses Yield Unity Check ................................................................................................ 5-20
    5.1.5.5 Unity Check Report for Shear, Pure Bending and Yield Unity Checks ............ 5-21
    5.1.5.6 Combined Stress Buckle Unity Check ............................................................... 5-21
 5.2 API Nominal Load Check (API WSD JOIN) ................................................................ 5-25
   5.2.1 Overview...................................................................................................................... 5-25
   5.2.2 API Nominal Load Check Reports .............................................................................. 5-29
   5.2.3 Nomenclature ............................................................................................................... 5-30
    5.2.3.1 Dimensional ....................................................................................................... 5-30
    5.2.3.2 Acting Forces and Stresses ................................................................................ 5-30
    5.2.3.3 Allowable Stresses and Unity Checks ............................................................... 5-31
   5.2.4 API Allowable Nominal Loads and Unity Checks ...................................................... 5-32
    5.2.4.1 Basic Capacity ................................................................................................... 5-32
    5.2.4.2 Strength Factor Qu ............................................................................................. 5-33
    5.2.4.3 Chord Load Factor Qf ........................................................................................ 5-34
    5.2.4.4 Joints with Thickened Cans ............................................................................... 5-34
    5.2.4.5 Nominal Load Unity Checks ............................................................................. 5-35
    5.2.4.6 Combined Axial and Bending Unity Checks ..................................................... 5-35
   5.2.5 Spectral Expansion for Joint Checks (API NOMI) ..................................................... 5-36
 5.3 API Hydrostatic Collapse Check (API WSD HYDR) ................................................... 5-37
   5.3.1 Overview...................................................................................................................... 5-37



Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.                                iv
BEAMST User Manual                                                                                                      Contents

  5.3.2 API Hydrostatic Unity Check Reports ........................................................................ 5-41
  5.3.3 Nomenclature ............................................................................................................... 5-44
    5.3.3.1 Dimensional ....................................................................................................... 5-44
    5.3.3.2 Acting Section Forces and Stresses ................................................................... 5-44
    5.3.3.3 Allowable Stresses and Unity Checks ............................................................... 5-44
  5.3.4 API Allowable Stresses and Unity Checks .................................................................. 5-45
    5.3.4.1 Limit Checks ...................................................................................................... 5-47
    5.3.4.2 Elastic Hoop Buckling Stress Fhe ....................................................................... 5-47
    5.3.4.3 Critical Hoop Buckling Stress Fhc ...................................................................... 5-48
    5.3.4.4 Allowable Critical Hoop Buckling Stress Fch ................................................... 5-48
    5.3.4.5 Critical Axial Elastic Local Buckling Stress Fxe .............................................. 5-48
    5.3.4.6 Allowable Axial Elastic Local Buckling Stress Faa ........................................... 5-49
    5.3.4.7 Inelastic Axial Elastic Local Buckling Stress Fxc .............................................. 5-49
    5.3.4.8 Hoop Compressive Unity Check UCH ............................................................... 5-49
    5.3.4.9 Axial Tension Unity Check UCT ....................................................................... 5-50
    5.3.4.10 Combined Compression and Hydrostatic Pressure Unity Check UCCH1/2 ......... 5-50
    5.3.4.11 Combined Tension and Hydrostatic Pressure Unity Check UCTH..................... 5-50
 5.4 API Punching Shear Joint Check (API WSD PUNC) ................................................... 5-51
  5.4.1 Overview...................................................................................................................... 5-51
  5.4.2 API Punching Shear Check Reports ............................................................................ 5-55
  5.4.3 Nomenclature ............................................................................................................... 5-59
    5.4.3.1 Dimensional ....................................................................................................... 5-59
    5.4.3.2 Acting Forces and Stresses ................................................................................ 5-59
    5.4.3.3 Allowable Stresses and Unity Checks ............................................................... 5-60
  5.4.4 API Allowable Stresses and Unity Checks .................................................................. 5-61
    5.4.4.1 Acting Punching Shear Vp ................................................................................. 5-61
    5.4.4.2 Chord Design Factor Qf ..................................................................................... 5-61
    5.4.4.3 Geometry and Load Factor Qq ........................................................................... 5-62
    5.4.4.4 Allowable Punching Shear Vp ........................................................................... 5-63
    5.4.4.5 Punching Shear Unity Checks ........................................................................... 5-63
    5.4.4.6 Combined Axial and Bending Stress Unity Checks .......................................... 5-64
    5.4.4.7 Joint Strength Unity Check ................................................................................ 5-64
  5.4.5 Spectral Expansion for Joint Checks (API PUNC) ..................................................... 5-65
 5.5 API Nominal Load Check (API WSD NOMI) .............................................................. 5-68
  5.5.1 Overview...................................................................................................................... 5-68
  5.5.2 API Nominal Load Check Reports .............................................................................. 5-72
  5.5.3 Nomenclature ............................................................................................................... 5-77
    5.5.3.1 Dimensional ....................................................................................................... 5-77
    5.5.3.2 Acting Forces and Stresses ................................................................................ 5-77
    5.5.3.3 Allowable Stresses and Unity Checks ............................................................... 5-78
  5.5.4 API Allowable Nominal Loads and Unity Checks ...................................................... 5-79
    5.5.4.1 Chord Design Factor Qf ..................................................................................... 5-79
    5.5.4.2 Ultimate Strength Factor Qu............................................................................... 5-80
    5.5.4.3 Allowable Nominal Loads ................................................................................. 5-81
    5.5.4.4 Nominal Load Unity Checks ............................................................................. 5-81
    5.5.4.5 Combined Axial and Bending Unity Checks ..................................................... 5-82
    5.5.4.6 Interpolated Joints .............................................................................................. 5-82
    5.5.4.7 Joint Strength Unity Check ................................................................................ 5-83
  5.5.5 Spectral Expansion for Joint Checks (API NOMI) ..................................................... 5-84




Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.                               v
BEAMST User Manual                                                                                                          Contents

 5.6 API Load and Resistance Factor Design Allowable Member Stress Check (API LRFD
 MEMB) .................................................................................................................................... 5-88
  5.6.1 Overview...................................................................................................................... 5-88
  5.6.2 API LRFD Allowable Unity Check Report ................................................................. 5-92
  5.6.3 Nomenclature ............................................................................................................... 5-97
    5.6.3.1 Dimensional ....................................................................................................... 5-97
    5.6.3.2 Acting Section Stresses ...................................................................................... 5-97
    5.6.3.3 Allowable Stresses and Unity Checks ............................................................... 5-98
    5.6.3.4 Parameters .......................................................................................................... 5-98
  5.6.4 API LRFD Allowable Stresses and Unity Checks ...................................................... 5-99
    5.6.4.1 API LRFD Partial Coefficients .......................................................................... 5-99
    5.6.4.2 Allowable Tension Stress, Ft ............................................................................. 5-99
    5.6.4.3 Allowable Compression Stress, Fa ................................................................... 5-100
    5.6.4.4 Allowable Bending Stress, Fb .......................................................................... 5-101
    5.6.4.5 Allowable Shear Stress, Fv and Fvt................................................................... 5-101
    5.6.4.6 Unity Checks .................................................................................................... 5-102
    5.6.4.7 Combined Stresses ........................................................................................... 5-103
  5.6.5 Spectral Loadcases..................................................................................................... 5-105
    5.6.5.1 Torsional Effects .............................................................................................. 5-105
    5.6.5.2 Axial Unity Check and the Axial Component of Combined Stress Buckle and
    Yield Unity Checks ........................................................................................................... 5-105
    5.6.5.3 Local Axes Shear Unity Checks and Maximum Shear Unity Check for Tubular
    Sections 5-105
    5.6.5.4 Local Axes Pure Bending Unity Checks and Bending Components of Combined
    Stresses Yield and Buckle Unity Checks .......................................................................... 5-106
    5.6.5.5 Unity Check Report for Spectral Cases ........................................................... 5-106
    5.6.5.6 Combined Stress Buckle Unity Check (Buckle CSR) ..................................... 5-106
 5.7 API Load and Resistance Factor Design Hydrostatic Collapse Check (API LRFD HYDR)
       5-109
  5.7.1 Overview.................................................................................................................... 5-109
  5.7.2 API Hydrostatic Unity Check Reports ...................................................................... 5-114
  5.7.3 Nomenclature ............................................................................................................. 5-117
    5.7.3.1 Dimensional ..................................................................................................... 5-117
    5.7.3.2 Acting Section Forces and Stresses ................................................................. 5-117
    5.7.3.3 Allowable Stresses and Unity Checks ............................................................. 5-118
    5.7.3.4 Parameters ........................................................................................................ 5-118
  5.7.4 API Allowable Stresses and Unity Checks ................................................................ 5-119
    5.7.4.1 Design Hydrostatic Pressure ............................................................................ 5-120
    5.7.4.2 Limit Checks .................................................................................................... 5-120
    5.7.4.3 Elastic Hoop Buckling Stress Fhe ..................................................................... 5-121
    5.7.4.4 Allowable Elastic Hoop Buckling Stress Fha ................................................... 5-121
    5.7.4.5 Critical Hoop Buckling Stress Fhc .................................................................... 5-122
    5.7.4.6 Allowable Critical Hoop Buckling Stress Fch .................................................. 5-122
    5.7.4.7 Critical Axial Elastic Local Buckling Stress Fxe .............................................. 5-122
    5.7.4.8 Allowable Axial Elastic Local Buckling Stress Fxa ......................................... 5-123
    5.7.4.9 Inelastic Axial Local Buckling Stress Fxc ........................................................ 5-123
    5.7.4.10 Allowable Inelastic Axial Local Buckling Stress Fca ...................................... 5-123
    5.7.4.11 Hoop Compressive Unity Check UCH ............................................................. 5-124
    5.7.4.12 Allowable Tension Stress Ft ............................................................................ 5-124
    5.7.4.13 Allowable Axial Compression Stress Fa ......................................................... 5-125



Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.                                   vi
BEAMST User Manual                                                                                                           Contents

    5.7.4.14 Allowable Bending Stress Fb ........................................................................... 5-126
    5.7.4.15 Axial Tension Check UCax .............................................................................. 5-127
    5.7.4.16 Combined Tension and Hydrostatic Pressure Unity Check UCc ..................... 5-127
    5.7.4.17 Combined Compression and Hydrostatic Pressure Unity Checks ................... 5-128
 5.8 API Load and Resistance Factor Design Nominal Load Check (API LRFD JOIN) ... 5-129
   5.8.1 Overview.................................................................................................................... 5-129
   5.8.2 API Joint Check Reports ........................................................................................... 5-133
   5.8.3 Nomenclature ............................................................................................................. 5-138
    5.8.3.1 Dimensional ..................................................................................................... 5-138
    5.8.3.2 Acting Forces and Stresses .............................................................................. 5-138
    5.8.3.3 Allowable Stresses and Unity Checks ............................................................. 5-139
    5.8.3.4 Parameters ........................................................................................................ 5-139
   5.8.4 API Allowable Nominal Loads and Unity Checks .................................................... 5-140
    5.8.4.1 Chord Design Factor Qf ................................................................................... 5-140
    5.8.4.2 Ultimate Strength Factor Qu............................................................................. 5-141
    5.8.4.3 Allowable Nominal Loads ............................................................................... 5-142
    5.8.4.4 Load Transfer Across Chords .......................................................................... 5-143
    5.8.4.5 Nominal Load Unity Checks ........................................................................... 5-143
    5.8.4.6 Combined Axial and Bending Unity Checks UCco .......................................... 5-144
    5.8.4.7 Interpolated Joints ............................................................................................ 5-144
    5.8.4.8 Load Transfer Check UCx................................................................................ 5-144
    5.8.4.9 Joint Strength Unity Check UCjt ...................................................................... 5-145
   5.8.5 Spectral Expansion for Joint Checks ......................................................................... 5-146
6.    BS59 Code Check............................................................................................................... 6-1
 6.1 BS5950 Allowable Member Check (BS59 MEMB)........................................................ 6-2
   6.1.1 Overview........................................................................................................................ 6-2
   6.1.2 BS5950 Allowable Unity Check Reports ...................................................................... 6-6
   6.1.3 Nomenclature ............................................................................................................... 6-10
    6.1.3.1 Dimensional ....................................................................................................... 6-10
    6.1.3.2 Acting Forces and Stresses ................................................................................ 6-11
    6.1.3.3 Allowable Stresses and Unity Checks ............................................................... 6-11
   6.1.4 BS5950 Local Cross Section Checks .......................................................................... 6-13
    6.1.4.1 Section Classification......................................................................................... 6-13
    6.1.4.2 Axial Tension Unity Check ............................................................................... 6-18
    6.1.4.3 Major Axis Shear Unity Check .......................................................................... 6-18
    6.1.4.4 Minor Axis Shear Unity Check.......................................................................... 6-19
    6.1.4.5 Major Axis Bending Unity Checks .................................................................... 6-20
      6.1.4.5.1 Major Axis Bending, Low Shear Load ........................................................... 6-20
      6.1.4.5.2 Major Axis Bending, High Shear Load .......................................................... 6-23
    6.1.4.6 Minor Axis Bending Unity Check ..................................................................... 6-27
      6.1.4.6.1 Minor Axis Bending, Low Shear Load ........................................................... 6-27
      6.1.4.6.2 Minor Axis Bending, High Shear Load .......................................................... 6-30
    6.1.4.7 Axial Force plus Moment Unity Check ............................................................. 6-33
    6.1.4.8 Simplified Axial Force and Moment ................................................................. 6-42
   6.1.5 BS5950 Overall Member Checks ................................................................................ 6-43
    6.1.5.1 Major and Minor Axis Compressive Buckling .................................................. 6-43
      6.1.5.1.1 Major Axis Buckling ...................................................................................... 6-43
      6.1.5.1.1 ............................................................................................................................ 6-45
      6.1.5.1.2 Minor axis buckling ........................................................................................ 6-46
    6.1.5.2 Lateral Torsional Buckling ................................................................................ 6-48



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    6.1.5.3 Overall Buckling ................................................................................................ 6-53
      6.1.5.3.1 Overall Buckling - Simplified Method ........................................................... 6-54
   6.1.6 Thin or Slender Webs .................................................................................................. 6-55
7.    DS449 Code Check ............................................................................................................ 7-1
 7.1 DS449 Member Checks (DS44 MEMB) ......................................................................... 7-2
   7.1.1 Overview........................................................................................................................ 7-2
   7.1.2 DS449 Member Unity Check Reports ........................................................................... 7-5
   7.1.3 Nomenclature ................................................................................................................. 7-9
    7.1.3.1 Dimensional ......................................................................................................... 7-9
    7.1.3.2 Acting Section Forces and Stresses ..................................................................... 7-9
    7.1.3.3 Allowable Stresses and Unity Checks ............................................................... 7-10
   7.1.4 DS449 Member Unity Check Calculations ................................................................. 7-11
    7.1.4.1 Partial Material Coefficients .............................................................................. 7-11
    7.1.4.2 von Mises Stress ................................................................................................ 7-12
    7.1.4.3 Total Buckling ................................................................................................... 7-13
    7.1.4.4 Local Buckling Axial and Bending Stresses ...................................................... 7-15
    7.1.4.5 Local Buckling Hydrostatic Overpressure ......................................................... 7-16
    7.1.4.6 Local Buckling Combined Actions .................................................................... 7-18
    7.1.4.7 Unity Check Values ........................................................................................... 7-19
 7.2 DS449 Joint Checks (DS44 JOIN)................................................................................. 7-20
   7.2.1 Overview...................................................................................................................... 7-20
   7.2.2 DS449 Joint Unity Check Reports ............................................................................... 7-24
   7.2.3 Nomenclature ............................................................................................................... 7-28
    7.2.3.1 Dimensional ....................................................................................................... 7-28
    7.2.3.2 Acting Forces and Stresses ................................................................................ 7-29
    7.2.3.3 Allowable Stresses and Unity Checks ............................................................... 7-29
    7.2.3.4 Parameters .......................................................................................................... 7-29
   7.2.4 DS449 Joint Checks ..................................................................................................... 7-30
    7.2.4.1 Partial Material Coefficients .............................................................................. 7-30
    7.2.4.2 Critical Load Capacity ....................................................................................... 7-31
    7.2.4.3 Joint Capacity..................................................................................................... 7-33
    7.2.4.4 Unity Checks ...................................................................................................... 7-34
8.    NPD Code Check ............................................................................................................... 8-1
 8.1 NPD and NS3472 Member Checks (NPD MEMB) ......................................................... 8-2
   8.1.1 Overview........................................................................................................................ 8-2
   8.1.2 NPD Allowable Unity Check Reports ........................................................................... 8-6
   8.1.3 Nomenclature ............................................................................................................... 8-11
    8.1.3.1 Dimensional ....................................................................................................... 8-11
    8.1.3.2 Acting Forces and Stresses ................................................................................ 8-12
    8.1.3.3 Allowable Stresses and Unity Checks ............................................................... 8-12
    8.1.3.4 Parameters .......................................................................................................... 8-12
   8.1.4 Methods of von Mises stress calculation for NPD code checks .................................. 8-13
   8.1.5 NPD and NS3472 Ultimate Limit State Compliance Checks ..................................... 8-18
   8.1.6 NPD 1992 Member Checks - Tubular Members ......................................................... 8-19
    8.1.6.1 Material and Structural Coefficients .................................................................. 8-19
    8.1.6.2 von Mises Unity Check ...................................................................................... 8-19
    8.1.6.3 Elastic Buckling Resistance for Unstiffened Cylindrical Shells........................ 8-20
    8.1.6.4 Global Buckling Check ...................................................................................... 8-22
   8.1.7 NPD Member Checks - Non-Tubular Members .......................................................... 8-25
    8.1.7.1 Material and Structural Coefficients .................................................................. 8-25



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    8.1.7.2 Global Buckling ................................................................................................. 8-25
    8.1.7.3 Torsional Buckling............................................................................................. 8-28
    8.1.7.4 Lateral Buckling................................................................................................. 8-29
    8.1.7.5 Unity Check Values ........................................................................................... 8-30
 8.2 NPD Joint Checks (NPD JOIN) ..................................................................................... 8-33
   8.2.1 Overview...................................................................................................................... 8-33
   8.2.2 NPD Joint Unity Check Reports .................................................................................. 8-37
   8.2.3 Nomenclature ............................................................................................................... 8-42
    8.2.3.1 Dimensional ....................................................................................................... 8-42
    8.2.3.2 Acting Forces and Stresses ................................................................................ 8-42
    8.2.3.3 Allowable Stresses, Capacities and Unity Checks ............................................. 8-43
    8.2.3.4 Parameters .......................................................................................................... 8-43
   8.2.4 NPD 1992 Joint Checks ............................................................................................... 8-44
    8.2.4.1 Characteristic Capacities .................................................................................... 8-45
   8.2.5 Unity Checks ............................................................................................................... 8-47
9.    NORSOK Code Check ....................................................................................................... 9-1
 9.1 NORSOK Member Code Check (NORS MEMB) .......................................................... 9-2
   9.1.1 Overview........................................................................................................................ 9-2
   9.1.2 NORSOK Allowable Unity Check Report .................................................................... 9-5
   9.1.3 Nomenclature ................................................................................................................. 9-9
    9.1.3.1 Dimensional ......................................................................................................... 9-9
    9.1.3.2 Acting Section Stresses ........................................................................................ 9-9
    9.1.3.3 Design Strengths and Unity Checks .................................................................. 9-10
    9.1.3.4 Parameters .......................................................................................................... 9-10
   9.1.4 NORSOK Design Strengths and Unity Checks ........................................................... 9-11
    9.1.4.1 Design Tension Strength, Nt .............................................................................. 9-11
    9.1.4.2 Design Compression Strength, Na ..................................................................... 9-12
    9.1.4.3 Design Bending Strength, MR ............................................................................ 9-13
    9.1.4.4 Design Shear Strengths, VR and MTR................................................................. 9-13
    9.1.4.5 Material factor, γm .............................................................................................. 9-14
    9.1.4.6 Unity Checks ...................................................................................................... 9-15
    9.1.4.7 Combined Forces ............................................................................................... 9-16
 9.2 NORSOK Hydrostatic Member Collapse Checks (NORS HYDR)............................... 9-18
   9.2.1 Overview...................................................................................................................... 9-18
   9.2.2 NORSOK Hydrostatic Collapse Member Unity Check Report .................................. 9-20
   9.2.3 Nomenclature ............................................................................................................... 9-27
    9.2.3.1 Dimensional ....................................................................................................... 9-27
    9.2.3.2 Acting Section Forces and Stresses ................................................................... 9-27
    9.2.3.3 Allowable Stresses and Unity Checks ............................................................... 9-28
    9.2.3.4 Parameters .......................................................................................................... 9-28
   9.2.4 NORSOK Unity Checks .............................................................................................. 9-29
    9.2.4.1 Design Hydrostatic Pressure .............................................................................. 9-30
    9.2.4.2 Limit Checks ...................................................................................................... 9-30
    9.2.4.3 Elastic Hoop Buckling Strength, fhe ................................................................... 9-31
    9.2.4.4 Characteristic Hoop Buckling Strength, fh......................................................... 9-32
    9.2.4.5 Hoop Compressive Unity Check UCh................................................................ 9-32
    9.2.4.6 Combined Tension and Hydrostatic Pressure Unity Check ............................... 9-33
    9.2.4.7 Combined Compression and Hydrostatic Pressure Unity Check ...................... 9-35
 9.3 NORSOK Joint Strength Checks (NORS JOIN) ........................................................... 9-40
   9.3.1 Overview...................................................................................................................... 9-40



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   9.3.2 NORSOK Joint Check Reports ................................................................................... 9-45
   9.3.3 Nomenclature ............................................................................................................... 9-50
    9.3.3.1 Dimensional ....................................................................................................... 9-50
    9.3.3.2 Acting Forces and Stresses ................................................................................ 9-50
    9.3.3.3 Allowable Forces, Moments, Stresses and Unity Checks.................................. 9-51
    9.3.3.4 Parameters .......................................................................................................... 9-51
   9.3.4 NORSOK Design Strengths and Unity Checks ........................................................... 9-52
    9.3.4.1 Chord Action Factor Qf ...................................................................................... 9-52
    9.3.4.2 Strength Factor Qu.............................................................................................. 9-53
    9.3.4.3 Characteristic Resistances .................................................................................. 9-54
    9.3.4.4 Combined Axial and Bending Unity Checks UCco .......................................... 9-54
    9.3.4.5 Interpolated Joints .............................................................................................. 9-55
10. POST Command Data (POST)......................................................................................... 10-1
 10.1 Overview ........................................................................................................................ 10-1
 10.2 Reports ........................................................................................................................... 10-4
Appendix - A Preliminary Data for BEAMST......................................................................... A-1
 A.1 Introduction ..................................................................................................................... A-1
 A.2 SYSTEM Command ....................................................................................................... A-2
 A.3 PROJECT Command ...................................................................................................... A-2
 A.4 JOB Command ................................................................................................................ A-2
 A.5 FILES Command ............................................................................................................ A-3
 A.6 TITLE Command ............................................................................................................ A-4
 A.7 TEXT Command ............................................................................................................. A-4
 A.8 STRUCTURE Command ................................................................................................ A-5
 A.9 COMPONENT Command .............................................................................................. A-6
 A.10 OPTIONS Command ...................................................................................................... A-7
 A.11 SAVE Command............................................................................................................. A-9
 A.12 UNITS Command ......................................................................................................... A-10
 A.13 LIBRARY Command ................................................................................................... A-12
 A.14 END Command ............................................................................................................. A-13
 A.15 ANSYS Command ........................................................................................................ A-14
Appendix - B Running BEAMST ............................................................................................ B-1
 B.1 ASAS Files Required by BEAMST ................................................................................ B-1
 B.2 Files required by BEAMST in Stand-Alone Mode ......................................................... B-1
 B.3 Files Produced by BEAMST........................................................................................... B-1
 B.4 Saving Plot Files Produced by BEAMST ....................................................................... B-1
 B.5 Running Instructions for BEAMST ................................................................................ B-1
Appendix - C Examples ........................................................................................................... C-1
Appendix - D Section Descriptions .......................................................................................... D-1
 D.1 Section Specific Data ...................................................................................................... D-1
Appendix - E Graphical Display of BEAMST Results ............................................................. E-1
 E.1 BEAMST Plot Files ......................................................................................................... E-1
 E.2 Presenting BEAMST Results in FEMVIEW ................................................................... E-7
   E.2.1 Member Force Results ................................................................................................... E-7
   E.2.2 Member Unity Check Results ........................................................................................ E-9
   E.2.3 Joint Unity Check Results ........................................................................................... E-10
Appendix - F Using BEAMST in Stand-alone Mode ............................................................... F-1
 F.1 Additional Stand-Alone Data Requirements .................................................................... F-1
Appendix - G References ......................................................................................................... G-1
Appendix - H Superseded Commands ..................................................................................... H-1



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BEAMST
Post-Processing and Code Checking for Beam Elements


1.     Introduction


1.1 General Description
BEAMST is a post-processing program designed specifically for processing the results of engineering beam
elements analysed by ASAS (Linear or Non-Linear), RESPONSE and LOCO.

There are three options available in BEAMST:

•           Post-processing alone

•           Post-processing plus code checking

•           Stand-alone post-processing plus code checking


The Post-processing facility allows individual members to be selected for further processing. This includes the
formation of factored and combined loadcases, calculation of forces and stresses at intermediate points along the
member and presentation of results on an element by element basis.

The code checking facilities include all the functionality of the standard post-processing together with extensive
code checking procedures for the following engineering codes of practice:

•      American Institute of Steel Construction (AISC) ‘Specification for Structural Steel Buildings. Allowable
       Stress Design and Plastic Design’, Ninth Edition, June 1, 1989.
       (and previous editions as applicable)

•      American Institute of Steel Construction (AISC) ‘Load and Resistance Factor Design Specification for
       Structural Steel Buildings’, Second Edition, December 1, 1993.

•      American Petroleum Institute (API) ‘Recommended Practice for Planning, Designing, and Constructing
       Fixed Offshore Platforms - Working Stress Design’, RP2A-WSD, Twentieth Edition, July 1, 1993.
       (and previous editions as applicable)




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•       American Petroleum Institute (API) ‘Recommended Practice for Planning, Designing, and Constructing
       Fixed Offshore Platforms - Load and Resistance Factor Design’, RP2A-LRFD, First Edition, July 1,
       1993.

•       Danish Regulations for Pile Supported Offshore Steel Structures (DOR), comprising:

•       ‘Dansk Ingeniørforening’s Code of Practice for Pile Supported Offshore Steel Structures’, DS449,
        September 1984, including amendments to 1994 (DS480).

•       ‘Dansk Ingeniørforening’s Code of Practice for the Structural use of Steel’, DS412, March 1984,
        including amendments to 1994 (DS480).

•       Norwegian Petroleum Directorate (NPD), ‘Acts, regulations and provisions for the petroleum activity,’
        January 1992.

•       NS3472 E ‘Steel Structures - Design Rules’ June 1984.

•       British Standard BS5950: Part 1: 1992 ‘Structural use of steelwork in building’

•       NORSOK Edition 1: Dec 1998 ‘Design of Steel structures’


The program has been designed to facilitate the incorporation of other codes of practice and report formats.

The stand-alone facility includes all the above functionality together with additional input commands to allow
member geometry and results to be entered from sources other than the standard ASAS database. This enables
the comprehensive facilities of BEAMST to be used either in a design context or to process results from other
analysis systems.

For all versions the results may be written out to plotfiles for graphical display in FEMVIEW or the database
saved for use with the ASAS Visualiser program.



1.2 About this Manual
This manual is specifically for the ‘post-processing and code checking’ version of BEAMST and also includes
the commands relevant to the use of the manual in ‘Stand-alone’ mode.

This manual is arranged in the following sections:

Chapter         1        Introduction to BEAMST and the user manual (this section)

Chapter         2        Summarises the various facilities available in BEAMST

Chapter         3        Describes the general form of the commands and parameters in the data and describes each
                         BEAMST command in detail.




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Chapter         4-9      The remaining chapters describe in detail the latest version of the code checks currently
                         supported by BEAMST. Where several versions of a specific code check are maintained,
                         previous versions are not described but may be obtained from the authors, if required.

Chapter         4        AISC

Chapter         5        API

Chapter         6        BS5950

Chapter         7        DS449, DS412

Chapter         8        NPD, NS3472

Chapter         9.       NORSOK

Chapter         10       POST Command Data (POST)

Appendix        -A       Describes the preliminary data block

Appendix        -B       Running instructions for BEAMST

Appendix        -C       Example BEAMST data

Appendix        -D       Provides details of cross-sections recognised by BEAMST

Appendix        -E       Details the interfacing to plotting programs for displaying BEAMST results

Appendix        -F       Using BEAMST in Stand-alone mode

Appendix - G References

Appendix        H        Superseded Commands




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2.      Facilities in BEAMST


2.1 Selection of Members and Joints

BEAMST allows selective processing of individual members and joints. This allows successive runs of
BEAMST to target problem areas, printing more detailed check data and examining the effect of local
changes in section dimensions.

The elements to be processed may be selected by reference to individual user element numbers using
the ELEM command or by groups of elements using the GROU command. These commands may be
used together or individually to build up a complete set of elements to be processed. Elements may
also be removed from a previously defined set by using a NOT ELEM command. Used on its own the
NOT ELEM command invokes all the elements except those listed.

Joints are referenced by the number of the node or, in the case of API WSD JOIN, a maximum of 3
nodes forming the joint. The elements attached to each node are assumed to be the members forming
the joint. It is possible to define which of these are chord and brace members and any elements not to
be considered as part of the joint. The joints to be processed are selected using the JOIN command to
specify the nodes included for joint checks in a similar fashion to the ELEM command above.



2.2 Section Properties for BEAMST
The calculation of extreme fibre stresses for beams requires more information than is necessary for the
basic structural analysis. The determination of forces in ASAS only needs areas and inertias to be
specified, whereas the calculation of stresses in BEAMST requires section dimensions. The additional
information can come from one of two sources:

1.    If sections have been utilised in the ASAS analysis, either directly or from an external section
      library, the dimensions will be automatically accessed by BEAMST. No further input is necessary
      (except to define the library name, if appropriate).

2.    If sections were not used in the ASAS analysis, or if it is required to modify those specified for the
      structural definition, a DESI command is necessary. Note that changing the section may alter the
      section stiffness to a degreee where the analysis results become invalid. In such a case, a full re-
      analysis should be performed, using the updated sections.

Section types CHAN, TEE and ANG are only available for force and stress post-processing. No
facility as yet exists for code checking these section profiles.

The conventions used for choosing which properties are used in the computations are as follows:

(a)     All section areas (Ax, Ay, Az) and inertias (Ix, Iy, Iz) (‘geometric properties’) available from the
        preceding ASAS analysis are chosen initially. All quantities not available default to zero.




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(b)      If sections have been utilised in the ASAS analysis, section dimensions (d,b,tw etc.) specified are
        chosen initially. In the case of a TUBE element section dimensions default to those from
        ASAS. Any non TUBE elements not assigned to sections will require DESI commands.

(c)     All section dimensions (d,b,tw etc.) assigned using DESI commands in BEAMST override the
        respective values adopted in (b) above if appropriate. Beam extreme fibre distances are based on
        these settings. Flexural properties associated with DESI information will also override the
        respective values adopted in (a) above. All optional properties not specified on the DESI
        command such as radii of gyration default to zero at this time.

(d)      Any section area or inertia not available from the preceding ASAS run is calculated according to
         the section type as described in Appendix -D.



2.3 Beam Local Axes Considerations
For any beam analysis it is critical that the local axes for beams are defined correctly. BEAMST uses a
subset of three ASAS beam elements, ie BEAM, BM3D and TUBE elements. The method of defining
the local axes varies according to the beam type as follows:

1.       The local X axis for all beam types is along the beam neutral axis from end1 towards end2.
         Thus the moments of inertia are about the local Y and Z axes.

2.      For the BEAM element the direction of the local Y and Z axes is predefined according to the
        orientation of the element itself as follows:

        Local Z always lies in the global XY plane with local Y positive on the positive side of the
        global XY plane. If the local Y is also in the global XY plane (ie the element is parallel to the
        global Z axis) then the local Y lies in the global Y direction.


3.      For the BM3D and TUBE elements the direction of the local Y and Z axes may be defined
        explicitly in the ASAS geometric data for the element.

The default axes definition of the BEAM element means its use with BEAMST should be restricted to
models with the global Z vertically upwards and to the following cases:

(a)     a horizontal member with the section depth (d) (local Y axis) vertical

(b)      a vertical member with the section depth (d) (local Y axis) in the global Y direction

(c)      a sloping member with the section width (b) (local Z axis) horizontal


For all other cases BM3D and TUBE element types should be used. A TUBE element may only be
used to model tubular elements.




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2.4 Section Orientation
As a general rule the section depth (d) is parallel to the element’s local Y direction and the section
width (b) to the element’s local Z direction.

For BOX, RHS and PRI the section depth (d) is always the larger dimension and the section width (b)
the smaller.

For I sections, Izz should be the strong axis inertia and Iyy the weak axis inertia. BEAMST will then
assume that the web is in the local XY plane. The resulting BEAMST Izz will then equate to the Ixx
values as listed in standard section tables (and the BEAMST Iyy equates to the Iyy values).


2.5 Member Stress Evaluation
For beam elements, ASAS produces force and moment results at the ends of the element only. The
element nodal results may be supplemented by force, moment and stress results at discrete sections
along the element defined by the SECT command. These intermediate results are calculated from the
end forces and moments together with any applied point or distributed member loading. Intermediate
results are also calculated automatically at the position of step changes in cross-section properties.

Extreme fibre stresses are calculated depending on the cross-section type associated with the beam (e.g.
I, BOX, CHAN, etc). If sections have been utilised in the ASAS-H analysis, the shape and dimensions
will automatically be picked up from the data base. Where sections have not already been specified,
DESI commands must be included to define the additional information required. The methods used to
evaluate the stresses for each section type are detailed in Appendix -D.




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2.6 Loadcase Combinations, Origin and Classification
BEAMST accesses the results from the loadcases analysed in the preceding ASAS, RESPONSE or
LOCO run.         These loadcases are referred to as basic loadcases in BEAMST.                            Individual basic
loadcases may be selected for processing using the CASE command.

Further loadcases may be created in BEAMST by factoring and combining the basic loadcases to form
combined loadcases. These combined cases are defined from basic loadcases using the COMB and
CMBV commands. The CMBV command allows a number of different combination methods to be
used.

BEAMST processes all selected basic loadcases in increasing user loadcase number order followed by
all selected combined loadcases in the order that they are defined in.

In order to process the basic loadcases, BEAMST needs to know the origin of the loadcase. By default
this is assumed to be a static analysis. Unsigned basic loadcases from a response spectrum analysis
should be specified on a SPEC command to indicate their origin. Response spectrum loadcases may,
however, be treated as linear static if so desired.

For the purposes of checking members to AISC WSD and API design codes, (‘and joints to API’) and
joints to API        any basic loadcase specified as spectral will be subject to the ‘automatic signed
expansion procedure’ described in Section                      4.1.5, whereby the unsigned member forces are
systematically assigned all possible signed values. For such cases BEAMST will establish and report
the signed expansion which maximises each unity check as appropriate. When a combined loadcase
has more than one spectral basic loadcase constituent the unsigned basic loadcases are combined prior
to the application of the ‘signed expansion procedure.’

Combined Loadcases which involve static-spectral summation should not be formed in a previous
LOCO run. In such cases a LOCO run should be used to factor and combine the static components and
to separately include, but not combine, the spectral components. BEAMST should then be used to
combine the final static and spectral components together. This method of combining results between
LOCO and BEAMST is the most efficient way of performing such combinations. The BYUE Option
must be used in LOCO during this process.

Allowable stresses in working stress design codes may be increased above those appropriate to
‘Ordinary’ conditions for ‘Extreme’/Storm and ‘Earthquake’/Seismic conditions. Any basic loadcase or
combined loadcase selected in BEAMST for reporting may be specified as being of the Extreme or
Earthquake ‘Type’ using the EXTR and QUAK commands respectively.




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2.7 Code Checking in BEAMST
BEAMST may be used to assess beam structures against the following engineering design codes:

•        AISC design specification

•        API design recommendations

•        British Standard BS5950

•        Danish Standards DS449 and DS412

•        NPD design regulations

•        NORSOK Design Standard


The choice of code is made by supplying a code header command followed by data relevant for the
code check. A single BEAMST run may process a number of different code checks by simply
appending the data for each in the datafile. Details of this are given in Section 3.2.

The code checks fall into two types, member and joint checks. Member checks examine the stress
levels within individual members taking into account the cross-section. The stress levels are calculated
at the member ends, the position of any steps in cross-section dimension and any intermediate points
specified in the data (SECT command). The member checks consider both the static stress levels and
buckling failure modes.

Joint checks examine the stresses around the intersection of tubular members and consider such effects
as yield and punching shear.

Detailed description of each type of code check may be found from Section 4 onwards of this manual.




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2.8 Output Reports
BEAMST has a number of different types of output reports that may be printed selectively using the
PRIN command. The reports available are described in the following sections and are summarised in
Tables 2.1 and 2.2.

Note, this table indicates those reports which will be output when using the command PRIN ALL.


 Report                          AISC/      AISC          API       API WSD      API WSD      API WSD       API    API      API
                                  API       LRFD         WSD         NOMI         PUNC          JOIN       LRFD   LRFD     LRFD
                                 WSD        MEMB         HYDR       (<ED21)       (<ED21)     (>ED21)      MEMB   HYDR     JOIN
                                 ALLO

 Data Echo                                                                                                          
 Command Summary                                                                                                    
 Cross Check                                                                                                        

 Member Properties                                                   -             -            -                       -
 Member Force                                                        -             -            -                       -
 Member Stress                                                       -             -            -                       -

 Unity Check                                                                                                        

 Summary Reports
 No. 1                                                               -             -            -                      
 No. 1 (FAIL)                                                        -             -            -                      
 No. 2                                         -           -           -             -            -         -     -         -
 No. 2 (FAIL)                                  -           -           -             -            -         -     -         -
 No. 3                                                    -                                                  -        
 No. 3 (FAIL)                                             -                                                  -        
 No. 4                                         -           -                                             -     -         -
 No. 4 (FAIL)                                  -           -                                             -     -         -
 No. 5                              -           -           -           -             -            -         -     -         -


                      Table 2.1 Output Reports Available for API/AISC Code Checks




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BEAMST User Manual                                                                                       Facilities in BEAMST



  Report                                         AISC/            API            BS59            DS449         NPD     POST
                                                  API            HYDR            MEMB            MEMB*        MEMB
                                                 ALLO

  Data Echo                                                                                                        

  Command Summary                                                                                                  

  Cross Check                                                                                                      

  Member Properties                                                                               -                 

  Member Force                                                                                    -                 

  Member Stress                                                                                   -                 

  Unity Check                                                                                                       -

  Summary Reports

  No. 1                                                                                           -                  -
  No. 1 (FAIL)                                      -                              -                -          -        -

  No. 2                                                            -               -                -                  -

  No. 2 (FAIL)                                      -               -               -                -          -        -

  No. 3                                                            -                               -                  -

  No. 3 (FAIL)                                      -               -               -                -          -        -

  No. 4                                                            -                               -                  -

  No. 4 (FAIL)                                                     -               -                -          -        -

  No. 4 (FAIL)                                      -               -               -                -          -        -

  No. 5                                                                                                            


                      Table 2.2 Output Reports Available for European Code Checks


2.8.1        Data Echo Report

The Data Echo Report echoes the input data for BEAMST together with any input error or warning
messages that may result.

A typical Data Echo Report is shown in Figure 2.1 .


2.8.2        Command Summary Report

The Command Summary Report contains details of the type and extent of the post-processing selected.
For code checking runs of BEAMST, this report begins with an expanded form of the header and sub-
header commands detailing the code checks being performed. For all BEAMST runs the details of the
input and output dimensional units, selected loadcases and selected reports are summarised next.




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Finally any member (‘or joint’)or joint invariant data that is pertinent to the type of post-processing
selected is specified.

The Command Summary Report contains details of the input and output dimensional units, selected
loadcases and selected reports.

A typical Command Summary Report is shown if Figure 2.2 .




2.8.3        Input Data Cross Check Report

The Input Data Cross Check Report presents the input data in an expanded tabular format. This
enables the user to quickly validate the data and also enables BEAMST to highlight exactly where any
conflicts or data errors occur in the data.

For member calculations a list of sections to be reported is included for all elements selected. By
default only the end points and any step positions are reported. Other sections may be requested using
the SECT command.

A typical Input Data Cross Check Report is shown in Figure 2.3 .




2.8.4        Member Reports

Three member reports are available: Member Properties, Member Forces and Member Stresses. These
reports are printed for each selected element in sequential order,

                          Property - Force - Stress

These reports are not available for joint checks and are optional for all other types.



2.8.4.1          Member Property Report


The Member Property Report gives all the relevant geometric and material data for each selected
member (element). The element number and element group is given at the top of the report along with
the units in use. The element’s nodes and coordinates are printed next along with the element’s length
and associated effective and unbraced lengths. The slenderness ratio, kℓ/r is also printed.


The cross-section properties are then printed for each step of the element in turn. These consist of the

flexural properties (from ASAS or those associated with DESI commands)• (ASAS), the material

properties (from      • (ASAS)ASAS         s   (Mate command)MATE command and YIEL command) and the

section dimensions (from• (ASAS) ASAS or DESI command).

A typical Member Property Report is shown in Figure 2.4 .



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2.8.4.2          Member Force Report


The Member Force Report gives the six components of force at each section for each selected member
(element). The element number, its node numbers and group number are given at the top of the report
along with the units in use. The forces are then printed for each of the element’s sections for each
loadcase in turn. The section positions are identified by number and ratio of position to element length.
The first and last sections will be at position 0.00 and 1.00 and relate to the ends of the element. Any
intermediate sections are either those specified by a SECT command or at the position of a step change
in cross-section properties. The section values are followed by the maximum value found at any
section within the element and also the position at which the maximum occurs.

When the SEAR command is in use the maximum may occur at a section position not reported in the
section data above. This is because the SEAR command causes additional sections on the element to
be searched without reporting.

The final two columns of the Member Force Report give the free moments in the local Y and Z
directions.

A typical Member Force Report is shown in Figure 2.5.



2.8.4.3          Member Stress Report


The Member Stress Report gives the member stresses at each section for each selected member
(element). The element number, its node numbers and group number are given at the top of the report
along with the units in use. The stresses are then printed for each of the element’s sections for each
loadcase in turn. The section positions are identified by number and ratio of position to element length.
The first and last sections will be at position 0.00 and 1.00 and relate to the ends of the element. Any
intermediate sections are either those specified by a SECT command or at the position of a step change
in cross-section properties. The section stresses are followed by the maximum stress found at any
section within the element and also the position at which the maximum occurs.

When the SEAR command is in use the maximum may occur at a section position not reported in the
section data above. This is because the SEAR command causes additional sections on the element to
be searched without reporting.

The final four columns of the Member Stress Report give the combined axial stress at four locations on
the section denoted A, B, C and D. These locations and the methods of combining the stress are given
individually for each section type in Appendix -D.

A typical Member Stress Report is shown in Figure 2.6.




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2.8.5        Unity Check Report

A single Unity Check Report is available in BEAMST for each type of Command data block which
performs a stress check to a design code and the PRIN parameter UNCK will select it. The report
comprises member acting stresses where such stresses differ or are not available from the Member
Stress Report, allowable stresses and unity checks appropriate to the design code check selected.
Messages appropriate to the allowable stresses and unity check(s) which result appear on the right-hand
side of the report as a four letter code and are expanded in a Glossary printed at the end of the report.
Members ‘(or joints’)or joints which ‘FAIL’ the unity check(s) or violate any design code clause are
indicated so in this messages column. All unity check values printed are limited to a maximum of
99.99.

The Unity Check Report for member checks is printed as a separate report for each element selected
and if selected together with Member Reports will be printed in the sequential order

                          Properties - Force - Stress - Unity Check.

For joint checks, the Unity Check Reports for all selected joints are printed together.

The Unity Check Reports are further explained in the appropriate code check detailed description
sections.




2.8.6        Summary Reports

Five types of Unity Check Summary Reports are in general available, examples of which are described
in the individual code check sections of this manual. For availability of each type refer to Table 2.1 and
Table 2.2.

Summary Report number 1 comprises the highest yield and buckle combined stress unity checks and
their components for each selected element over all loadcases selected.

Summary Report number 2 comprises the highest buckle check and all unity checks at the section with
the highest yield combined stress unity check for each selected element over all loadcases selected.

Summary Report number 3 comprises the highest unity check for each selected loadcase for each
element or joint selected.

Summary Report number 4 comprises the three worst unity checks for each selected group or joint
together with a distribution of unity check values. The distribution is characterised by the number of
unity checks exceeding 1.0, the number less than 0.5 and the number in the mid-range. These default
‘exceedence values’ may be altered by the user by the addition of further parameters to the PRIN
SUM4 command.

The Force Summary Report number 5 provides information about the highest member forces and
moments for each selected group. For each force type (axial, shear, torque and bending) the worst four
values are reported together with the element number, loadcase number and position along the element.



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Separate tables are printed for maximum positive and maximum negative force values. If spectral
loadcases have been specified then the maximum and minimum values for each of the force types are
determined from the sixteen spectral expansion cases prior to comparing with the forces from other
loadcases. A spectral loadcase, therefore, can appear only once for a given element/force type within a
group. An example of a Summary Report number 5 is shown in Figure 2.7.

If Summary Reports are selected in any Command data block presented to BEAMST, the program will
automatically open an additional results file and write the Summary Reports selected to it. This
additional output file allows the Summary Reports to be accessed and viewed quicker by the user. The
name of the file written to is the four character file name (fname - Appendix A.5) appended with the
characters BM (see Appendix -B).

For examples of the Unity Check Reports, see the appropriate code check detailed description sections.



2.9 Saving Results for Graphical Display

Results from BEAMST may be saved on a plot file for subsequent graphical presentation in
FEMVIEW or opened in the ASAS Visualiser program. Within these programs the results may be
presented as bending moment and shear force diagrams in two forms:

•       bending moment and shear force diagrams

•        unity check values superimposed on the mesh


A more detailed description of the plot files is given in Appendix -E.




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                                                                                                                                                                                             BEAMST User Manual
    Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.


                                                                                                            ..API ED17 ALLO
                                                                                                            ..UNITS M KN
                                                                                                            ..YIEL 233.0 ELEM ALL
                                                                                                            ..GROUP 1
                                                                                                            ..TEXT *******************************************
                                                                                                            ..TEXT **   CENTRAL MEMBER SECTIONS REDEFINED   **
                                                                                                            ..TEXT *******************************************
                                                                                                            ..DESI TUB 1.484 .164 STEP 1 ELEM 5
                                                                                                            ..DESI TUB 1.404 .104 STEP 2 ELEM 5
                                                                                                            ..DESI TUB 1.564 .204 STEP 3 ELEM 5
                                                                                                            ..TEXT *******************************************
                                                                                                            ..TEXT **   SEARCH FOR MAXIMUM STRESS VALUES    **
                                                                                                            ..TEXT *******************************************
                                                                                                            ..SEARCH
                                                                                                            ..TEXT ***********************************************
                                                                                                            ..TEXT **   SELECT BASIC LOADCASES FOR PROCESSING   **
                                                                                                            ..TEXT ***********************************************
                                                                                                            ..CASE 1 2 3
                                                                                                            ..TEXT **************************************
                                                                                                            ..TEXT **   FORM A NEW COMBINED LOADCASE   **
                                                                                                            ..TEXT **************************************
                                                                                                            ..COMB 10 10.0 1 5.0 2 4.75 3
                                                                                                            ..SELE 10 COMBINED LOAD CASE
                                                                                                            ..TEXT **********************************************
                                                                                                            ..TEXT **   SELECT ALL REPORT TYPES FOR PRINTING   **
                                                                                                            ..TEXT **********************************************
                                                                                                            ..PRINT ALL
                                                                                                            ..END




                                                                                                                                                                                                 Facilities in BEAMST
                                                                                                                                                       Figure 2.1 Typical Data Echo Report
Page 2-15
                                                                                                                                 *********************************************************************
                                                                                                                                 *                                                                   *




                                                                                                                                                                                                           BEAMST User Manual
    Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.
                                                                                                                                 *                   API RP2A(20TH.ED. JUL. 1993)                    *
                                                                                                                                 *       AMERICAN PETROLEUM INSTITUTE RECOMMENDED PRACTICE FOR       *
                                                                                                                                 *    PLANNING,DESIGNING AND CONSTRUCTING FIXED OFFSHORE PLATFORMS   *
                                                                                                                                 *                                                                   *
                                                                                                                                 *********************************************************************
                                                                                                                                 *                                                                   *
                                                                                                                                 *                         REFERRING TO THE                          *
                                                                                                                                 * AMERICAN INSTITUTE OF STEEL CONSTRUCTION     (9TH ED,JUN. 1,1989) *
                                                                                                                                 *     SPECIFICATION FOR THE DESIGN,FABRICATION AND ERECTION OF      *
                                                                                                                                 *                  STRUCTURAL STEEL FOR BUILDINGS                   *
                                                                                                                                 *                      FOR NON-TUBULAR MEMBERS                      *
                                                                                                                                 *                                                                   *
                                                                                                                                 *********************************************************************
                                                                                                                                 *                                                                   *
                                                                                                                                 *     M E M B E R   A L L O W A B L E   S T R E S S   C H E C K     *
                                                                                                                                 *                                                                   *
                                                                                                                                 *********************************************************************
                                                                                                            INPUT UNITS -
                                                                                                                                 ...ALL QUANTITIES          FORCE UNIT....KN         LENGTH UNIT...M
                                                                                                            OUTPUT UNITS -
                                                                                                                                 ...STRESSES                FORCE UNIT....KN         LENGTH UNIT...M
                                                                                                                                 ...OTHER QUANTITIES        FORCE UNIT....KN         LENGTH UNIT...M
                                                                                                            LOAD CASES SELECTED -
                                                                                                                               ...NO. OF BASIC LOAD CASES...............       3
                                                                                                                               ...NO. OF COMBINED LOAD CASES............       1
                                                                                                            REPORTS SELECTED -
                                                                                                                                 ...INPUT DATA X-CHECK REPORT.................................     PRINT
                                                                                                                                 ...MEMBER PROPERTIES REPORT..................................     PRINT
                                                                                                                                 ...MEMBER FORCE REPORT.......................................     PRINT
                                                                                                                                 ...MEMBER STRESS REPORT......................................     PRINT
                                                                                                                                 ...UNITY CHECK REPORT........................................     PRINT
                                                                                                                                 ...UN CHK SUMMARY REPORT NO. 1...............................     PRINT
                                                                                                                                 ...UN CHK SUMMARY REPORT NO. 1.....FAILED MEMBERS/JOINTS.....NO   PRINT




                                                                                                                                                                                                               Facilities in BEAMST
                                                                                                                                 ...UN CHK SUMMARY REPORT NO. 2...............................     PRINT
                                                                                                                                 ...UN CHK SUMMARY REPORT NO. 2.....FAILED MEMBERS/JOINTS.....NO   PRINT
                                                                                                                                 ...UN CHK SUMMARY REPORT NO. 3...............................     PRINT
                                                                                                                                 ...UN CHK SUMMARY REPORT NO. 3.....FAILED MEMBERS/JOINTS.....NO   PRINT
                                                                                                                                 ...UN CHK SUMMARY REPORT NO. 4...............................     PRINT
                                                                                                                                 ...UN CHK SUMMARY REPORT NO. 4.....FAILED MEMBERS/JOINTS.....NO   PRINT
                                                                                                                                 ...FORCES SUMMARY REPORT NO. 5...............................NO   PRINT
Page 2-16




                                                                                                                                                       Figure 2.2 Typical Command Summary Report
                                                                                                                                                                                                                                                   BEAMST User Manual
    Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.
                                                                                                            API   CODE                                 CROSS CHECKS ON INPUT DATA REPORT                        STRESS UNITS (KN   ,M   )   XCHK
                                                                                                            ---   ----                                 ----- ------ -- ----- ---- ------                              OTHERS (KN   ,M   )   ====

                                                                                                              ELEMENT       STEP   YIELD STRESS     EFFECTIVE LENGTH FACTORS                     SECTIONS
                                                                                                              -------       ----   ----- ------     --------- ------ -------                     --------

                                                                                                                      1       1        2.3300E+02     1.0000E+00   1.0000E+00                    0.00   0.78
                                                                                                                      1       2        2.3300E+02     1.0000E+00   1.0000E+00                    0.78   1.00
                                                                                                                      2       1        2.3300E+02     1.0000E+00   1.0000E+00                    0.00   0.78
                                                                                                                      2       2        2.3300E+02     1.0000E+00   1.0000E+00                    0.78   1.00
                                                                                                                      3       1        2.3300E+02     1.0000E+00   1.0000E+00                    0.00   0.78
                                                                                                                      3       2        2.3300E+02     1.0000E+00   1.0000E+00                    0.78   1.00
                                                                                                                      4       1        2.3300E+02     1.0000E+00   1.0000E+00                    0.00   0.78
                                                                                                                      4       2        2.3300E+02     1.0000E+00   1.0000E+00                    0.78   1.00
                                                                                                                      5       1        2.3300E+02     1.0000E+00   1.0000E+00                    0.00   0.02
                                                                                                                      5       2        2.3300E+02     1.0000E+00   1.0000E+00                    0.02   0.91
                                                                                                                      5       3        2.3300E+02     1.0000E+00   1.0000E+00                    0.91   1.00

                                                                                                              BASIC
                                                                                                            LOAD CASE       TYPE         ORIGIN                   BASIC LOAD CASE TITLE
                                                                                                            ---------       ----         ------                   ---------------------
                                                                                                                1         ORDINARY       STATIC                   NODAL LOAD - UNIT CASE
                                                                                                                2         ORDINARY       STATIC                   DISTRIBUTED LOAD - UNIT CASE
                                                                                                                3         ORDINARY       STATIC                   POINT LOADING - UNIT CASE

                                                                                                            COMBINED
                                                                                                            LOAD CASE       TYPE         ORIGIN     METHOD        COMBINED LOAD CASE TITLE
                                                                                                            ---------       ----         ------     ------        ------------------------
                                                                                                               10         ORDINARY      COMBINED     SSUM         COMBINED LOAD CASE

                                                                                                                          BASIC CASE     ORIGIN       FACTOR                TITLE
                                                                                                                          ----------     ------       ------                -----




                                                                                                                                                                                                                                                       Facilities in BEAMST
                                                                                                                  1         STATIC        10.000                NODAL LOAD - UNIT CASE
                                                                                                                  2         STATIC         5.000                DISTRIBUTED LOAD - UNIT CASE
                                                                                                                  3         STATIC         4.750                POINT LOADING - UNIT CASE
Page 2-17




                                                                                                                                                             Figure 2.3 Typical Input Data Cross Check Report
                                                                                                            ****************************************




                                                                                                                                                                                                                                                    BEAMST User Manual
                                                                                                            . ELEMENT      5 . TUBE . GROUP      1 .                     MEMBER PROPERTIES REPORT                STRESS UNITS (KN   ,M   )   PROP
    Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.
                                                                                                            ****************************************                     ------------------------                      OTHERS (KN   ,M   )   ====
                                                                                                                  NODE      3   NODE      4     MEMBER LENGTH     EFFE.LENGTH       UNBRACED      MAX KL/R
                                                                                                                  -----------   -----------     -------------      FACTOR (K)      LENGTH (L)     --------
                                                                                                            X-COORD   0.000D+00   0.000D+00
                                                                                                            Y-COORD   0.000D+00   0.000D+00          1.127D+01        1.000(Y)    1.127D+01(Y)        24.438
                                                                                                            Z-COORD   1.200D+01   0.000D+00     ULCF 1.127D+01        1.000(Z)    1.127D+01(Z)        24.438

                                                                                                                                                   **** STEP NUMBER      1 ****

                                                                                                            SECTION PROPERTIES     3               MATERIAL PROPERTIES     1                  TUBULAR SECTION
                                                                                                            ------------------------               -------------------------                  ---------------
                                                                                                            CROSS SECTION AREA =   6.801D-01       YOUNGS MODULUS   =   2.100D+05             OUTSIDE DIAMETER    =   1.484D+00
                                                                                                            SHEAR AREA         =   3.435D-01       POISSON RATIO    =   0.300                 WALL THICKNESS      =   1.640D-01
                                                                                                            TORSIONAL INERTIA =    3.008D-01       EXPANSION COEFF =    1.000D-01
                                                                                                            BENDING INERTIA    =   1.504D-01       YIELD STRESS     =   2.330D+02
                                                                                                            STEP LENGTH        =   2.680D-01

                                                                                                                                                   **** STEP NUMBER      2 ****

                                                                                                            SECTION PROPERTIES     3               MATERIAL PROPERTIES     1                  TUBULAR SECTION
                                                                                                            ------------------------               -------------------------                  ---------------
                                                                                                            CROSS SECTION AREA =   4.247D-01       YOUNGS MODULUS   =   2.100D+05             OUTSIDE DIAMETER    =   1.404D+00
                                                                                                            SHEAR AREA         =   2.133D-01       POISSON RATIO    =   0.300                 WALL THICKNESS      =   1.040D-01
                                                                                                            TORSIONAL INERTIA =    1.806D-01       EXPANSION COEFF =    1.000D-01
                                                                                                            BENDING INERTIA    =   9.030D-02       YIELD STRESS     =   2.330D+02
                                                                                                            STEP LENGTH        =   1.000D+01

                                                                                                                                                   **** STEP NUMBER      3 ****

                                                                                                            SECTION PROPERTIES     3               MATERIAL PROPERTIES     1                  TUBULAR SECTION
                                                                                                            ------------------------               -------------------------                  ---------------
                                                                                                            CROSS SECTION AREA =   8.716D-01       YOUNGS MODULUS   =   2.100D+05             OUTSIDE DIAMETER    =   1.564D+00




                                                                                                                                                                                                                                                        Facilities in BEAMST
                                                                                                            SHEAR AREA         =   4.423D-01       POISSON RATIO    =   0.300                 WALL THICKNESS      =   2.040D-01
                                                                                                            TORSIONAL INERTIA =    4.121D-01       EXPANSION COEFF =    1.000D-01
                                                                                                            BENDING INERTIA    =   2.060D-01       YIELD STRESS     =   2.330D+02
                                                                                                            STEP LENGTH        =   1.000D+00
Page 2-18




                                                                                                                                                                 Figure 2.4 Typical Member Properties Report
                                                                                                            ..................................................................................................................................




                                                                                                                                                                                                                                                 BEAMST User Manual
                                                                                                            . ELEMENT      5 . NODES      3      4 . GROUP      1 . MEMBER FORCE REPORT                         UNITS (KN ,M    )     FORC
    Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.
                                                                                                            ....................................................... -------------------                         -----                 ====
                                                                                                            LOAD CASE   SECTION      AXIAL-FX     SHEAR-FY     SHEAR-FZ    TORQUE-MX    MOMENT-MY    MOMENT-MZ       FREE MT.-MY FREE MT.-MZ
                                                                                                            ---------   NO POSN      --------     --------     --------    ---------    ---------    ---------       ----------- -----------

                                                                                                                1       1 0.00        -4.629        0.000        0.000        0.000*        0.000           0.000        0.000        0.000
                                                                                                                1       2 0.02        -4.629        0.000        0.000        0.000         0.000           0.000        0.000        0.000
                                                                                                                1       3 0.02        -4.629        0.000        0.000        0.000         0.000           0.000        0.000        0.000
                                                                                                                1       4 0.91        -4.629        0.000        0.000        0.000         0.000           0.000        0.000        0.000
                                                                                                                1       5 0.91        -4.629        0.000        0.000        0.000         0.000           0.000        0.000        0.000
                                                                                                                1       6 1.00        -4.629        0.000        0.000        0.000         0.000           0.000        0.000        0.000
                                                                                                                1      MAXIMUM        -4.629        0.000        0.000        0.000         0.000           0.000        0.000        0.000
                                                                                                                1         POSN         0.00         0.00         0.00         0.00          0.00            0.00         0.00         0.00

                                                                                                                2       1 0.00         0.000      -35.715        0.000        0.000         0.000          64.663        0.000        0.000
                                                                                                                2       2 0.02         0.000      -34.359        0.000        0.000         0.000          55.273        0.000       -9.885
                                                                                                                2       3 0.02         0.000      -34.359        0.000        0.000         0.000          55.273        0.000       -9.885
                                                                                                                2       4 0.91         0.000       39.017        0.000        0.000         0.000          41.589        0.000      -42.024
                                                                                                                2       5 0.91         0.000       39.017        0.000        0.000         0.000          41.589        0.000      -42.024
                                                                                                                2       6 1.00         0.000       48.795        0.000        0.000         0.000          85.458        0.000        0.000
                                                                                                                2      MAXIMUM         0.000       48.795        0.000        0.000         0.000          85.458        0.000     -119.032
                                                                                                                2         POSN         0.00         1.00         0.00         0.00          0.00            1.00         0.00         0.50

                                                                                                                3       1 0.00         0.000        0.000       -6.573        0.000         9.113           0.000        0.000        0.000
                                                                                                                3       2 0.02         0.000        0.000       -6.573        0.000         7.351           0.000       -1.729        0.000
                                                                                                                3       3 0.02         0.000        0.000       -6.573        0.000         7.351           0.000       -1.729        0.000
                                                                                                                3       4 0.91         0.000        0.000        3.427        0.000         4.305           0.000       -3.550        0.000
                                                                                                                3       5 0.91         0.000        0.000        3.427        0.000         4.305           0.000       -3.550        0.000
                                                                                                                3       6 1.00         0.000        0.000        3.427        0.000         7.732           0.000        0.000        0.000
                                                                                                                3      MAXIMUM         0.000        0.000       -6.573        0.000       -15.574           0.000      -24.227        0.000
                                                                                                                3         POSN         0.00         0.00         0.00         0.00          0.33            0.00         0.33         0.00

                                                                                                               10       1 0.00       -46.287     -178.573      -31.220        0.000        43.286         323.317        0.000        0.000




                                                                                                                                                                                                                                                     Facilities in BEAMST
                                                                                                               10       2 0.02       -46.287     -171.793      -31.220        0.000        34.919         276.365       -8.211      -49.425
                                                                                                               10       3 0.02       -46.287     -171.793      -31.220        0.000        34.919         276.365       -8.211      -49.425
                                                                                                               10       4 0.91       -46.287      195.087       16.280        0.000        20.448         207.943      -16.862     -210.120
                                                                                                               10       5 0.91       -46.287      195.087       16.280        0.000        20.448         207.943      -16.862     -210.120
                                                                                                               10       6 1.00       -46.287      243.977       16.280        0.000        36.728         427.290        0.000        0.000
                                                                                                               10      MAXIMUM       -46.287*     243.977*     -31.220*       0.000       -73.976*        427.290*    -115.077*    -595.162*
Page 2-19




                                                                                                               10         POSN         0.00         1.00         0.00         0.00          0.33            1.00         0.33         0.50



                                                                                                                                                                 Figure 2.5 Typical Member Force Report
                                                                                                            ..................................................................................................................................




                                                                                                                                                                                                                                                   BEAMST User Manual
                                                                                                            . ELEMENT      5 . NODES      3      4 . GROUP      1 . MEMBER STRESS REPORT                        UNITS (KN ,M    )     STRE
    Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.
                                                                                                            ....................................................... --------------------                        -----                 ====
                                                                                                             LOAD   SECTION AXIAL - X SHEAR - Y SHEAR - Z TORSION ----- BENDING ----- MAX SHEAR -------------- COMBINED ---------------
                                                                                                             CASE   NO POSN --------- --------- --------- ---------      Y         Z     ---------      A         B         C         D

                                                                                                               1    1 0.00     -6.81       0.00       0.00    0.00*      0.00       0.00      0.00       -6.81      -6.81      -6.81      -6.81
                                                                                                               1    2 0.02     -6.81       0.00       0.00    0.00       0.00       0.00      0.00       -6.81      -6.81      -6.81      -6.81
                                                                                                               1    3 0.02    -10.90       0.00       0.00    0.00       0.00       0.00      0.00      -10.90     -10.90     -10.90     -10.90
                                                                                                               1    4 0.91    -10.90       0.00       0.00    0.00       0.00       0.00      0.00      -10.90     -10.90     -10.90     -10.90
                                                                                                               1    5 0.91     -5.31       0.00       0.00    0.00       0.00       0.00      0.00       -5.31      -5.31      -5.31      -5.31
                                                                                                               1    6 1.00     -5.31       0.00       0.00    0.00       0.00       0.00      0.00       -5.31      -5.31      -5.31      -5.31
                                                                                                               1   MAXIMUM    -10.90       0.00       0.00    0.00       0.00       0.00      0.00      -10.90     -10.90     -10.90     -10.90
                                                                                                               1      POSN      0.02       0.00       0.00    0.00       0.00       0.00      0.00        0.02       0.02       0.02       0.02

                                                                                                               2    1 0.00      0.00    -103.96       0.00    0.00       0.00     319.00    103.96     -319.00       0.00     319.00       0.00
                                                                                                               2    2 0.02      0.00    -100.02       0.00    0.00       0.00     272.67    100.02     -272.67       0.00     272.67       0.00
                                                                                                               2    3 0.02      0.00    -161.10       0.00    0.00       0.00     429.69    161.10     -429.69       0.00     429.69       0.00
                                                                                                               2    4 0.91      0.00     182.94       0.00    0.00       0.00     323.31    182.94     -323.31       0.00     323.31       0.00
                                                                                                               2    5 0.91      0.00      88.22       0.00    0.00       0.00     157.84     88.22     -157.84       0.00     157.84       0.00
                                                                                                               2    6 1.00      0.00     110.32       0.00    0.00       0.00     324.33    110.32     -324.33       0.00     324.33       0.00
                                                                                                               2   MAXIMUM      0.00     182.94       0.00    0.00       0.00     429.69    182.94     -429.69       0.00     429.69       0.00
                                                                                                               2      POSN      0.00       0.91       0.00    0.00       0.00       0.02      0.91        0.02       0.00       0.02       0.00

                                                                                                               3    1 0.00      0.00       0.00     -19.13    0.00      44.96       0.00     19.13         0.00    -44.96       0.00      44.96
                                                                                                               3    2 0.02      0.00       0.00     -19.13    0.00      36.27       0.00     19.13         0.00    -36.27       0.00      36.27
                                                                                                               3    3 0.02      0.00       0.00     -30.82    0.00      57.15       0.00     30.82         0.00    -57.15       0.00      57.15
                                                                                                               3    4 0.91      0.00       0.00      16.07    0.00      33.47       0.00     16.07         0.00    -33.47       0.00      33.47
                                                                                                               3    5 0.91      0.00       0.00       7.75    0.00      16.34       0.00      7.75         0.00    -16.34       0.00      16.34
                                                                                                               3    6 1.00      0.00       0.00       7.75    0.00      29.35       0.00      7.75         0.00    -29.35       0.00      29.35
                                                                                                               3   MAXIMUM      0.00       0.00     -30.82    0.00    -121.07       0.00     30.82         0.00    121.07       0.00    -121.07
                                                                                                               3      POSN      0.00       0.00       0.02    0.00       0.33       0.00      0.02         0.00      0.33       0.00       0.33

                                                                                                              10    1 0.00    -68.06    -519.82     -90.88    0.00     213.54    1594.98    527.71    -1663.04    -281.60    1526.92     145.48




                                                                                                                                                                                                                                                       Facilities in BEAMST
                                                                                                              10    2 0.02    -68.06    -500.09     -90.88    0.00     172.26    1363.35    508.28    -1431.41    -240.32    1295.29     104.20
                                                                                                              10    3 0.02   -108.98    -805.50    -146.38    0.00     271.46    2148.45    818.69    -2257.43    -380.44    2039.48     162.49
                                                                                                              10    4 0.91   -108.98     914.72      76.33    0.00     158.97    1616.55    917.89    -1725.52    -267.94    1507.57      49.99
                                                                                                              10    5 0.91    -53.11     441.08      36.81    0.00      77.61     789.19    442.62     -842.30    -130.71     736.09      24.50
                                                                                                              10    6 1.00    -53.11     551.62      36.81    0.00     139.39    1621.66    552.85    -1674.77    -192.50    1568.56      86.29
                                                                                                              10   MAXIMUM   -108.98*    914.72*   -146.38*   0.00    -575.09*   2148.45*   917.89*   -2257.43*    466.11*   2039.48*   -684.06*
Page 2-20




                                                                                                              10      POSN      0.02       0.91       0.02    0.00       0.33       0.02      0.91        0.02       0.33       0.02       0.33




                                                                                                                                                                 Figure 2.6 Typical Member Stress Report
                                                                                                            ********************************************************************************************************************************
                                                                                                            *                                       MAX/MIN FORCES AND MOMENTS FOR GROUP NUMBER    1                                       *




                                                                                                                                                                                                                                               BEAMST User Manual
    Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.
                                                                                                            ********************************************************************************************************************************
                                                                                                                                     AXIAL-FX     SHEAR-FY     SHEAR-FZ    TORQUE-MX    MOMENT-MY    MOMENT-MZ      FREE MT.-MY   FREE MT.MZ
                                                                                                                                     --------     --------     --------    ---------    ---------    ---------      -----------   ----------
                                                                                                                POSITIVE MAXIMUM      121.989      243.977       16.280       27.122       43.286      427.290            0.000        0.000
                                                                                                                        POSITION        0.000        1.000        0.400        0.000        0.000        1.000            0.778        0.778
                                                                                                                         ELEMENT            4            5            5            1            5            5                3            3
                                                                                                                        LOADCASE           10           10           10           10           10           10               10           10
                                                                                                            --------------------------------------------------------------------------------------------------------------------------------
                                                                                                            2ND POSITIVE MAXIMUM       89.286      105.275       15.610       21.466       38.162      316.702            0.000        0.000
                                                                                                                        POSITION        0.000        0.000        0.000        0.000        1.000        1.000            0.778        1.000
                                                                                                                         ELEMENT            3            2            1            4            1            2                4            4
                                                                                                                        LOADCASE           10           10           10           10           10           10               10            2
                                                                                                            --------------------------------------------------------------------------------------------------------------------------------
                                                                                                            3RD POSITIVE MAXIMUM       24.398       87.794        8.140        5.710       32.083      258.655            0.000        0.000
                                                                                                                        POSITION        0.000        0.000        0.000        0.000        0.000        1.000            0.778        1.000
                                                                                                                         ELEMENT            4            3            2            1            3            3                3            1
                                                                                                                        LOADCASE            2           10           10            3           10           10                3            1
                                                                                                            --------------------------------------------------------------------------------------------------------------------------------
                                                                                                            4TH POSITIVE MAXIMUM       17.857       48.795        3.427        4.519       19.900       85.458            0.000        0.000
                                                                                                                        POSITION        0.000        1.000        0.400        0.000        1.000        1.000            1.000        1.000
                                                                                                                         ELEMENT            3            5            5            4            2            5                1            3
                                                                                                                        LOADCASE            2            2            3            3           10            2                3            1
                                                                                                            --------------------------------------------------------------------------------------------------------------------------------
                                                                                                                NEGATIVE MAXIMUM     -121.989     -178.573      -31.220      -27.122      -73.337     -203.544         -114.000     -584.052
                                                                                                                        POSITION        0.000        0.000        0.000        0.000        0.400        1.000            0.400        0.600
                                                                                                                         ELEMENT            2            5            5            3            5            4                5            5
                                                                                                                        LOADCASE           10           10           10           10           10           10               10           10
                                                                                                            --------------------------------------------------------------------------------------------------------------------------------
                                                                                                            2ND NEGATIVE MAXIMUM      -89.286      -58.988      -15.610      -21.466      -38.162     -198.351          -24.000     -116.810
                                                                                                                        POSITION        0.000        0.000        0.000        0.000        1.000        0.600            0.400        0.600
                                                                                                                         ELEMENT            1            4            3            2            3            5                5            5
                                                                                                                        LOADCASE           10           10           10           10           10           10                3            2
                                                                                                            --------------------------------------------------------------------------------------------------------------------------------
                                                                                                            3RD NEGATIVE MAXIMUM      -46.287      -35.715       -8.140       -5.710      -32.083     -157.033            0.000        0.000
                                                                                                                        POSITION        0.000        0.000        0.000        0.000        0.000        0.000            0.778        0.778
                                                                                                                         ELEMENT            5            5            4            3            1            2                1            4
                                                                                                                        LOADCASE           10            2           10            3           10           10               10           10
                                                                                                            --------------------------------------------------------------------------------------------------------------------------------




                                                                                                                                                                                                                                                   Facilities in BEAMST
                                                                                                            4TH NEGATIVE MAXIMUM      -24.398      -34.081       -6.573       -4.519      -19.900     -136.418            0.000        0.000
                                                                                                                        POSITION        0.000        0.000        0.000        0.000        1.000        0.000            0.778        0.778
                                                                                                                         ELEMENT            2            1            5            2            4            3                2            1
                                                                                                                        LOADCASE            2           10            3            3           10           10               10           10
                                                                                                            --------------------------------------------------------------------------------------------------------------------------------
Page 2-21




                                                                                                                                                                  Figure 2.7 Force Summary Report
BEAMST User Manual                                                                                      Input Data




3.      Input Data

As with other programs of the ASAS suite, the input of information and data is divided into two sections. The
first is the Preliminary Data followed by the main BEAMST Data.

The Preliminary Data defines the relationship of the run to all the other runs already completed in the project, the
backing files required and also specifies the title of the run. If subsequent processing is required after BEAMST,
the data to be saved from the run must also be defined in the Preliminary Data. The full details of these
commands, along with examples, are given in Appendix -A of this manual.

A summary of the BEAMST commands available is given in Table 3.1. Detailed descriptions of each of the
commands will be found in the remainder of Chapter 3, listed in alphabetical order.

The available commands for each type of code check are summarised in Tables 3.1 to 3.17.                    Detailed
descriptions of each of the commands will be found in the remainder of Chapter 3


3.1 Command Structures


3.1.1       Command Syntax

Each command consists of a command word followed by a number of parameters and, where applicable, an
assignment list to which the parameters are attributed. This is shown diagramatically as follows.




Within each command line, each horizontal branch represents a possible input instruction. Input instructions are
composed of keywords (shown in UPPER-CASE), numerical values or alphanumerics (shown in lower-case
characters) and special symbols (see Sections 3.1.2 and 3.1.3). Each item in the list is separated from each other
by a comma or one or more blank spaces.

Only the first four characters of a command are interpreted. Thus the following commands will produce the
same results.

                EFFE        2.0      ELEM       ALL
                EFFECTIVE_LENGTH                  2.0       ELEM       ALL
                EFFECTIVE            2.0       ELEM       ALL

Some data lines require an integer or real list to be input where length is variable. This is shown by a horizontal
arrow around the list variable.




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                list




Optional data items are indicated by an arrow which bypasses the item(s)
                 item




Alternatively, where optional items are part of a list of values they may be represented by enclosing brackets.

                value1               (value2... value n)




Where one or more possible alternative items may appear in the line, these are shown by separate branches for
each. These branches may rejoin further along the command if appropriate.
                    KEYWORD1


                    KEYWORD2




An input line must not be longer than 80 characters.




3.1.2         Data Types

Data is entered in three forms:

(a)     Integer Number and Lists


If an integer number is required a decimal point must not be supplied. When a list of integer numbers is
required, the following abbreviations may be used:

      (i).     Where the integer list represents all items from an existing list (for example, choosing all groups for
               processing) the list may be replaced by the word ALL. For example

                                       GROU ALL               generates all possible groups.

      (ii).    A sequence of integers may be generated by giving the first and last values separated by the
               keyword TO. For example 5 TO 8 generates the numbers 5,6,7 and 8.




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(b)     Real Number


If a real number is required the decimal point may be omitted if the value is a whole number. Exponent formats
may be utilised when real numbers are required. For example

                         0.004         4.0E-3 4.0D-3 are equivalent
similarly                410.0         410          4.10E2 have the same value

(c)     Alphanumeric


Alphanumeric data is used for keywords and text strings. Alphanumerics are any non-numeric strings which
may include the letters A-Z, numbers 0-9, and the characters +, -, / and :. The letters A-Z may be supplied in
either upper or lower case but no distinction is made between the upper and lower case form. Hence “A” is
assumed identical with “a”, “B” with “b” and so on. For example

                         COMB                   Comb               comb            are all identical strings.

Alphanumeric strings must not include any special symbols (see 3.1.3).




3.1.3       Special Symbols

The following is a list of characters which have a special significance to the BEAMST input.



*       An asterisk is used to define the beginning of a comment, whatever follows on the line will not be
        interpreted. It may appear anywhere on the line, any preceding data will be processed as normal. For
        example

                              * THIS IS A COMMENT FOR THE WHOLE LINE
                              CASE 4 2.7 * THIS IS A COMMENT FOR PART OF A LINE




,       A comma or one or more consecutive blanks will act as a delimiter between items in the line.

        For example               5, 10, 15                                is the same as           5   10      15




        Note that two commas together signify that an item has been omitted. This may be permissible for
        certain data blocks.

        For example               5,, 15                                  is the same as            5   0    15

        Unless otherwise stated in the section describing the data block, omitted numerical values are zero.




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:       A colon at the start of the line signifies that the line is a continuation from the previous line.

        For example

                                  5
                                  : 10                       is the same as             5    10         15
                                  : 15

@       A command @filename may appear anywhere in a data file. When such a command is encountered, the
        input of data switches to the file filename and data continues to be read from that file until either the end-
        of-file is reached or an @ command is encountered in the secondary file.

        When the end of the secondary file is reached, that file is closed and input switches back to the previous
        data file. If, however, an @ command is found in the secondary file, input switches to yet another file.
        This process can continue until a maximum of 5 secondary files are open simultaneously.

        For example

                  @prelim.dat
                  @select.dat
                  @geom.dat
                  @load.dat

        geom.dat might then contain the lines

                  @desi.dat
                  @effe.dat
                  @unbr.dat
                  @cm.dat

        finally

                  desi.dat contains the DESI commands
                  effe.dat contains the EFFE commands
                  etc




3.1.4       The NOT Command Modifier

The NOT command modifier may be used with ELEM                             (and join)and JOIN commands to switch off items
previously selected for processing. A typical use of the NOT command modifier is when all but a few elements
from a large group are to be processed. The group of elements may be selected first using the GROU command
and then the unwanted elements deselected using the NOT ELEM command. The order in which selections are




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made is important as the final setting for a particular element determines whether that element is processed.
Elements may be switched ‘on’ and ‘off’ repeatedly as in the example below.

                     GROU 1 2 3 4
                     NOT ELEM 1 TO 60
                     ELEM 8 TO 16
                     NOT ELEM 13

If groups 1, 2, 3 and 4 contain elements 1 to 100, then the above commands select elements:

                                  8 9 10 11 12 14 15 16 and 61 to 100


In the special case where the NOT ELEM command is the first to appear in the data it has the effect of switching
‘on’ all elements apart from those specified on the command.

The NOT JOIN command operates in a similar fashion to the NOT ELEM command.




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3.2 BEAMST Command Sets

BEAMST data is grouped into command sets according to the requirements of each type of code check. Each
command set consists of a header command for the code check, the commands applicable to the check and an
END command to terminate the set. It is permissible to run several different code checks by appending the
command sets in a single BEAMST datafile. It should be noted however that if plot files are to be saved then
command sets should not be appended.

The structure of a typical BEAMST datafile for multiple check types is shown below:



        SYSTEM

        data
                                                   Preliminary data. See Appendix A for details
        END


        POST

        data                                      POST run commands

        END



        API      LRFD       edition       HYDR

        data                                                     API LRFD HYDRostatic code check data

        END


        API      LRFD       edition      MEMB

        data                                                     API LRFD MEMBer stress code check

        END

                                                  Further code check data sets as required
        data

                                                  BEAMST datafile terminator
        STOP



The header command for each command set consists of a keyword defining the design code, a second keyword
(or sub-header) defining the particular requirements from the code and in some instances further keywords
defining editions, amendments and check classes. The BEAMST command sets are summarised in the table
below. The commands relevant to each command set are summarised in the tables that follow, the reference for
each is also given in the table below.



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                                                                                                         Table of
    Header              Sub-Header                                     Description
                                                                                                        Commands
   AISC               WSD ALLO                   Member stress checks to allowable stresses to             3.2
                                                 AISC design specification.
   AISC               LRFD MEMB                  Member design checks to AISC LRFD                         3.3
                                                 recommendations.
   API                WSD ALLO                   Tubular member stress checks to allowable                 3.2
                                                 stresses to API WSD recommendations.
   API                LRFD MEMB                  Tubular member stress checks to API LRFD                  3.4
                                                 recommendations.
   API                WSD HYDR                   Hydrostatic collapse check for members to API             3.5
                                                 WSD recommendations.
   API                LRFD HYDR                  Hydrostatic collapse check for members to API             3.6
                                                 LRFD recommendations.
   API                WSD NOMI                   Joint nominal load check for tubular joints to            3.7
                                                 API WSD recommendations. (N/A for Ed21
                                                 onwards)
   API                WSD PUNC                   Joint punching shear checks for tubular joints to         3.7
                                                 API WSD recommendations. (N/A for Ed21
                                                 onwards)
   API                WSD JOIN                   Joint strength check (only applicable to API              3.7
                                                 WSD 21st Edition onwards)
   API                LRFD JOIN                  Joint ultimate limit state checks to API LRFD             3.8
                                                 recommendations.
   BS59               MEMB                       Member ultimate limit state checks to British             3.9
                                                 Standards BS5950.
   DS449              MEMB                       Member ultimate limit state checks to Danish              3.10
                                                 Standards DS449.
   DS449              JOIN                       Joint ultimate limit state checks to Danish               3.11
                                                 Standards DS449.
   NPD                MEMB                       Member yield and buckling checks to                       3.12
                                                 NPD/NS3472 regulations.
   NPD                 JOIN                      Joint punching shear checks to NPD/NS3472                 3.13
                                                 regulations.
   NORS               MEMB                       Tubular Member stress checks to NORSOK                    3.14
   NORS               HYDR                       Hydrostatic collapse check to NORSOK                      3.15
   NORS               JOIN                       Joint load check for tubular joints to NORSOK             3.16
   POST                                          Post processing without code checks.                     3.177




                                             Table 3.1 BEAMST Command Sets




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         Command                                               Description                              Usage    Note
    AISC ALLO                      AISC allowable stress header command
                                                                                                         C
    API WSD ALLO                   API allowable stress header command
    UNIT                           Units of length and force                                                       1
    YIEL                           Yield stress                                                          C
    MCOF                           Partial Material Coefficient
    GROU                           Groups to be reported
                                                                                                         C         2
    ELEM                           Elements to be reported
    SECT                           Sections to be reported
    SEAR                           Search for maximum forces and stresses
    SECO                           Secondary members
    DESI                           Defines design section properties                                      C        3
    PROF                           Section profiles for use in design
    EFFE                           Effective lengths/factors
    CB                             Pure bending Cb coefficient
    CMY/CMZ                        Amplification reduction factors Cmy/Cmz
    UNBR                           Unbraced lengths of element
    ULCF                           Unbraced length of compression flange
    CASE                           Basic loadcases to be reported
    COMB                           Define a combined loadcase for processing                             C
                                                                                                                   4
    CMBV                           Define a combined loadcase for processing
    SELE                           Select/redefine a combined/basic loadcase title
    SPEC                           Basic loadcases from response spectrum analysis
    HARM                           Loadcases originating from harmonic steady state
                                   response analysis
    RENU                           Renumber a ‘basic loadcase’
    EXTR                           Loadcases allowing 33% overstress
    QUAK                           Loadcases with earthquake permitted overstress

    PRIN                           Reports to be printed
    TEXT                           Text or comment command
    TITL                           Redefine global title
    END                            Terminates Command data block                                         C


Usage
C        Compulsory command, but see notes below where applicable.
Notes
1. See Sections 3.4 and A.12.
2. At least one GROUP or ELEM command must be included.
3. Compulsory for non-tubulars unless Sections have been used in the preceding analyses for all elements to be
    processed.
4. At least one CASE, COMB or CMBV command must be included.

                               Table 3.2 AISC ALLO and API WSD ALLO Commands




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         Command                                                Description                             Usage    Note
    AISC LRFD MEMB                    AISC Load and Resistance Factor Design header                      C
                                      command
    UNIT                              Units of length and force                                                    1
    YIEL                              Yield stress                                                       C

    GROU                              Groups to be reported
                                                                                                         C         2
    ELEM                              Elements to be reported
    SECT                              Sections to be reported
    SEAR                              Search for maximum forces and stresses
    SECO                              Secondary members
    DESI                              Defines design section properties
    PROF                              Section profiles for use in design
    EFFE                              Effective lengths/factors
    CB                                Pure bending Cb coefficient
    CMY/CMZ                           Amplification reduction factors Cmy/Cmz
    UNBR                              Unbraced lengths of element
    ULCF                              Unbraced length of compression flange
    CASE                              Basic loadcases to be reported                                               3
                                                                                                         C
    COMB                              Define a combined loadcase for processing
    CMBV                              Define a combined loadcase for processing
    SELE                              Select/redefine a combined/basic loadcase title
    RENU                              Renumber a ‘basic loadcase’


    PRIN                              Reports to be printed
    TEXT                              Text or comment command
    TITL                              Redefine global title
    END                               Terminates Command data block                                      C


Usage
C       Compulsory command, but see notes below where applicable.

Notes
1. See Sections 3.4 and A.12.
2. At least one GROUP or ELEM command must be included.
3. At least one CASE, COMB or CMBV command must be included.


                                         Table 3.3 AISC LRFD MEMB Commands




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        Command                                                Description                              Usage     Note
    API LRFD MEMB                  API Load and Resistance Factor Design header command                  C

    UNIT                           Units of length and force                                                        1
                                                                                                         C
    YIEL                           Yield stress
    GROU                           Groups to be reported
                                                                                                         C          2
    ELEM                           Elements to be reported
    SECT                           Sections to be reported
    SEAR                           Search for maximum forces and stresses
    SECO                           Secondary members
    DESI                           Defines design section properties
    PROF                           Section profiles for use in design
    EFFE                           Effective lengths/factors
    CB                             Pure bending Cb coefficient
    CMY/CMZ                        Amplification reduction factors Cmy/Cmz
    UNBR                           Unbraced lengths of element
    ULCF                           Unbraced length of compression flange
    ABNO                           Abnormal loadcases                                                               3
    CASE                           Basic loadcases to be reported
    COMB                           Define a combined loadcase for processing                             C
    CMBV                           Define a combined loadcase for processing
    SELE                           Select/redefine a combined/basic loadcase title
    SPEC                           Basic loadcases from response spectrum analysis
    RENU                           Renumber a ‘basic loadcase’


    PRIN                           Reports to be printed
    TEXT                           Text or comment command
    TITL                           Redefine global title
    END                            Terminates Command data block                                         C


Usage
C       Compulsory command, but see notes below where applicable.

Notes
1. See Sections 3.4 and A.12.
2. At least one GROUP or ELEM command must be included.
3. At least one CASE, COMB or CMBV command must be included.


                                          Table 3.4 API LRFD MEMB Commands




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        Command                                               Description                               Usage     Note
    API WSD HYDR                  API hydrostatic collapse header command                                C

    UNIT                          Units of length and force                                              C          1
    YIEL                          Yield stress

    ELEV                          Water depth and density                                                C
    MOVE                          Water axis origin in global structure axis system
    WAVE                          Wave height and period
    GRAV                          Gravitational acceleration relative to structure axis system           C

    GROU                          Groups to be reported
                                                                                                                    2
    ELEM                          Elements to be reported                                                C
    SECT                          Sections to be reported


    DESI                          Defines design section properties
    PROF                          Section profiles for use in design
    ULCF                          Length of tubular members between stiffening rings,
                                  diaphragms etc

    CASE                          Loadcases to be reported                                                          3
    COMB                          Define a combined loadcase for processing                              C
    CMBV                          Define a combined loadcase for processing
    SELE                          Select/redefine a combined/basic loadcase title
    HARM                          Loadcases originating from harmonic steady state response
                                  analysis
    RENU                          Renumber a basic loadcase
    EXTR                          Loadcases allowing 33% overstress
    QUAK                          Loadcases with earthquake permitted overstress
    SAFE                          Safety factors for axial compressive, tensile and hoop
                                  compressive loading

    PRIN                          Reports to be printed
    TEXT                          Text or comment command
    TITL                          Redefine global title

    END                           Terminates Command data block                                          C


Usage
C       Compulsory command, but see notes below where applicable.

Notes
1.    See Sections 3.4 and A.12.
2.    At least one GROUP or ELEM command must be included.
3.    At least one CASE, COMB or CMBV command must be included.


                                           Table 3.5 API WSD HYDR Commands




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        Command                                                Description                              Usage     Note
    API LRFD HYDR                  API Load and Resistance Factor Design hydrostatic                     C
                                   collapse header command

    UNIT                           Units of length and force                                             C          1
    YIEL                           Yield stress

    ELEV                           Water depth and density                                               C
    MOVE                           Water axis origin in global structure axis system
    WAVE                           Wave height and period
    GRAV                           Gravitational acceleration relative to structure axis system          C

    GROU                           Groups to be reported
                                                                                                                    2
    ELEM                           Elements to be reported                                               C
    SECT                           Sections to be reported


    DESI                           Defines design section properties
    PROF                           Section profiles for use in design
    ULCF                           Length of tubular members between stiffening rings,
                                   diaphragms etc

    ABNO                           Abnormal loadcases                                                               3
    CASE                           Loadcases to be reported
    COMB                           Define a combined loadcase for processing
                                                                                                         C
    CMBV                           Define a combined loadcase for processing
    HYDR                           Load factors for design hydrostatic head
    SELE                           Select/redefine a combined/basic loadcase title
    RENU                           Renumber a basic loadcase

    PRIN                           Reports to be printed
    TEXT                           Text or comment command
    TITL                           Redefine global title

    END                            Terminates Command data block                                         C


Usage

C       Compulsory command, but see notes below where applicable.

Notes
1.    See Sections 3.4 and A.12.
2.    At least one GROUP or ELEM command must be included.
3.    At least one CASE, COMB or CMBV command must be included.


                                          Table 3.6 API LRFD HYDR Commands




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       Command                                               Description                                Usage     Note
     API WSD NOMI              API nominal load check header command
     API WSD PUNC              API joint check header command                                            C
     API WSD JOIN

     UNIT                      Units of length and force                                                 C          1
     YIEL                      Yield stress

     JOIN                      Joint numbers to be reported
     TYPE                      Joint type and brace element definition
     CHOR                      Chord elements at a joint
     SECO                      Secondary members to be ignored in checks

     DESI                      Defines design section properties
     GAPD                      Define default gap dimension
     PROF                      Section profiles for use in design
     STUB                      Tubular member end stub dimensions

     CASE                      Basic loadcases
     COMB                      Define a combined loadcase for processing                                 C               2
     CMBV                      Define a combined loadcase for processing
     SELE                      Select/redefine a combined/basic loadcase title
     SPEC                      Loadcases originating from response spectrum analysis
     RENU                      Renumber a basic loadcase
     QUAK                      Loadcases with earthquake permitted overstress
     EXTR                      Loadcase allowing extreme loading overstress

     PRIN                      Reports to be printed
     TEXT                      Text or comment command
     TITLE                     Redefine global title

     END                       Terminates command data block                                             C


Usage
C.         Compulsory command, but see notes below where applicable.

Notes

1.         See Sections 3.4 and A.12.

2.         At least one CASE, COMB or CMBV command must be included.


                               Table 3.7 API WSD: NOMI, PUNC and JOIN Commands




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       Command                                              Description                                 Usage     Note
     API LRFD JOIN             API Load and Resistance Factor Design joint check header                  C
                               command

     UNIT                      Units of length and force                                                 C          1
     YIEL                      Yield stress

     JOIN                      Joint numbers to be reported
     TYPE                      Joint type and brace element definition
     CHOR                      Chord elements at a joint and associated parameters                       C          2
     SECO                      Secondary members to be ignored in checks

     DESI                      Defines design section properties
     GAPD                      Define default gap dimension
     PROF                      Section profiles for use in design
     STUB                      Tubular member end stub dimensions

     ABNO                      Abnormal loadcases
     CASE                      Basic loadcases
     COMB                      Define a combined loadcase for processing                                 C              3
     CMBV                      Define a combined loadcase for processing
     SELE                      Select/redefine a combined/basic loadcase title
     SPEC                      Basic loadcases from response spectrum analysis
     RENU                      Renumber a basic loadcase

     PRIN                      Reports to be printed
     TEXT                      Text or comment command
     TITLE                     Redefine global title

     END                       Terminates command data block                                             C


Usage
C.         Compulsory command, but see notes below where applicable.

Notes

1.         See Sections 3.4 and A.12.

2.         CHORd parameters are compulsory if load transfer across chord checks at cross joints are to be
           undertaken.

3.         At least one CASE, COMB or CMBV command must be included


                                           Table 3.8 API LRFD JOIN Commands




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     Command                                              Description                                   Usage     Note
     BS59 MEMB            BS59 member check header command                                               C

     UNIT                 Units of length and force                                                      C          1
     YIEL                 Yield Stress

     GROU                 Groups to be reported                                                          C
     ELEM                 Elements to be reported                                                                   2
     SECT                 Sections to be reported
     SEAR                 Search for maximum forces and stresses                                                    2


     SIMP                 Select elements for simple checks
     MFAC                 Define moment reduction factors for overall buckling check
     MLTF                 Define L.T.B. moment reduction factor for overall buckling
                          check

     DESI                 Defines design section properties                                              C          3
     PROF                 Section profiles for use in design
     EFFE                 Effective lengths/factor
     ULCF                 Unbraced length of compression flange
     UNBR                 Unbraced lengths of element

     CASE                 Basic loadcases to be reported
     COMB                 Define a combined loadcase for processing                                      C          4
     CMBV                 Define a combined loadcase for processing
     SELE                 Select/redefine a combined/basic loadcase title
     HARM                 Loadcases originating from harmonic steady state response
                          analysis                                                                       C          4
     RENU                 Renumber a basic loadcase

     PRIN                 Reports to be printed
     TEXT                 Text or comment command
     TITL                 Redefine global title

     END                  Terminates Command data block                                                  C


Usage
C.      Compulsory command, but see notes below where applicable.

Notes
1.    See Sections 3.4 and A.12.
2.    At least one GROUP or ELEM command must be included.
3.    Compulsory for non-tubulars unless Sections have been used for all elements to be processed in the
      preceding analyses.
4.    At least one CASE, COMB or CMBV command must be included.


                                              Table 3.9 BS59 MEMB Commands




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    Command                                                 Description                                 Usage     Note
   DS449 MEMB                DS449 member check header command

   UNIT                      Units of length and force                                                   C          1
   YIEL                      Yield stress
   MCOF                      Partial Material Coefficient

   ELEV                      Water depth and density                                                      C              2
   MOVE                      Water axis origin in global structure axis system
   WAVE                      Wave height and period
   GRAV                      Gravitational accelerations relative to structure axis system                C              2

   GROU                      Groups to be reported
                                                                                                                         3
   ELEM                      Elements to be reported                                                     C
   SECT                      Sections to be reported
   SEAR                      Additional sections to be reported automatically

   DESI                      Defines design section properties                                                      4
   PROF                      Section profiles for use in design
   EFFE                      Effective lengths/factors
   ULCF                      Length of tubular members between stiffening rings,
                             diaphragms etc
   UNBR                      Unbraced lengths of element

   CASE                      Basic loadcases
   COMB                      Define a combined loadcase for processing                                   C          5
   CMBV                      Define a combined loadcase for processing
   SELE                      Select/redefine a combined/basic loadcase title
   HARM                      Loadcases originating from harmonic steady state response
                             analysis
   RENU                      Renumber a ‘basic loadcase’

   PRIN                      Reports to be printed
   TEXT                      Text or comment command
   TITL                      Redefine global title

   END                       Terminates command data block                                               C


Usage
C.    Compulsory command, but see notes below where applicable.
Notes
1.      See Sections 3.4 and A.12.
2.      Compulsory only if hydrostatic pressure effects to be examined.
3.      At least one GROUP or ELEM command must be included.
4.      Not compulsory because DS449 only checks tubular members.
5.      At least one CASE, COMB or CMBV command must be included.

                                            Table 3.10 DS449 MEMB Commands




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     Command                                             Description                                    Usage     Note
     DS449 JOIN          DS449 joint check header command                                                C

     UNIT                Units of length and force                                                       C          1
     YIEL                Yield stress
     MCOF                Partial Material Coefficient

     JOIN                Joint numbers to be reported
     TYPE                Joint type and brace element definition
     CHOR                Chord elements at a joint
     SECO                Secondary members to be ignored in checks

     DESI                Defines design section properties
     GAPD                Define default gap dimension
     PROF                Section profiles for use in design
     STUB                Tubular member end stub dimensions

     CASE                Basic loadcases
     COMB                Define a combined loadcase for processing                                       C              2
     CMBV                Define a combined loadcase for processing
     SELE                Select/redefine a combined/basic loadcase title
     RENU                Renumber a basic loadcase

     PRIN                Reports to be printed
     TEXT                Text or comment command
     TITLE               Redefine global title

     END                 Terminates command data block                                                   C


Usage
C.         Compulsory command, but see notes below where applicable.

Notes

1.         See Sections 3.4 and A.12.

2.         At least one CASE, COMB or CMBV command must be included.


                                             Table 3.11 DS449 JOIN Commands




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     Command                                              Description                                   Usage     Note
     NPD MEMB             NPD member check header command                                                C
     UNIT                 Units of length and force                                                      C          1
     YIEL                 Yield Stress
     MCOF                 Partial material coefficient
     ELEV                 Water depth and density                                                        C          2
     MOVE                 Water axis origin in global structure axis system
     WAVE                 Wave height and period
     GRAV                 Gravitational acceleration relative to structure axis system                   C          2
     GROU                 Groups to be reported
                                                                                                         C          3
     ELEM                 Elements to be reported
     SECT                 Sections to be reported
     SEAR                 Search for maximum forces and stresses

     DESI                 Defines design section properties                                              C          4
     PROF                 Section profiles for use in design
     EFFE                 Effective lengths/factors
     PHI                  Loadcase dependent parameter for lateral buckling
     UNBR                 Unbraced lengths of elements
     ULCF                 Unbraced length of compression flange
     CASE                 Basic loadcases to be reported
     COMB                 Define a combined loadcase for processing                                      C          5
     CMBV                 Define a combined loadcase for processing
     SELE                 Select/redefine a combined/basic loadcase title
     HARM                 Loadcases originating from harmonic steady state response
                          analysis
     RENU                 Renumber a basic loadcase
     PRIN                 Reports to be printed
     TEXT                 Text or comment command
     TITL                 Redefine global title
     END                  Terminates Command data block                                                  C


Usage
C.      Compulsory command, but see notes below where applicable.

Notes
1.      See Sections 3.4 and A.12.
2.      Compulsory only if hydrostatic pressure effects to be examined.
3.      At least one GROUP or ELEM command must be included.
4.      Compulsory for non-tubulars unless Sections have been used for all elements to be processed in the
        preceding analyses.
5.      At least one CASE, COMB or CMBV command must be included.


                                             Table 3.12 NPD MEMB Commands




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     Command                                              Description                                   Usage     Note

     NPD JOIN            NPD joint check header command                                                  C

     UNIT                Units of length and force                                                       C          1
     YIEL                Yield Stress
     MCOF                Partial material coefficient

     JOIN                Joint numbers to be reported                                                    C
     CHOR                Chord elements at a joint
     SECO                Secondary elements to be ignored in checks

     DESI                Defines design section properties
     PROF                Section profiles for use in design
     STUB                Tubular member end stub dimensions

     CASE                Basic loadcases to be reported
     COMB                Define a combined loadcase for processing                                       C          2
     CMBV                Define a combined loadcase for processing
     SELE                Select/redefine a combined/basic loadcase title
     HARM                Loadcases originating from harmonic steady state response
                         analysis
     RENU                Renumber a basic loadcase

     PRIN                Reports to be printed
     TEXT                Text or comment command
     TITL                Redefine global title

     END                 Terminates command data block                                                   C



Usage

C.      Compulsory command, but see notes below where applicable.

Notes

1.      See Sections 3.4 and A.12.

2.      At least one CASE, COMB or CMBV command must be included.


                                               Table 3.13 NPD JOIN Commands




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        Command                                                Description                              Usage     Note
    NORS MEMB                      NORSOK allowable stress header command                                C

    UNIT                           Units of length and force                                             C          1
    YIEL                           Yield stress
    MCOF                           Partial Material Coefficient
    GROU                           Groups to be reported
                                                                                                         C          2
    ELEM                           Elements to be reported
    SECT                           Sections to be reported
    SEAR                           Search for maximum forces and stresses
    SECO                           Secondary members
    DESI                           Defines design section properties
    PROF                           Section profiles for use in design
    EFFE                           Effective lengths/factors
    CMY/CMZ                        Amplification reduction factors Cmy/Cmz
    UNBR                           Unbraced lengths of element
    ULCF                           Unbraced length of compression flange
    CASE                           Basic loadcases to be reported
    COMB                           Define a combined loadcase for processing
                                                                                                         C          3
    CMBV                           Define a combined loadcase for processing
    SELE                           Select/redefine a combined/basic loadcase title
    RENU                           Renumber a ‘basic loadcase’


    PRIN                           Reports to be printed
    TEXT                           Text or comment command
    TITL                           Redefine global title
    END                            Terminates Command data block                                         C


Usage
C       Compulsory command, but see notes below where applicable.

Notes
1.    See Sections 3.4 and A.12.
2.    At least one GROUP or ELEM command must be included.
3.    At least one CASE, COMB or CMBV command must be included.


                                          Table 3.14 NORSOK MEMB Commands




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        Command                                                Description                              Usage     Note
    NORS HYDR                      NORSOK hydrostatic collapse header command                            C

    UNIT                           Units of length and force                                             C          1
    YIEL                           Yield stress
    MCOF                           Partial Material Coefficient

    ELEV                           Water depth and density                                               C
    MOVE                           Water axis origin in global structure axis system
    WAVE                           Wave height and period
    GRAV                           Gravitational acceleration relative to structure axis system          C

    BRIG                           Selects rigorous buoyancy method for calculation

    GROU                           Groups to be reported                                                 C          2
    ELEM                           Elements to be reported
    SECT                           Sections to be reported


    DESI                           Defines design section properties
    PROF                           Section profiles for use in design
    ULCF                           Length of tubular members between stiffening rings,
                                   diaphragms etc

    CASE                           Loadcases to be reported
    COMB                           Define a combined loadcase for processing                                        3
                                                                                                         C
    CMBV                           Define a combined loadcase for processing
    SELE                           Select/redefine a combined/basic loadcase title
    RENU                           Renumber a basic loadcase


    PRIN                           Reports to be printed
    TEXT                           Text or comment command
    TITL                           Redefine global title

    END                            Terminates Command data block                                         C


Usage

C       Compulsory command, but see notes below where applicable.

Notes
1.    See Sections 3.4 and A.12.
2.    At least one GROUP or ELEM command must be included.
3.    At least one CASE, COMB or CMBV command must be included.


                                           Table 3.15 NORSOK HYDR Commands




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       Command                                              Description                                 Usage     Note
     NORS JOIN                 NORSOK joint check header command                                         C

     UNIT                      Units of length and force                                                 C          1
     YIEL                      Yield stress
     MCOF                      Partial Material Coefficient

     JOIN                      Joint numbers to be reported
     TYPE                      Joint type and brace element definition
     CHOR                      Chord elements at a joint and associated parameters                       C          2
     SECO                      Secondary members to be ignored in checks

     DESI                      Defines design section properties
     GAPD                      Define default gap dimension
     PROF                      Section profiles for use in design
     STUB                      Tubular member end stub dimensions

     CASE                      Basic loadcases
     COMB                      Define a combined loadcase for processing                                 C          3
     CMBV                      Define a combined loadcase for processing
     SELE                      Select/redefine a combined/basic loadcase title

     RENU                      Renumber a basic loadcase

     PRIN                      Reports to be printed
     TEXT                      Text or comment command
     TITLE                     Redefine global title

     END                       Terminates command data block                                             C


Usage
C.         Compulsory command, but see notes below where applicable.

Notes

1.         See Sections 3.4 and A.12.

2.         CHORd parameters are compulsory if load transfer across chord checks at cross joints are to be
           undertaken.

3.         At least one CASE, COMB or CMBV command must be included


                                           Table 3.16 NORSOK JOIN Commands




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     Command                                              Description                                   Usage    Note

     POST              BEAMST Post-processing Header command                                             C

     UNIT              Specify dimensional units                                                                  1

     GROU              Select groups of elements for processing
     ELEM              Select individual elements for processing                                                  2
                                                                                                         C
     SECT              Define sections at which results are required


     DESI              Defines design section properties                                                 C        3
     PROF              Section profiles for use in design

     CASE              Select a basic loadcase for processing
     COMB              Define a combined loadcase for processing                                         C        4
     CMBV              Define a combined loadcase for processing
     SELE              Specify a loadcase title
     SPEC              Select loadcases for a spectral analysis
     HARM              Loadcase originating from harmonic steady state response analysis
                       Renumber Loadcase
     RENU

     PRIN              Specify output reports required
     TEXT              Add text to output
     TITL              Redefine the run title

     END               Terminate BEAMST data                                                             C



Usage


C.         Compulsory command for POST processing, but see notes below where applicable.

Notes


1.         See Sections 3.4 and A.12.

2.         At least one GROUP or ELEM command must be included.
3.         Compulsory for non-tubulars unless Sections have been used for all elements to be processed in the
           preceding analyses.

4.         At least one CASE, COMB or CMBV command must be included.


                                                  Table 3.17 POST Commands




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3.3 Priority of Data Assignments
There are a number of commands that allow element and element ‘step’ data to be assigned in terms of element,
group or property numbers. These appear in the command syntax diagrams in the following format:




The priority of such assignments is defined below.

Element data        -    use element data assigned to individual elements (ELEM)
       if none      -    use element data assigned to the group the element belongs to (GROU)
       if none      -    use element data assigned to the property integer used by the element (PROP or MATE)
       if none      -    no element data assigned to element.

Step data           -    use step data assigned to individual elements (ELEM)
       if none      -    use step data assigned to the group the element belongs to (GROU)
       if none      -    use step data assigned to the property integer used by the element (PROP or MATE)
       if none      -    use element data assigned to individual elements (ELEM)
       if none      -    use element data assigned to the group the element belongs to (GROU)
       if none      -    use element data assigned to the property integer used by the element (PROP or MATE)
       if none      -    no step data assigned to element.

Element and step data assignment is not order dependant. This is demonstrated by the following example:

                                COMMand .... data1 ELEM 1
                                COMMand .... data2 GROU 5
                                COMMand .... data3 ELEM 2
                                COMMand .... data4 PROP 1

Assuming elements 1 and 2 are in group 5:

       Element 1 has data1 assigned

       Element 2 has data3 assigned

       All other elements in group 5 have data 2 assigned

       All elements with property integer 1, except elements 1 and 2 and elements in group 5, have data4
       assigned.




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It should be noted that when step data is explicitly being defined it overrides any element assignments even if the
step data is assigned to a group or property and the element data assigned to an individual element. Thus in the
following example:

                                 COMMand .... data1 STEP 2 GROU 5
                                 COMMand .... data2 STEP 2 PROP 1
                                 COMMand .... data3 ELEM 1
                                 COMMand .... data4 STEP 2 ELEM 2

Step 2 of element 1 has data1 assigned because the group assignment overrides the property assignment. In this
instance the step specific group assignment also overrides the element assignment which is not step specific.

       Step 2 of element 2 has data4 assigned.

       Step 2 of all other elements in group 5 have data1 assigned.

       Step 2 of all elements with property integer 1, except those in group 5, have data2 assigned.

       All steps, except step 2, of element 1 have data3 assigned.

       No data is assigned to any steps, other than step 2, for any elements other than element 1.




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3.4 BEAMST Commands

ABNO Command

The ABNORMAL command is used to specify which basic and/or combined loadcases are to utilise improved
resistance factors for structures subjected to abnormal loading conditions, typically those required for
progressive collapse analyses.




Parameters

ABNO               Keyword

load list          List of basic and/or combined user loadcase numbers (Integer)

Usage

Optional, applicable to API LRFD code check only.

Notes

1.        All user loadcase numbers must be explicitly defined, no shorthand syntax is permissible.

2.        For loadcases defined as abnormal, all resistance factors utilised will be set to unity. The resistance
          factors, and their values are given below.

     Factor                                                                        Default Value
     φc - resistance factor for axial compressive strength                         0.85
     φt - resistance factor for axial tensile strength                             0.95
     φh - resistance factor for hoop buckling strength                             0.80
     φv - resistance factor for beam shear strength                                0.95
     φb - resistance factor for bending strength                                   0.95
     φj - resistance factor for joint connection                                   0.95*
     φq - resistance factor for yield                                              0.95



*The connection resistance factor depends upon the joint type and load component being considered. The value
of 0.95 is used for all variants except axial tension for T, Y and X joints, where a value of 0.90 is utilsed.

Example

ABNO 2 4




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AISC Header Command

The AISC header command selects stress checks to the AISC design specifications (Ref. 1 and Ref. 23)




Parameters

WSD               : selects working stress design methods

LRFD              : selects limiting resistance and factored load design methods

edition           : selects the edition of AISC - valid keywords are:

                         ED2                        for LRFD
                         ED3


                         ED8                        for WSD
                         ED9


ALLO/MEMB            :        selects member design checks

Usage

Compulsory for all AISC checks. Must be the first command within the command data block.

Notes

1.      A list of all commands applicable to the AISC command data block is given in Tables 3.2 and 3.3.

2.      In the absence of any sub-commands, this command defaults to WSD ALLO.

3.      In the absence of the edition sub-command AISC ALLO will default to the 8th edition. AISC ED9
        ALLO is required to invoke the 9th edition




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API Header Command

The API command selects stress checks to the API design recommendations.




Parameters

WSD               : selects working stress design methods

LRFD              : selects limiting resistance and factored load design methods

edition           : selects the edition of API - valid keywords are:

                         ED1               for LRFD
                         ED13
                         ED16
                         ED17
                                          for WSD
                         ED18
                         ED19
                         ED20
                         ED21



ALLO/MEMB            :        selects member stress checks

HYDR              : selects the hydrostatic collapse check for tubulars

NOMI              : selects the joint nominal load check for tubulars (not valid with ED13) to WSD

PUNC              : selects the joint punching shear check for tubulars to WSD

JOIN              : selects joint check for tubulars to LRFD


Usage

Compulsory for all API stress checks. Must be the first command within the command data block



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Notes


1.      A list of all commands applicable to the API Command data block is given in Tables 3.2 -3.8.

2.      If the design method is omitted WSD is assumed.

3.      The edition of API must be specified using one of the valid keywords listed above.

4.      If the sub-command defining the check type is omitted (MEMB, ALLO etc) the check defaults to ALLO
        for WSD, and MEMB for LRFD.

5.      ALLO checks tubular members to API WSD recommendations and non-tubular members to AISC as
        referred to in the API recommendations. (See Section 5)

6.      MEMB, HYDR, JOIN, NOMI and PUNC check tubular members only to API recommendations.




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BRIG Command

The BRIG command selects whether rigorous buoyancy should or should not be used in the hydrostatic member
checks.


        BRIG                     (ON)
                                  OFF




Parameters




ON          : Keyword to select rigorous buoyancy for this command deck
OFF         : Keyword to de-select buoyancy for this command deck

Usage

Optional. If omitted all hydrostatic code checks will NOT consider the effects of rigorous buoyancy.

Notes

1.      If on the preceeding ASAS-WAVE analysis BRIG was present on the options data line then a BRIG
        command should be included in the BEAMST data.

2.      BRIG alone or BRIG ON has the same effect as BRIG being specified in the BEAMST options data.




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BS59 Command

The BS59 command selects ultimate limit state checks to BS5950 (Ref. 4)




Parameters

MEMB              : keyword to select member stress checks to BS5950.

Usage

Compulsory for all BS5950 checks. This must be the first command within the BS59 Command data block.

Note

1.      A list of all commands applicable to the BS59 Command data block is given in Table 3.9.

2.      In the absence of a sub-command, keyword defaults to MEMB




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CASE Command

The CASE command is used to specify which basic loadcases from the previous ASAS, ASAS(NL),
RESPONSE or LOCO analysis are to be reported.




Parameters

integer list      : list of basic loadcases to be reported (Integer)

Usage

Optional for all command data blocks. At least one CASE, COMB or CMBV command must be present in
each command data block.

Notes


Optional. At least one CASE, COMB or CMBV command must be present.

1.      All basic (CASE) loadcase numbers and all combined (COMB and CMBV) loadcase numbers selected
        for reporting must be unique.

2.      The load case numbers for an ASAS(NL) analysis are the increment numbers.

Examples

     CASE     1 3 5
     CASE     ALL




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CB Command

The CB command specifies a default value of the pure bending coefficient, Cb to be used for selected elements.




Parameters

value             : pure bending coefficient (Real)

ELEM              : keyword to denote element list follows

integer list      : list of user element numbers (Integer)


Usage

Optional - applicable to AISC/API ALLO Command data blocks only.

Note

If omitted the program will calculate a Cb value based on the acting force distribution on each element. See
Section 4.1.4.9.

Examples

            CB       1.0         ELEM       5       77 TO        100      742
            CB       2.0         ELEM       973




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CHOR Command

The CHOR command is used to define the chord member(s) at a node and optional chord parameters.




Parameters

node              : node number (Integer);

ELEM              : keyword to denote element list follows

member1
member2             : user element number(s) defining chord member(s) (Integer)

EFFE              : keyword to denote chord parameters follows

thick             : chord nominal thickness away from the joint (Real)

length            : chord effective length (Real)

LTOD              : keyword to denote length to diameter ratio follows

ratio             : maximum chord length between nodes to be used when forming a multi-noded joint; given as
                     ratio of length over diameter. (Real)

Usage

Optional for tubular joint punching shear and nominal load joint checks. The chord parameters are currently
ONLY used by the API LRFD nominal load joint check and the API WSD JOIN check.


Notes


1.      For single noded joints the node number is the same as the joint number, for multiple noded joints the
        chor command can be used for one or more nodes forming the joints .

2.      In the absence of any CHOR command(s) pertaining to a node, the chord will be identified as that
        member at the joint with the greatest diameter. If several members have the same diameter, BEAMST
        will check their wall thickness and choose the most appropriate member for API WSD JOIN checks. The
        member length will also be considered as nodes within the ratio specified, this defaults to 0.25 (D/4) and
        the chords. will be connected to form a multi-noded joint.




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3.     In the API LRFD nominal load joint check, cross joints should be checked for chord crushing if the chord
       is reinforced only by a can having increased thickness local to the joint. To undertake this check an
       effective chord length and nominal thickness must be provided using this command.

4.     In the API WSD JOIN check clause 4.3.5 for thickened cans will only be invoked if chord parameters are
       provided.

Examples

            CHORD        16        122
            CHORD        16        120        122
            CHORD        16        ELEM       122
            CHORD        16        EFFE       20.0         1500.0




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CMBV Command

The CMBV command is used to select a new combined loadcase to be reported and to specify the loadcase
numbers and factors to be combined into the new loadcase. It differs from the COMB command in that the
combination may be carried out in several different ways. Combinations which include other combinations are
permissible.



     CMBV             ctype            new case                 factor           case




Parameters

ctype         : describes the combination method (see note 2)

newcase : combined loadcase number (Integer)

factor        : multiplicative factor to be applied to case (Real)

case          : user loadcase number, either a basic loadcase or another combination loadcase number (Integer)

Usage


Optional for all command data blocks. At lease one CASE, COMB, or CMBV command must be present in
each command data block.

Notes


1.       All basic (CASE) loadcase numbers and all combined (COMB and CMBV) loadcase numbers selected
         for reporting must be unique.

2.       Five combination types are permitted using the CMBV command

                SSUM              simple summation
                                  The factored forces and moments for each of the constituent loadcases are simply
                                  added together.

                MAXE              maximum envelope
                                  The factored forces and moments for each of the constituent loadcases are
                                  considered in turn. The final results consist of the highest (positive) force values
                                  found in the constituent loadcases for each force type.

                MINE              minimum envelope
                                  The factored forces and moments for each of the constituent loadcases are




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                                  considered in turn. The final results consist of the lowest (negative) force values
                                  found in the constituent loadcases for each force type.

                ABSS              absolute sum
                                  The absolute values of the factored forces and moments for each of the constituent
                                  loadcases are added together. All resulting forces and moments will be positive.

                SRSS              square root sum square
                                  The factored forces and moments for each of the constituent loadcases are squared
                                  and then added together. The resulting forces are then square rooted. All resulting
                                  forces will be positive. This is useful for combining spectral loadcases.

3.     For combinations other than SSUM care must be exercised in the processing of these results because they
       do not necessarily represent a consistent set of fixed end forces and distributed loads.

4.     Loadcase combination is generally invalid in a non-linear analysis.

Examples


                CMBV          SSUM               10       1.5       14     2.0      101
                CMBV          ABSS               303      1.4        6     1.6          7




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CMY/CMZ Command

The CMY/CMZ command specifies the amplification reduction factors Cmy and Cmz to be used in the AISC/API
member combined stress buckle unity check.
            CMY
                                      v alue           ELEM             integer list
            CMZ



Parameters

value             : Cmy or Cmz value (Real)

ELEM              : keyword to denote element list follows

integer list      : list of user element numbers (Integer)

Usage

Optional - applicable to AISC/API ALLO Command data blocks only.

Note

If omitted the program will calculate Cmy and Cmz values appropriate to each element based on the acting force
distribution. See Section 4.1.4.10.


Examples

            CMY        0.85        ELEM       5     77     TO      742
            CMZ        0.40        ELEM       973




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COMB Command

The COMB command is used to select a new combined loadcase to be reported and to specify the loadcase
numbers and factors to be combined into the new loadcase. Combinations which include other combinations are
permissible.

         COMB             new case               factor          case




Parameters

newcase : user loadcase number (Integer)

factor        : multiplicative factor to be applied to case (Real)

case          : user loadcase number, either a basic loadcase or another combination loadcase number (Integer)

Usage

Optional for all command data blocks. At least one CASE, COMB, or CMBV command must be present in
each command data block.

Optional. At least one CASE, COMB or CMBV command must be present.

Notes

1.       All basic (CASE) loadcases and all combined (COMB and CMBV) loadcase numbers selected for
         reporting must be unique.

2.       Loadcase combination is generally invalid in a non-linear analysis.

Examples

             COMBINE          16        0.9        14       1.2         3050

             COMB           303         1.4             6     1.6        7




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DESI Command

The DESI command enables section information from the structural analysis to be overridden to account for
design requirements. The analyst should note that making large changes to section properties will cause
modifications to the element stiffness which will invalidate the results of the analysis. It is recommended that
upon obtaining a satisfactory section, a full re-analysis is performed. Geometric section properties will be
calculated for all section types (except PRI). A section name may be specified instead of providing explicit
section dimensions. The section name may be one already specified in the ASAS analysis, exist in an external
library file, or may be defined using a PROF command.




Parameters

type              : alphanumeric keyword specifying the section type for this list of elements, groups or geometric
                     properties. Section types currently available are:

                     TUB        -      Tube
                     WF         -      Doubly symmetric Rolled I-section (e.g. UB, UC, Joist,WFC, WF)
                     RHS        -      Rectangular Hollow Section (RHS)
                     BOX        -      Fabricated Box Section
                     PRI        -      Rectangular Solid Section
                     FBI        -      Fabricated I-section (NS3472 only)
                     CHAN -            Channel Section
                     ANGL -            Angle Section
                     TEE        -      Tee Section


sdims             : section dimensions (Real)

GYRA              : keyword to denote that radii of gyration follow

gvals             : radii of gyration. Up to two values may be specified for RY and RZ respectively. A third value,
                     RT, may be given for WF and FBI section types. Values not provided are automatically
                     computed by the program. (Real)

PROF              : keyword to denote that a section name follows




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section           : name of the section (up to 12 alphanumeric characters)

END1              : keyword to denote that the section properties are applied to the first step of the element

END2              : keyword to denote that the section properties are applied to the last step of the element

STEP              : keyword to denote that a step number follows

integer           : step number to which the section properties are referenced (Integer)

ELEM              : keyword to denote selection by element numbers

GROU              : keyword to denote selection by element group numbers

PROP              : keyword to denote selection by geometric property integer

integer list      : list of user element numbers, groups or geometric property numbers. If a step reference is
                     given only that step for elements specified within the element list, group list or geometric
                     property number list are assigned the section property values (Integer)

Usage

Optional for command data selecting TUBE elements or when sections have been specified in the ASAS
analysis, otherwise compulsory for all other available section types.

Notes

1.      A detailed description of each section type is given in Appendix -D.

2.      TUBE elements must not be assigned non-tubular sections.

3.      See Section 3.3 for the priority of assigning data.

4.      If sections have been specified in the ASAS analysis any values not defined will default to those available
        from the structural database. If sections were not utilised in the ASAS analysis, no defaults exist.

5.      The channel, angle tee and non-symmetric fbi and box sections are only available for stress calculations
        using the POST command set. No code checking is currently possible on these section types.

6.      If a section is referenced using PROF, the section definition will be searched for in the following order
                In a PROF command within the current data file
                In the ASAS structural database for this analysis
                In a specified external section library

7.      A prismatic section, PRI, must be defined using PROF.




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Examples

   DESI         FBI       1.4        O.9          O.O2         O.O15         PROP       427
   DESI         BOX 1.2   0.8    0.02                          0.02          ELEM       20 TO           26
   DESI         PROF  W12x8   STEP    2                                      ELEM       147262
   DESI         RHS       1.2        0.8          0.025        END1          ELEM       100 101 104
   DESI         WF        1.3        0.8          0.015        0.012         GYRA       0.18 0.55 0.21 GROU 20
   DESI         TUB       1.0        0.1          ELEM         500




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DS449 Header Command

The DS449 (or DS44) command requests ultimate limit state strength checks to the Danish Standards DS449
(Ref. 9) and DS412 (Ref. 10) for tubular members.
                                                                                     AO

                                                        HIGH                        A
      DS449                  MEMB                                                   B
                                                        NORM                         C
                              JOIN
                                                                                     D




Parameters

MEMB              : keyword to select member ultimate limits state checks

JOIN              : keyword to select joint ultimate limit state checks

HIGH              : keyword to specify the high safety class

NORM              : keyword to specify the normal safety class

AO
A
B                  : keywords to select the curve type from the DS412 column buckling curves
C
D


Usage

Compulsory for DS449 stress checks. Must be first command within the DS449 Command data block.

Notes

1.      A list of all commands applicable to the DS449 Command data block is given in Tables 3.10 and 3.11.

2.      If none of the parameters are specified the defaults are:

                         DS449 MEMB HIGH A


Examples

            DS449        MEMB NORM
            DS449        JOIN




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EFFE Command

The EFFE command is used to specify the effective length factors Ky and Kz used in calculating slenderness
ratios Kℓ/r for column buckling calculations about each axis.




value1
                  : Ky and Kz respectively (Real)
value2

ELEM              : keyword to denote element list follows

GROU              : keyword to denote selection by element group number

integer list      : list of user element numbers. (Integer)

Usage

Optional for all member checking command data blocks.


Notes

1.      If only value1 is specified, Ky and Kz are both set to it; otherwise Ky is set to value1 and Kz to value2.

2.      Elements for which the effective length factors are not specified have default value of 1.0.

3.      If Ky or Kz exceeds 1.0 then the member is deemed free to sway in the relevant plane.

Examples

            EFFE           O.8 ELEM 21 TO 35
            EFFE           O.8 1.O ELEM 1O8 1O9 112




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ELEM Command

The ELEM command specifies the elements to be reported.

Elements are referenced by their ASAS User Element Numbers. This command can be repeated as many times
as required. It is sometimes convenient to be able to specify a range of elements and subsequently exclude some
of that range - the NOT command word is provided for this purpose. When used in this way, the order of the
ELEM commands is important. The final setting for each element is the one used to produce the report. The
ELEM command may also be used in conjunction with the GROU command to select elements for reporting not
referenced by the GROU command and the NOT ELEM command to exclude any such referenced elements.
See Section 3.1.4 for a detailed description of the NOT command modifier.




Parameters

NOT               : keyword to denote that the specified elements are not to be processed

integer list      : list of user element numbers (Integer)

The NOT command word has a special effect if it is used on the first ELEM command: all the elements are
selected except for those specified in this command. On all subsequent ELEM commands it merely has the
effect of rejecting the specified elements.

Usage

Optional for POST Command data block and all member checking command data blocks. At least one ELEM
or GROU command must be present in such command data.

•Optional. At least one ELEM or GROU command must be present.

Examples

        ELEM ALL

        ELEM 6 to 1O
        ELEM 12 14 16 TO 2O

        ELEM 1 TO 1O
        NOT ELEM 4 6




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ELEV Command

The ELEV command is used to specify mean water and seabed levels, tide and surge heights and sea water
density for calculation of hydrostatic pressure.

       ELEV          v alue1           v alue2          v alue3            v alue4             v alue5




Parameters

value1            : Mean Water Level relative to the water axes (Real)

value2            : Sea Bed Level relative to the water axes (Real)

value3            : Density of Sea Water (Real)

value4            : Tide Height (Real)

value5            : Surge Height (Real)


Usage

Compulsory for all command data blocks examining hydrostatic pressure effects.

Note

The static water depth is taken to be the sum of Mean Water Depth, Tide and Surge Heights.

Examples

            ELEV 150.0              -5.0            1.025
            ELEV 450.0              10.0          63.0               9.0          4.0
            ELEV 454.0              10.0          63.0               9.0




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END Command

The END command is used to terminate a command data block.

           END




Parameters

None

Usage


Compulsory to terminate all command data blocks.

Note


The END command must be followed by the next command data block header or a STOP command to
terminate the BEAMST data.




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EXTR Command

The EXTR command is used to specify which basic and/or combined loadcases are allowed overstress for
extreme/storm conditions.




Parameters

integer list      : list of basic and/or combined user loadcase numbers (Integer)

Usage

Optional for all stress checking command data blocks.


Note

All user loadcase numbers must be explicitly defined, no shorthand syntax is permissible.

Examples

            EXTR 2 4
            EXTREME 1            5    7     10




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GAPD Command

The GAPD command is used to specify a default gap or eccentricity dimension. This value is used if none is
specified in the TYPE command. A negative value is not allowed.

     GAPD               value




Parameters

value             : gap dimension (Real)

Usage

Optional, for X or K joint punching shear and nominal load command data blocks only. The command is not
used for Y joints.


Note

If an entered value is less than the default of 50.8mm/2 inches a warning message is printed.

If the GAPD command is omitted then:


            For API 21st Edition: the geometry is used to calculate the gap; unless specified in the TYPE
            command


            For Pre-API 21st Edition: a default value of 50.8mm or 2 inches is used and this is only applied to K
            joints.




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GRAV Command

The GRAV command is used to define the relationship of structure to water surface axes by specifying the value
and direction of the gravitational acceleration relative to the structure axis system.

     GRAV              value1               value2                value3




Parameters

value1            : gravitational acceleration component in the global X axis of the structure (Real)

value2            : component in the global Y axis (Real)

value3            : component in the global Z axis (Real)

Usage

Compulsory for all command data blocks examining hydrostatic pressure effects.


Note

1.      The GRAV command defines the direction of the gravitational vector (-Zwater) with respect to the
        structure (global) axis system.

2.      If the components of gravitational acceleration are given as (0,0,-g) the structure and water axes are
        coincident with the Z-axis directed vertically upwards.

Examples

            GRAV               0.0          0.0          -9.81
            GRAVITY          7.246        -2.473           6.133




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GROU Command

The GROU command is used to select which ASAS groups are to be reported. This command can be repeated
as many times as required. It is sometimes convenient to be able to select elements by their group numbers and
to be able to extend or exclude discrete elements or ranges of elements from the report. The ELEM and NOT
ELEM commands may be used in conjunction with the GROU command for this purpose. For extension and
exclusion purposes, the order of the ELEM commands can be important (see ELEM Command).




Parameters

integer list :           list of ASAS group numbers (Integer)

Usage

Optional for POST command data block and all member checking command data blocks. At least one ELEM
or GROU command must be present in member command data blocks.

Examples

        GROU       1    3       6        10        TO    15
        NOT ELEM            8       10        16

        GROU ALL
        NOT ELEM            8       10        16

        GROU       1    3       6        10        TO    15
        ELEM       96       105          TO        123




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HYDR Command

The HYDR command is used to specify loadcase dependent hydrostatic pressure load factors used in the
computation of the design hydrostatic head in API LRFD hydrostatic checks.




Parameters

gammad          :        hydrostatic pressure load factor (Real)

CASE            :        keyword denoting loadcase numbers follow

integer list :           list of user selected basic and/or combined loadcases (Integer)

Usage

Only used for API LRFD HYDR checks. Optional (see Note 1 below).

Notes


1.      For loadcases not specified using this command a value of 1.3 will be assumed. This corresponds to the
        operating conditions.

2.      All user loadcase numbers must be explicitly defined, no shorthand syntax is permissible.

Example

        HYDR         1.1        CASE         5       6




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JOIN Command

The JOIN command is used to select the nodes to be included in joint checks. This command can be repeated as
many times as required. It is sometimes convenient to be able to specify a range of node numbers and
subsequently exclude some of that range - the NOT command word is provided for this purpose. In this way the
order of the JOIN commands can be important. The final setting for each node is the one used. See Section
3.1.4 for a fuller description of the NOT command.

              NOT                  JOIN                  nodes




Parameters

NOT               : keyword to denote that specified joints are not to be processed

nodes             : list of node numbers (Integer)

Usage

Compulsory for all joint command data blocks.

Note

The NOT command parameter has a special effect if it is used on the first JOIN command: all the joints are
selected except for those specified in this command. On all subsequent JOIN commands it merely has the effect
of rejecting the specified joints.

For a joint to be identified as multi-noded all nodes must be included in the joint check.

Examples

        JOIN ALL

        JOIN 6 TO 1O
        JOIN 12 14 16 TO 2O

        JOIN 1 TO 1O
        NOT JOIN 4 6




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LIMIT Command

The limiting values defined below are built into BEAMST, but for API WSD JOIN these may be overwritten at
the user’s discretion, using one or more LIMIT commands.

     LIMIT              limval            minval              maxval




Parameters

LIMIT             : compulsory keyword

limval            : keyword indicating parameter for which default applicability limit is to be overwritten.
                     (Alphanumeric.) Permitted values are:


                     BETA
                     GAMMA
                     THETA

minval            : lower applicability limit for parameter limval. (Real)

maxval            : upper applicability limit for parameter limval. (Real)

Notes


1.      Default applicability limits are as follows (using the standard parameter definitions).
         0.2 ≤ β ≤ 1.0
         10 ≤ γ ≤ 50
         30  ≤ θ ≤ 90 




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MCOF Command

This command is used to specify the global partial material coefficient utilised in the NPD, NORSOK and
DS449 code checks. The coefficient(s) may be loadcase dependent.




Parameters

value             : partial material coefficient (Real)

PARA              : optional keyword to denote that the value defined is to be assigned to a particular material
                    parameter given by the following keyword.

YIEL              : keyword to denote yield stress parameter

PUNC              : keyword to denote punching strength parameter. Only applicable to DS449

ELAS              : keyword to denote modulus of elasticity parameter. Only applicable to DS449

LOAD              : keyword to denote that loadcase numbers follow

case              : list of loadcase numbers to which the value of the material coefficient is to be assigned. ALL
                    is not permitted. (Integer)

Usage

Optional - applicable to NPD, NORSOK and DS449 Command data blocks only

Notes

1.      If PARA and its associated keywords are omitted, then PARA YIEL is assumed.

2.      Explicit definition of a parameter coefficient (using the PARA keyword) will override any definition
        without a parametric statement.

3.      For loadcases not defined using a MCOF command the following defaults will be utilised. The DS449
        values reflect the strict material control definition in that code.

4.      For NORSOK the default material partial safety factor is 1.15 for tension and joint strength. It varies for
        compression (including hydro-static checks).

        If a value of 1.15 is input here the default calculations will be assumed for hydrostatic and compression
        cases. Values other than 1.15 + 0.001 will use the input value for all checks




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                                                                                                        DS449 Safety Class
                       Parameter                      Keyword              NPD           NORSOK
                                                                                                        Normal       High
          Material Coefficient              γm            YIEL                1.15           1.15          -           -
          Yield Stress                      γy            YIEL                 -               -          1.09        1.21
          Punching Strength                 γp            PUNC                 -               -          1.21        1.34
          Modulus of Elasticity             γE            ELAS                 -               -          1.34        1.48



Example

            MCOF         1.5        PARA          PUNC         LOAD       2
            MCOF         1.38       LOAD          1 8 9




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MFAC Command

The MFAC command is used to define the moment reduction factors to be used in the BS5950 overall buckling
check.




Parameters

facy              : moment reduction factor for My (Real)

facz              : moment reduction factor for Mz (Real)

LOAD              : keyword to denote that loadcase number follows

lcn               : loadcase number (Integer)

ELEM              : keyword to denote that element list follows

integer list      : is a list of user element numbers (Integer)

Usage

Optional for BS59 Command data block only.

Notes

1.       For elements with no MFAC data line facy and facz will be taken as 1.0.

2.       If facz is omitted from the MFAC data line facz will be taken as equal to facy.

3.       If LOAD and lcn are omitted from the MFAC data line then the specified facy and facz values will be
         assumed to apply to all loadcases.

Examples

            MFAC         0.7        0.5         LOAD         1       ELEM         6      8
            MFAC         0.6        ELEM            1        2




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MLTF Command

The MLTF command is used to define the moment reduction factor to be applied to the lateral torsional buckling
component in the BS5950 overall buckling check.




Parameters

value             : lateral torsional buckling moment reduction factor (Real)

LOAD              : keyword to denote that loadcase number follows

lcn               : the loadcase number (Integer)

ELEM              : keyword to denote that element list follows

integer list      : list of user element numbers (Integer)

Usage

Optional for BS59 Command data block.

Notes

1.      For elements with no MLTF data lines, value will be taken as 1.0

2.      If LOAD and lcn are omitted from the MLTF data line then the specified value of value will be assumed
        to apply to all loadcases

Examples

            MLTF         0.6        ELEM          ALL
            MLTF         0.8        LOAD          1        ELEM         10




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MOVE Command

The MOVE command is used to specify the origin of the Water Axes relative to the structure Global Axes
origin.

    MOVE                value1            value2              value3




Parameters

value1            : X-coordinate of the Water Axes origin in the Global Axes (Real)

value2            : Y-coordinate of the Water Axes origin in the Global Axes (Real)

value3            : Z-coordinate of the Water Axes origin in the Global Axes (Real)

Usage

Optional for all command data blocks examining hydrostatic pressure effects.

Note

If omitted the origins of the Water and the Global Axes origin are assumed coincident.

Examples

            MOVE           5.0          20.0           15.0
            MOVE       -24.0          -10.0            14.6




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NORS Command

The NORS command selects the NORSOK check (Ref. 24).




Parameters

editcm                   : selects the edition of the NORSOK code to be used in the checks. Valid keyword is
                             ED98 (1998 Edition)

MEMB                     : selects member capacity checks

HYDR                     : selects hydro-static collapse checks for tubulars

JOIN                     : selects joint checks for tubulars




Usage

Compulsory for all NORSOK code checks. Must be the first command within the command data block.

Note

A list of all commands applicable to the NORS command data block appears in tables 3.12 - 3.14.




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NPD Command

The NPD command selects ultimate limit state compliance checks to NPD/NS3472 regulations (Ref. 5, Ref. 6
and Ref. 7)




Parameters

MEMB              : keyword to select member yield and buckling checks

JOIN              : keyword to select joint punching shear checks

ED92              : keyword to select NPD code Edition 1992

Usage

Compulsory for all NPD limit state checks. This must be the first command within the NPD Command data
block.

Notes

1.       A list of all commands applicable to the NPD Command data block is given in Tables 3.15 and 3.16.

2.       If no sub-command is present, MEMB is assumed.

3.       If ED92 not selected then Edition 1985 is assumed.

Example

            NPD MEMB ED92




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PHI Command

This command is used to specify the load dependent parameter, φ, used in the determination of the lateral
buckling strength of beams for NS3472E.




value              : is the explicitly defined parameter (Real)

AUTO               : requests that automatic calculation of PHI is carried out using the formula
                                                              2
                                               
                          φ = 1.7 - M 2 + 0.3  M 2  ≤ 2.3
                                    M1         M1 
                     where M1 and M2 are the moments at the ends of the beam about the strong axis
                     and M1 ≥ M2

LOAD               : keyword to denote that loadcase number follows

case               : loadcase number to which the value of φ is to be assigned (Integer)

ELEM               : keyword to denote that element list follows

integer list       : list of user element numbers (Integer)

Usage

Optional - applicable to NPD Command data blocks only

Notes

1.      If the loadcase number is not defined all loadcases will be assigned the value of φ for the elements
        specified.

2.      Explicit definition of φ on a loadcase basis will override any definition without a loadcase number for a
        given element. Automatic calculation of φ will be overridden by an explicit definition for a given
        element.

3.      If AUTO is chosen for loadcase specific data, this will override any specific value of φ defined for an
        element without the loadcase provided.

4.      In the absence of a PHI definition for an element a default value of 1.0 will be utilised.

Examples




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            PHI          2.0          LOAD           2         ELEM           1     5    6
            PHI          AUTO         ELEM           ALL
            PHI          1.5          ELEM           5 TO 10




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POST Command

The POST header command is used to request property, force and stress reports but without checks to a specific
design code of practice.

     POST




Usage

Compulsory for all general post-processing. Must be the first command within the POST Command data block.

Notes

1.      A list of all commands applicable to the POST command data block is given in Table 3.17.

2.      There are no sub-commands




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PRIN Command

The PRIN command specifies the reports to be printed (see Section 2.8).




Parameters

type              : keyword indicating type of report required or units to be used.
                     See table below for available keywords.

params            : additional parameters applicable to each type

   Type                                          Meaning                                                Additional Parameters

  XCHK          Input Data Cross Check Report                                                                   None

  PROP          Member Geometry and Material Property Report                                                    None

  FORC          Member Force Report                                                                             None

  STRE          Member Stress Report                                                                            None

  UNCK          Unity Check Report                                                                              None

  SUM1          Unity Check Summary Reports:                                                      ex1, ex2 specify exceedence
  SUM2          Highest yield and buckle combined stress unity checks                                      values (report
                                                                                                           SUM4 only)
                Highest buckle check plus all unity checks at section with
  SUM3          highest yield combined stress unity check                                         FAIL        report failed
                                                                                                              members only
  SUM4          Highest unity check
                                                                                                  BOTH        print both full
  SUM5          3 worst unity checks plus distribution of unity check values                                  summary and failed
                Highest member forces and moments                                                             member reports
                                                                                                  uclim       utilisation limit for
                                                                                                              failure reports

  FUNI          Change force units in reports                                                     name1      length unit
                                                                                                  name2      force unit

  SUNI          Change stress units in reports                                                    name1      length unit
                                                                                                  name2      force unit

  ALL           Print all appropriate reports                                                                   None




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                                          Table 3.18 PRINT Command Parameters

Usage


Optional - for defaults see note 8

Notes


1.      Full descriptions of each report is given in Section 2.8

2.      A list of the reports applicable to each type of command data block is given in Table 2.1 .

3.      BEAMST automatically filters out requested reports which are not available for the type of check/post-
        processing selected. Such redundant requests do not induce data or execution errors.

4.      Exceedence values are only appropriate for summary report number 4 (SUM4) and if omitted default to
        1.0 and 0.5.

5.      Utilisation limits are available for summary reports 1-4. For summary report number 4 (SUM4), the
        exceedence values MUST precede BOTH/FAIL.

6.      If units are specified both length and force units must be supplied. The valid unit names are listed under
        the UNIT command. These units override any results units defined in the Preliminary data (Appendix -
        A).

7.      FUNI is only valid for NPD Unity Check Reports.

8.      If this command is omitted the following defaults apply:

                PRIN SUM1              AISC WSD ALLO command
                                       AISC LRFD MEMB command
                                       API WSD ALLO command
                                       API LRFD MEMB command
                                       API WSD HYDR command
                                       API LRFD HYDR command
                                       NORS MEMB command
                                       NORS HYDR command

                PRIN SUM3              API WSD PUNC command
                                       API WSD NOMI command
                                       API LRFD JOIN command
                                       NPD JOIN command
                                       NORS JOIN command

                no default             DS449 command
                                       POST command
                                       NPD MEMB command
                                       BS59 command




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Example
PRIN XCHK PROP STRE SUNI MILLIMETRE KNEWTON
PRIN SUM3 SUM4 1.33 0.5 FAIL SUNI MM KN
PRIN SUM3 BOTH 0.95 SUM4 1.33 0.5 FAIL 0.85 SUNI MM KN




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PROF Command

The PROF command enables a section profile to be defined in terms of type, dimensions and properties for use
with the DESI command.




Parameters

section           : name of the section (up to 12 alphanumeric characters)

type              : alphanumeric keyword specifying the section type. Section types currently available are:

                     TUB        -      Tube
                     WF         -      Doubly symmetric Rolled I-section (e.g. UB, UC, Joist,WFC, WF)
                     RHS        -      Rectangular Hollow Section (RHS)
                     BOX        -      Fabricated Box Section
                     PRI        -      Rectangular Solid Section
                     FBI        -      Fabricated I-section (NS3472 only)
                     CHAN -            Channel Section
                     ANGL -            Angle Section
                     TEE        -      Tee Section


XSEC              : keyword to denote that section dimensions follow

dimensions : section dimensions. See Appendix -D for the details of which dimensions are required for each
                     section type. (Real)

FLEX              : keyword to denote that section properties follow

flexprops         : section geometric properties. (Real)
                     For all section types this is AX, IZ, IY, J, AY, AZ where
                     AX       cross sectional area
                     IZ       principal moment of inertia about element local Z axis
                     IY       principal moment of inertia about element local Y axis




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                     J        torsion constant
                     AY       effective shear area for forces in element local Y direction
                     AZ       effective shear area for forces in element local Z direction

proptype          : name of the geometric property to be defined. Valid names are AX, IZ, IY, J, AY, AZ with the
                     meaning as above.

prop              : value to be assigned to the named geometric property.

GYRA              : keyword to denote that radii of gyrations follow.

radg              : radii of gyration. Up to two values may be specified for RY and RZ respectively. A third value,
                     RT, may be given for WF and FBI section types.

radtype           : name of radius of gyration to be defined.

radius            : value to be assigned to the specified radius of gyration.

Usage


Optional for all command data blocks.

Notes


1.      For a given section identifier the XSEC information must be provided. FLEX and/or GYRA values may
        also be supplied with the following interpretations.

        If only XSEC is defined, the geometric flexural properties and radii of gyration will be automatically
        calculated by the program from the section dimensions.


        If both XSEC and FLEX commands are utilised, any geometric properties explicitly defined will
        overwrite those calculated from the section dimensions. This feature should be used with care since many
        codes of practice compute effective section properties, which may be incompatible with those provided
        explicitly.

        If both XSEC and GYRA commands are utilised, any radii explicitly defined will overwrite those
        calculated from the flexural properties.

        The FLEX and GYRA commands may not be defined without an associated XSEC command.

2.      If FLEX and/or GYRA data is required, this must be provided on separate PROF command lines.

Examples


     PROFILE RHS22x16 RHS XSEC 22.5 16.8 0.2 0.8

            PROFILE RHS22x16 FLEX 15.32 1164.5 749.81 1443.6

            PROFILE BOX19x11 BOX XSEC 19.2 11.6 0.4 0.2




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            PROFILE RHS22x16 GYRA




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QUAK Command

The QUAK command is used to specify which basic and/or combined loadcases are allowed earthquake
permitted overstress for earthquake/seismic conditions.




Parameters

integer list      : list of basic and/or combined user loadcase numbers (Integer)

Usage

Optional for member allowable stress, hydrostatic collapse and tubular joint punching shear command data
blocks.

Note

All user loadcase numbers must be explicitly defined, no shorthand syntax is permissible.

Examples

            QUAK 2           4
            QUAK l           19       40          67       72




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RENU Command

The RENU command is used to alter the loadcase numbers of basic loadcases presented to BEAMST on files
saved from a previous ASAS, RESPONSE or LOCO analysis.




Parameters

oldcase           : basic loadcase number existing on the files saved for BEAMST by a previous analysis.
                     (Integer)

INTO              : keyword

newcase           : new loadcase number to be assigned to the oldcase. (Integer)

Usage

Optional - may be used in any command data block.

Note

The user is strongly advised if using the RENU command to position it within the command data block
immediately following the Header Command. Any command following it which refers to basic loadcases must
refer to newcase(s).

Examples

            RENU             17     INTO        77
            RENUMBER                84      INTO       23
            RENU             72     INTO        1071




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SAFE Command

The SAFE command is used to specify loadcase dependent safety factors for hydrostatic collapse checks and
their associated basic and/or combined user loadcase numbers.




Parameters

value1             : safety factor for axial compressive loading (Real)

value2             : safety factor for axial tensile loading (Real)

value3             : safety factor for hoop compressive loading (Real)

CASE               : keyword denoting loadcase numbers follow

integer list       : list of user selected basic and/or combined loadcases (Integer)

Usage

Optional for hydrostatic collapse data blocks.

Notes

1.      All values not defined default according to loadcase type (as defined by EXTR or QUAK commands) as
        follows:

               loadcase type                         value1                            value2           value3

          not defined                                 2.00                                1.67           2.00

          EXTR                                         1.5                                1.25           1.5

          QUAK                                        1.20                                1.00           1.20



2.      The value for axial compressive loading is checked against the AISC safety factor for column buckling
        under axial compression and the greater of the two is taken.

3.      All user loadcase numbers must be explicitly defined, no shorthand syntax is permissible.

Examples

            SAFE           1.67         CASE         16
            SAFE           1.30         1.25         CASE          1      6       10
            SAFE           1.30         0.90         1.430         CASE         99         102
            SAFE           1.30         0.90         1.30              CASE          99          102



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SEAR Command

The SEAR command is used to request a search for the maximum value of force, stress or unity check at a series
of sections along a beam, in addition to those explicitly requested on the SECT command.




Parameters

values            : beam search section position (Real)

ELEM              : keyword to denote selection by element number

GROUP             : keyword to denote selection by element group number

integer list      : list of user element numbers or group numbers (Integer)

Usage

Optional - applicable to all member checking and post-processing command data.

Notes

1.      Beam section search positions are defined in the range 0.0 to 1.0 where 0.0 and 1.0 refer to beam ends 1
        and 2 respectively.

2.      Element definition of section information overrides group number definition. See Section 3.3.

3.      If no values are supplied, a default set of up to five positions will be used for each beam. For unstepped
        beams, search positions of 0.25, 0.5 and 0.75 will be used. For stepped beams, search positions of
        0.1667, 0.3333, 0.5, 0.6667 and 0.8333 will be used.

4.      The forces and stresses used in the calculation of the coefficients Cb, Cmy and Cmz and the combined
        buckle unity check are obtained by taking the maximum values from all of the sections checked i.e. the
        beam ends, step positions for stepped beams and any sections defined by way of SEAR and/or SECT
        commands.

5.      Results are only reported for sections defined by the SEAR command if they give maximum forces,
        moments, stresses or unity check values.

Examples

        SEAR         0.25       0.50       0.75        ELEM       17     84 TO 214

        SEARCH                 0.50       ELEM        ALL




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       SEAR          0.1      0.9       GROU       0     2    6

       SEARCH             ELEM 1 TO 55

       SEARCH




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SECO Command

The SECO command is used to specify that certain elements defined by their element, group or geometric
property numbers are to be classed as secondary members for checking against allowable stresses or to be
excluded from joint punching shear checks.




Parameters

ELEM              : keyword to denote selection by element number

GROU              : keyword to denote selection by element group number

PROP              : keyword to denote selection by geometric property number

integer list      : list of user element numbers, groups or geometric property numbers (Integer)

Usage

Optional for member allowable stress check and joint punching shear checking command data blocks.

Example

            SECONDARY ELEMENTS                      10        15      21
            SECO GROUPS                 16 TO        24
            SECO PROPERTIES                   14         17        19 TO 2
            SECO ELEM              20 TO 44
            SECO GROUP             19 26
            SECO PROP              16       14 TO 19




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SECT Command

The SECT command is used to specify the intermediate beam section positions which are to be reported for the
selected elements or groups.




Parameters

value             : beam section position (Real)

ELEM              : keyword to denote selection by element number

GROUP             : keyword to denote selection by element group number

integer list      : list of user element numbers or group numbers (Integer)

Usage

Optional - applicable to all member checking and post-processing command data.

Notes

1.      Beam section positions are defined in the range 0.0 to 1.0 where 0.0 and 1.0 refer to beam ends 1 and 2
        respectively.

2.      Element definition of section information overrides group number definition. See Section 3.3.

3.      Beam end positions (plus step positions for stepped beams) by default are reported in addition to any
        beam section positions specified on SECT commands.

4.      For a stand-alone BEAMST run, all sections defined by the FORC command together with any sections
        defined on the SECT commands are reported. However, those sections which are not given
        force/moment values on a FORC command will report zero values, except for the Free Moments.

Examples

        SECT         0.25       0.50       0.75        ELEM       17     84 TO 214

        SECTION                0.50       ELEM         ALL

        SECT         0.1      0.9       GROU       0     2    6




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SELE Command

The SELE command is used to define a combined loadcase title. It may also be used to redefine basic loadcase
titles presented to BEAMST on files saved from a previous ASAS, RESPONSE or LOCO analysis.

        SELE               case                   title




Parameters

case           : combined or basic loadcase number (Integer)

title          : new loadcase title, up to 40 characters

Usage

Optional and may be used in any command data block.

Notes


1.       A blank space must exist between case and title

2.       Continuation lines are not permitted

3.       If omitted, the basic loadcase titles remain as from the previous analysis and the combined loadcase titles
         are blank.

Examples

         SELE        17       COMBINED LOADCASE TITLE EXAMPLE

         SELECT 82            REDEFINED BASIC LOADCASE TITLE




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SIMP Command

The SIMP command is used to select elements for which the simplified code check methods described in
BS5950 are to be used. These simplified methods are applicable to plastic and compact members for the axial
plus moment and the overall buckling unity checks. Details of the simplified methods are given in Section 6




Parameters

ELEM              : keyword to denote element list follows

integer list      : list of user element numbers (Integer)

Usage

Optional for BS59 Command data block.

Note

By default the more rigorous checks will be carried out for all elements.

Examples

            SIMP ELEM ALL
            SIMP ELEM 20 TO 60
            SIMP ELEM 10 15 20




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SPEC Command

The SPEC command is used to specify which basic loadcases selected for reporting on CASE commands and
which basic loadcases referred to on COMB or CMBV commands originate from response spectrum analysis
and are to be subject to ‘automatic signed expansion procedures’ when stress checking to a design code.




Parameters

integer list      : list of response spectrum basic loadcases in the data, or ALL for all loadcases (Integer)

Usage

Optional - this command is only applicable for the following code checks

            AISC WSD ALLO
            API WSD ALLO
            API LRFD MEMB
            API WSD NOMI
            API WSD PUNC
            API LRFD JOIN


Notes

1.      This command is only required if ‘automatic signed expansion’ of response spectrum loadcases is
        required, otherwise they may be treated as linear static with the omission of this command.

2.      If omitted all basic loadcase are assumed to be linear static.

Examples

            SPEC         1     7    19          206
            SPEC         ALL
            SPEC         1 7        28 TO 99




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STUB Command

The STUB command is used to specify end stub diameter and wall thickness at both or either end of TUBE
elements, or other beam elements defined as having tubular cross-section.




Parameters

                         END1, END2:optional keywords

                         value1, value3:end stub outside diameter of END1 and END2 respectively (Real)

                         value2, value4:end stub wall thickness at END1 and END2 respectively (Real)

                         ELEM:keyword to denote selection by element number

                         GROU:keyword to denote selection by element group number

                         PROP:keyword to denote selection by geometric property number

                         integer list:list of user element numbers, group numbers or geometric property numbers
                         (Integer)


Usage

Optional for tubular joint punching shear command data blocks

Notes

1.      Element definition of stub diameter and wall thickness overrides group definition, which in turn overrides
        geometric property number definitions. See Section 3.3.

2.      All tubular end diameters and wall thicknesses not redefined using the STUB command will default to
        those of ASAS analysis unless redefined via the DESI command.

3.      Stub data overrides data defined using the DESI command.

Examples

            STUB         0.702          0.052          ELEM 1 TO 16                 24       99
            STUB         END1         0.702          0.052           ELEM ALL
            STUB         END2         0.762          0.064           GROUP  77             92




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            STUB         0.072         0.052          0.762           0.064   PROP               64 72
            STUB         END1         0.072          0.052           END2   0.762                0.064 GROU 1 TO 9




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TITLE Command

The TITLE command is used to specify/redefine the global title (defined initially via the TITLE command in the
Preliminary Data data, see Appendix -A) which is printed at the top of each page of the BEAMST output.




Parameters

title         : new page title, up to 60 characters

Usage

Optional.

Notes

1.      If omitted, the global title defaults to that defined on the TITLE command in the BEAMST preliminary
        data.

2.      A blank space must exist between TITLE and title.

3.      The global title once redefined using the TITLE command remains as such until another TITLE
        command is processed from the BEAMST command data block.

4.      Any number of TITLE commands may be used.

Examples

            TITLE            Example Title Command - (CASE NO. 1 * 1.20)




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TYPE Command

The joint TYPE command is used to specify joint type and joint brace member.




Parameters

node              : node number to which the brace connects to form the joint.

per               : percentage denoting that portion of the brace punching load that is carried by a joint of
                     classification type1, the remainder being carried by type2. (Integer)

type1, type2 : joint type classifications, as follows:

                     K        K joints

                     T
                     Y
                     TY            T & Y joints
                     YT

                     X         X joints                      Cross joints
                     DT        Double-T joints

brace             : user element number of the brace (Integer)

brace2            : user element number of the second brace of a K joint or X joint (Integer).

                     This value is only valid for the following code checks

                    DS449              :        used to calculate mean brace diameter for gap/diameter ratios in
                                                K joint assessments.

                     NORSOK                     :       used to identiify balancing member for K joint assessments

                     API WSD JOIN               :       used to identify 2nd member for geometry based K and X joint
                                                                 gap calculations.

value             : gap dimension for K joints or offset for X joints (Real)

CASE              : keyword to denote that loadcase numbers follow

integer list      : list of basic and/or combined user loadcase numbers (Integer)




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ALL                : keyword to denote all loadcases

DEFL               : keyword denoting that the defaults type classifications follow

dtype1             : default joint (chord/brace pair) type for non “perpendicular” brace members (smaller included
                     angle between brace and chord is less than or equal to 80 degrees).

dtype2             : default joint type for “perpendicular” brace members (smaller included angle between brace
                     and chord is greater than 80 degrees). This value is optional, defaults to T.

Usage

Optional for K or T & Y joint punching shear and brace end fatigue command data blocks. Compulsory for
models containing cross joints that are to be processed in the current run, except for those being assessed using
the API WSD JOIN check. For the API WSD JOIN check a load dependant classification will be carried out. In
this case the axial load will determine the proportion of joint type for each brace member for each loadcase. In
this instance note 1 below does not apply and default values using TYPE DEFL are not applicable.

Notes

1.      In the absence of any TYPE command(s) at a joint, joints will automatically be classified as K or T & Y,
        depending upon each brace-chord pair geometry.

2.      If per is omitted, the joint is classified as 100% joint type1. If per is less than 100, type2 must be
        present.

3.      All joint types not specified with the TYPE command default to those in the TYPE DEFL command. If
        a TYPE DEFL command is not present joints are automatically classified. See the appropriate Sections
        for joint checks in the relevant codes of practice.

4.      If the gap dimension is omitted the default value specified by the GAPD command is assumed. If the
        GAPD command does not appear, or in the case of API WSD JOIN a second brace is not defined, a gap
        of 2 inches is used.

5.      All user loadcase numbers must be explicitly defined if the CASE keyword is employed. If not the
        shorthand syntax ALL is permissible.

6.      For X and K joints, separate type commands are required to fully define opposing braces.

Example

            TYPE 16            90             K   TY            14     CASE        1        10
            TYPE 20            K 46 ALL
            TYPE 240           60  K  X                    17        CASE      1        4        10     12   19
            TYPE 68            40 DT Y                92      ALL
            TYPE 79            75   YT            K         107   CASE             93
            TYPE 81   70                  K       X             15     100.0            ALL
            TYPE DEFL Y               T




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ULCF Command

The ULCF command is used to specify the unbraced length of the compression flange used in calculations for
lateral buckling due to bending in allowable stress command data blocks or the unstiffened length of cylinder
between stiffening rings, diaphragms or end connections in hydrostatic collapse command data blocks.




Parameters

FACT               : keyword to denote that unbraced length is to be specified as factor of element length

factor             : factor of element length (Real)

LENG               : keyword to denote that unbraced length is to be specified explicitly

length             : unbraced length (Real)

ELEM               : keyword to denote that element numbers follow

GROU               : keyword to denote that group numbers follow

integer list       : list of user element numbers or element group numbers (Integer)

Usage

Optional for all stress checks to design code command data blocks.

Notes

1.       If neither FACT nor LENG is specified, then LENG is assumed by default.

2.       A length of zero (0.0) can be provided to indicate that lateral and torsional buckling are to be restrained
         for I beams when carrying out allowable stress checks to NS3472E.

3.       If the ULCF command is omitted, the unbraced/unstiffened length is assumed equal to the element
         length.

4.       For column buckling checks an UNBR command is also required.

Examples

            ULCF 22.O            ELEM       10 TO 20
            ULCF FACT              0.7        GROUP          10       12 TO 19 49




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UNBR Command

                                                      ℓ
The UNBR command is used to specify the unbraced lengths                          y   and ℓ z used in calculating slenderness ratios
Kℓ/r for column buckling calculations about each axis. With this command either unbraced lengths can be
specified or factors by which the actual element length must be multiplied.




FACT              : keyword to denote that unbraced length is to be specified as factor of element length

factor1,          : factors of element length (Real)
                     factor2

LENG              : keyword to denote that unbraced length is to be specified explicitly

length1,          : unbraced lengths (Real)
                    length2

ELEM              : keyword to denote that element numbers follow

GROU              : keyword to denote that group numbers follow

integer list      : list of user element numbers or element group numbers (Integer)

Usage

Optional for AISC, API, BS59, DS449 and NORS member checking command data blocks.

Notes

1.      If neither LENG nor FACT is specified, then LENG is assumed by default.

2.      If only one value is specified, ℓ y and ℓz are both set to it; otherwise ℓy is set to value1 and ℓz to value2.

3.      If the UNBR command is omitted unbraced lengths are assumed equal to member lengths.

4.      For local buckling and hydrostatic checks an ULCF command is also required.

Examples

            UNBR 22.O            15.O       ELEM       1O1       1O6      112
            UNBR FACT            O.9      1.O       ELEM       1O TO 15
            UNBR LENG            33.O       ELEM       59




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UNIT Command

It is possible to specify units for the input data which are different to those employed for the analysis. This can
be achieved by specifying one or more UNITS commands within the main body of the BEAMST data thus
permitting a combination of unit systems within one data file.

       UNIT            name1                (name2)




Parameters

name1, name2 : names of a unit of force and/or unit of length. They may be input in either order.
                         See Appendix A.12 for valid unit names.

Usage

Optional.
Note


The UNIT command is optional and may be used repeatedly to change one or both units for the BEAMST input
data. The default is the units used in the previous analysis.

Examples

        (i)     UNITS         N M

        (ii)    UNITS         INCHES KIPS




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WAVE Command

The WAVE command is used to specify Wave Height and Period for the calculation of wave induced
hydrostatic pressure head.

     WAVE              value1              value2




value1            : wave Height (Real)

value2            : wave Period in seconds (Real)

Usage

Optional for hydrostatic collapse checks.

Notes

1.      If omitted, the still water level is used for hydrostatic check (see ELEV command).

2.      The unit of Wave Height must be identical with that specified on the current UNIT command.

Example

            WAVE 5.0             10.0




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YIEL Command

The YIEL command is used to specify the yield stress to be used for each element, group or material property in
the requested report. This yield stress may be referenced to a particular step number within the elements defined
by the element, group or material property lists.




Parameters

value             : the yield stress (Real)

STEP              : keyword to denote that step number follows

stepno            : step number to which the yield stress is referenced (Integer)

ELEM              : keyword to denote that element numbers follow

GROU              : keyword to denote that group numbers follow

MATE              : keyword to denote that material numbers follow

integer list      : list of user element, group or material property numbers to be assigned this yield stress
                    (Integer)

Usage

Compulsory for all stress checks to design code command data blocks.

Notes

1.      The yield stress must be entered in the same units as defined by the current UNIT command.

2.      If a step reference is given only that step for elements specified within the element list, group number list
        or material property number list is assigned this yield stress.

Examples

            YIELD        2.OE8        ELEM        ALL
            YIEL 20000.0              ELEM        75       TO    80
            YIEL 4.137E5 STEP 3 ELEM 1 6 16 TO 94                                              197
            YIELD 3.447E5 STEP 20   GROUP ALL
            YIELD        20000.0          MATE         5    8




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4.     AISC Code Checks

The AISC command data block is used to request checking of members to the AISC WSD standard (Ref. 1) and
AISC LRFD (Ref. 23). Currently tubular, I-shaped and hollow rectangular section types are supported.

Note, all the equations and formulae in this chapter assume units of Kips and Inches.




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4.1 AISC Working Stress Design Allowable Check (AISC WSD ALLO)


4.1.1       Overview

The AISC WSD ALLO command set is used to request that extreme fibre allowable stresses be calculated and
unity checks be performed according to the AISC design specification (Ref. 1).

The AISC WSD specification is written in terms of member yield strengths, so a YIELd command must be used
to specify the yield strength. The units of the yield strength must be those of the UNIT command (Section 3.4).

Members may be selected for processing by elements and/or groups. The member section types must be
specified (if not specified in the structural analysis) using DESI commands. Further commands are available for
defining structural characteristics of the members (EFFE, UNBR and ULCF) and for specifying members that
are classified as ‘secondary’ (SECO).

Loadcases from the preceding structural analysis may be selected for processing using the CASE command
and/or new loadcases formed from combinations of existing loadcases using the COMB and CMBV commands.
The AISC permitted one third increase in allowable stresses for wind or seismic loading may be requested on a
loadcase basis using the EXTR command.

The SECT command may be used to define intermediate points along a member at which member forces are to
be evaluated, checked and reported. These are in addition to results automatically printed at the member end
points and positions of any step change in cross-section properties. For the code checks it is necessary to ensure
the maximum acting bending moment and stresses are evaluated. Since this may not occur at one of the
‘selected’ locations, BEAMST has a SEARch command which causes the moments and stresses to be evaluated
at every L/4 and L/6 (L = beam length) for prismatic and stepped beams respectively. These extra locations are
in addition to those selected and the results at these locations are only presented if they give the maximum
moments or stresses.

The selection of output reports is made using the PRIN command with the appropriate parameters for the
required reports. The PRIN command is also used to request the various summary reports available and to set
exceedence values for the unity checks. Four summary reports are available.

Summary report 1 is requested with the PRIN SUM1 command and gives the highest local buckling, global
buckling and yield unity check values for each element.

Summary report 2 is requested with the PRIN SUM2 command and gives the highest buckle check and all unity
checks at the section with the highest yield combined stress unity check for each element.

Summary report 3 is requested with the PRIN SUM3 command and consists of the highest unity check for each
selected loadcase for each element selected.

Summary report 4 is requested with the PRIN SUM4 command and provides the three worst unity checks for
each selected group, together with the distribution of unity check values. The distribution provides information




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on the number of unity checks exceeding an upper limit (default 1.0), less than a lower limit (default 0.5), and
the number in the mid-range.

A complete list of the command set available for the AISC WSD code check is given in Table 4.3 . An example
data file is given in Figure 4.7.




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          Command                                              Description                                   Usage     Note
     AISC WSD ALLO                 AISC allowable stress header command                                        C

     UNIT                          Units of length and force                                                   C        1
     YIEL                          Yield stress
     GROU                          Groups to be reported
                                                                                                               C         2
     ELEM                          Elements to be reported
     SECT                          Sections to be reported
     SEAR                          Search other sections in addition to those requested on the
                                   SECT command for maximum forces and stresses
     SECO                          Secondary members
     DESI                          Defines design section properties                                           C        3
     PROF                          Section profiles for use in design
     EFFE                          Effective lengths/factors
     CB                            Pure bending Cb coefficient
     CMY/CMZ                       Amplification reduction factors Cmy/Cmz
     UNBR                          Unbraced lengths of element
     ULCF                          Unbraced length of compression flange
     CASE                          Basic loadcases to be reported
                                                                                                               C        4
     COMB                          Define a combined loadcase for processing
     CMBV                          Define a combined loadcase for processing
     SELE                          Select/redefine a combined/basic loadcase title
     SPEC                          Basic loadcases from response spectrum analysis
     RENU                          Renumber a ‘basic loadcase’
     EXTR                          Loadcases allowing 33% overstress
     QUAK                          Loadcases with earthquake permitted overstress
     PRIN                          Reports to be printed
     TEXT                          Text or comment command
     TITL                          Redefine global title
     END                           Terminates Command data block                                               C


Usage
C         Compulsory command, but see notes below where applicable
Notes

1.   See Sections 3.4 and A.12.

2.   At least one GROUP or ELEM command must be included

3.   Compulsory for non-tubulars unless Sections have been used in the preceding analyses for all elements to
     be processed.

4.   At least one CASE, COMB or CMBV command must be included


                                          Table 4.1 AISC WSD ALLO Commands




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       SYSTEM DATA AREA 100000
       TEXT BEAMST USER MANUAL EXAMPLE STRUCTURE T0847
       JOB POST
       PROJECT MANU
       COMPONENT PILE DECA
       OPTION GOON
       END
       AISC WSD ED9 ALLO
       *
       * Select all elements using the GROUP command except
       * elements 991 and 992 - dummy elements
       *
       GROUP ALL
       NOT ELEMENT 991 992
       UNIT KN M
       *
       * Define section properties for some elements that
       * used areas and inertia values in the ASAS run
       *
       UNITS MM
       DESI RHS 900.0 400.0 40.0 ELEMENT 851 TO 854 861
       :                                  931 TO 942
       UNITS M
       *
       * Examine two load cases including jacket loading
       *
       SELE 10 Extreme Wave 1 + Dead Loads + Topside Loads
       COMB 10 1.0 1 1.0 3 1.0 4
       SELE 11 Extreme Wave 2 + Dead Loads + Topside Loads
       COMB 11 1.0 2 1.0 3 1.0 4
       *
       * Indicate that these loadcases are extreme events
       *
       EXTR 10 11
       *
       * Yield Value Constant for all elements
       *
       YIELD 3.5E05 ELEM ALL
       *
       * Main deck beams use effective length
       * coefficient of 1.0
       * Deck columns use effective length coeff of 1.2
       * Note that the element definition overrides the
       * group definition irrespective of order
       *
       EFFE 0.8 ELEM 851 To 854
       EFFE 1.0 GROU ALL
       *
       * Unbraced lengths need redefining
       * assumes no lateral restraint from deck plating
       *
       UNBR FACT 1.0 2.0 ELEM 701 704
       UNBR FACT 2.0 1.0 ELEM 706 707
       UNBR FACT 2.0     ELEM 702 703
       UNBR LENG 4.875 19.5 ELEM 711 713
       UNBR LENG 9.75 19.5 ELEM 712
       *
       * Override program computed moment amplification RF
       *
       CMZ 0.85 ELEM 711 712 713
       CMZ 0.85 ELEM 701 TO 704
       CMY 0.85 ELEM 702 703
       CMY 0.85 ELEM 706 707
       *
       * Check mid-span and quarter point sections
       *
       SECT 0.25 0.5 0.75 ELEM ALL
       *
       * Ask explicitly for all reports
       *
       PRIN XCHK PROP UNCK FORC STRE SUNI N MM SUM1 SUM2 SUM3 SUM4 BOTH
       END
       STOP

                                         Figure 4.1 Example AISC ALLO data file




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4.1.2       AISC WSD Allowable Unity Check Report

The detailed unity check report is presented on an element by element basis. The header line displays the
element number, the associated node numbers, the element group number and the units in use. The results are
printed for each of the selected positions (or sections) on the element for each loadcase in turn. The first
columns of the report define the loadcase, section number and position as a ratio of the elements length.

The allowable stresses for axial, shear and bending (in local Y and Z axes) stresses are presented in the next
columns of the report. These are preceded by a alphanumeric descriptor (CODE) that indicates the derivation of
each of the allowable stresses. These descriptors are of the form:

                T.XVYZ or C.XVYZ

T or C defines whether the member is in tension or compression, XVYZ are individual alpha codes which relate
to the axial(X), shear(V), and bending(Y,Z) allowable stresses. These alpha codes specify the design code
clause or equation used to evaluate the allowable stresses and are defined in Table 4.2.




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         A     B7                                        axial tension - B7 satisfied
         B     B7                                        axial tension - B7 violated
         C     (E2-1)                                    axial compression - E2 satisfied
  X      D     (A-B5-9)                                  axial compression - E2 violated
         E     (A-B5-12)                                 axial compression,         kL exceeds Cc′
                                                                                     r
         G     B5.2.b                                    axial compression, tubular section, Appendix B controlling
         B     (F4-2)                                    shear buckle
  V      Y     (F4-1)                                    shear yield
         U                                               user defined
         A     (F3-1)                                    Major - I,H,Boxes/Major and Minor - Tube
         B     (F2-1)                                    Minor - I,H,Boxes and Solid Rectangular Sections
         D     (F1-4)                                    Major - I,H
         E     (F2-3)                                    Minor - I,H
         F     (F3-3)                                    Major and Minor - Boxes
          I    (A-B5-3)                                  Major and Minor - I,H
          J    (A-B5-4)                                  Major and Minor - I,H
  Y      K     (A-B5-7)                                  Major and Minor - Boxes
         L     (A-B5-9)                                  Major and Minor - Tube
  Z      M     AISC 1.5.1.4.5(1)                         Major and Minor - I, H
         N     F1.3                                      Major - I, H
         O     (F1-6)                                    Major - I, H
         P     (F1-7)                                    Major - I, H
         Q     (F1-8)                                    Major - I, H
         R     (F1-5)                                    Major - Solid Rectangular Sections
         S     (E2-1) (C-F3-1)                           Major - Boxes
         T     (E2-2) (C-F3-1)                           Major - Boxes




                                        Table 4.2 Allowable Stress alphabetic codes


For example, the unity check CODE combination

                C.CYBA

indicates that the member is in compression and that the following clause/equations were used to derive the
allowable stresses:




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       Axial             -    C =       (E2-1)                   axial compression - E2 satisfied
       Shear             -    Y =       (F4-1)                   shear yield
       Bending Y         -    B =       (F2-1)                   Minor - I,H,Boxes and Solid Rectangular Sections
       Bending Z         -    A =       (F3-1)                   Major - I and H


The final columns of the table, headed Message, flag all lines of results where any of the checks have failed.
These messages may be summarised as follows.

       FAIL          -            Code check failure for this member

       ***           -            Unity check value exceeds unity

       **            -            Unity check value exceeds 0.9

       SLRF          -            Slenderness ratio greater than 200 for a compression member

       SLRW          -            Slenderness ratio greater than 300 for a tension member

       SHYF          -            Shear yielding failure

                                                         13000
       DTRF          -            D/t ratio exceeds                 (ksi units)
                                                            fy

       WBIC          -            Web plate ineffective in axial compression

        FLIC         -            Flange plate ineffective in axial compression

        FLIB         -            Flange plate ineffective in major axis bending

        PEWB         -            Partially effective web(s), major axis bending allowable reduced

        PEFL         -            Partially effective flange(s), minor axis bending allowable reduced

        WBSF         -            Flange buckling requiring web stiffeners

       SHBF          -            Shear buckling failure

       WBHP          -            Web requires stiffening

       CONS          -            Unbraced length of compression flange less than element length, conservative
                                  assumption for CB, CM

       HAND          -            Unbraced length of compression flange exceeds element length, manual check
                                  required, CB, CM defaulted


The format of the detailed unity check report is shown in Figure 4.2. Examples of the summary reports available
are given in Figures 4.3 and 4.4 .



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                                                                                                              ..................................................................................................................................
                                                                                                              . ELEMENT    602 . NODES   6130   6150 . GROUP      6 . MEMBER UNITY CHECK REPORT                   UNITS (N   ,MM )      UNCK
                                                                                                              ....................................................... -------------------------                   -----                 ====
                                                                                                                             /-------------ALLOWABLE STRESSES--------------/              /--------UNITY CHECKS---------/ COMBINED /
                                                                                                               LOAD   SECTION/ CODE    AXIAL    SHEAR      -- BENDING --   / CB CMY CMZ / AXIAL SHEAR SHEAR PURE-BEND /UNITY CHECK/ MESSAGES
                                                                                                               CASE   NO POSN/                             Y           Z   /BEND          /         Y     Z     Y     Z /BUCKL.YIELD/
                                                                                                                             /                                             /              /                             /           /


                                                                                                                                             T.XVYZ    FA or FT         FV                Fby        Fbz     Cb    Cmy    Cmz     UCax         UCvy       UCvz   UCby   UCbz   UCB
                                                                                                                  UCY

                                                                                                                                                                                                                         BUCKLE CSR/   UCCSR          /


                                                                                                                  (1 line per element section position, plus 1 line for the buckle CSR)



                                                                                                                                                                             Figure 4.2 Detailed Member Check Report




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                                                                                                                                                              MEMBER UNITY CHECK SUMMARY REPORT NO. 1                                           SUM1
                                                                                                              AISC     ( 9TH.ED. JUN. 1989)                   =======================================                                           ==== ====

                                                                                                               ELEM     MAX. LOAD    UNITY COMPONENT VALUES    MAX. LOAD    UNITY COMPONENT VALUES   ELEM KLY/RY KLZ/RZ      NEXT HIGH /
                                                                                                                NO.    BUCKLE CASE   ----------------------   YIELD CASE    ----------------------   POSN ------ ------     YIELD LOAD /   MESSAGES
                                                                                                                        CHECK          AXIAL BEND-Y BEND-Z    CHECK           AXIAL BEND-Y BEND-Z                           CHECK CASE /   --------
                                                                                                                105      0.09    4      0.05   0.00   0.04    0.12C    4       0.05   0.01   0.06    1.00     1.5     1.5   0.11T    3 /
                                                                                                                120      0.06    4      0.03   0.00   0.03    0.08C    4       0.03   0.00   0.04    1.00     1.5     1.5   0.06C    4 /




                                                                                                                                                              MEMBER UNITY CHECK SUMMARY REPORT NO. 2                                           SUM2
                                                                                                              AISC     ( 9TH.ED. JUN. 1989)                   =======================================                                           ==== ====

                                                                                                                ELEM   NODE1   NODE2     MAX. LOAD / MAX.           UNITY CHECKS        LOAD   ELEM / NEXT LOAD /
                                                                                                                 NO.                   BUCKLE CASE / YIELD   /------------------------/ CASE   POSN / YIELD CASE /      MESSAGES




                                                                                                                                                                                                                                                            AISC Member Checks
                                                                                                                                        CHECK      / CHECK   AXIAL BEND-Y BEND-Z SHEAR              / CHECK      /      --------

                                                                                                                 105     105   1105     0.09    4 / 0.12C     0.05   0.01   0.06   0.10    4   1.00 / 0.11T     3 /
                                                                                                                 120     120   1120     0.06    4 / 0.08C     0.03   0.00   0.04   0.07    4   1.00 / 0.06C     4 /



                                                                                                                                                              Figure 4.3 Example AISC Allowable Summary Reports 1 and 2
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                                                                                                                                                              MEMBER UNITY CHECK SUMMARY REPORT NO. 3                                       SUM3
                                                                                                              AISC     ( 9TH.ED. JUN. 1989)                   =======================================                                       ==== ====

                                                                                                               ELEM    NODE1   NODE2   GROUP   WORST   LOAD   ELEM ------------UNITY CHECKS FOR REQUESTED LOAD CASES---------------------------------
                                                                                                                                               UN CK   CASE   POSN CASES    1       2       3       4       5       6
                                                                                                                105      105   1105       3    0.12Y      4   1.00      0.01 C 0.01 C 0.11 T 0.12 C 0.04 T 0.04 C
                                                                                                                120      120   1120       3    0.08Y      4   1.00      0.02 C 0.02 C 0.04 C 0.08 C 0.03 C 0.03 C




                                                                                                                                                              MEMBER UNITY CHECK SUMMARY REPORT NO. 4                                       SUM4
                                                                                                              AISC     ( 9TH.ED. JUN. 1989)                   =======================================                                       ==== ====

                                                                                                                                            THREE WORST UNITY CHECKS
                                                                                                                                            ------------------------                                   NUMBERS OF ELEMENTS IN EACH GROUP
                                                                                                                      ----------FIRST------- ---------SECOND-------     ----------THIRD-------       ----------- Y I E L D --- --- B U C K L E ------
                                                                                                              GROUP     ELEM     UNITY LOAD / ELEM       UNITY LOAD    / ELEM      UNITY LOAD    /   TOTAL    GE     GE     LT     GE     GE      LT
                                                                                                                                 CHECK CASE /            CHECK CASE    /           CHECK CASE    /           1.00   0.50   0.50   1.00   0.50    0.50
                                                                                                                 3       105     0.12C     4 /   195     0.11C     4   /   105     0.11T     3   /      15      0      0     15      0      0      15
                                                                                                                 4      1102     2.09B     4 / 1102      2.07C     4   / 1102      2.01T     3   /      89     13     31     45     14     24      51




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                                                                                                                                                               Figure 4.4 Example AISC Allowable Summary Reports 3 and 4
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4.1.3        Nomenclature


4.1.3.1         Dimensional

(a)     Rolled Sections




(b)     Welded Sections




        D            =            outer tube diameter
        t            =            tube thickness
        b            =            actual width of box flange plates, I flange effective width, solid rectangular
                                  overall width
        be           =            effective width of stiffened compression elements
        d            =            depth of I, box and solid rectangular sections
        h            =            clear distance between flanges
        he           =            effective depth of stiffened compression web elements




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       tf             =           flange plate thickness
       tw             =           web plate thickness
       k, ky, kz      =           effective length factors. Subscript refers to the associated axis. No subscript refers
                                  to either axis as appropriate.
       L              =           unbraced member length about either axis as appropriate
       LULCF          =           unstiffened length of the compression flange
       rT             =           torsional radius of gyration
       r, ry, rz      =           radii of gyration. Subscript refers to the associated axis. No subscript refers to
                                  either axis as appropriate.
        Aw            =           cross-sectional area of the web(s)
       Af             =           cross-sectional are of the flange(s)



4.1.3.2            Acting Stresses

       fa                 =       computed axial stress
       fb                 =       resultant bending stress for tubes
       fb, fby, fbz       =       computed bending stresses for non-tubulars. Subscript refers to the associated
                                  axis. No subscript refers to either axis as appropriate
       fvy, fvz           =       shear stresses. Subscript refers to the associated axis
       fvmax              =       shear stress for tube



4.1.3.3            Allowable Stresses

       Cb                 =       bending coefficient
       Cmy, Cmz           =       amplification reduction factors for y and z axis buckle checks
       E                  =       Young’s modulus
       Fa                 =       axial compression stress
       Fbcy, Fbcz         =       bending stress for compression. The last subscript refers to the associated axis
       Fbty, Fbtz         =       bending stress for tension. The last subscript refers to the associated axis
       Fe                 =       Euler buckling stress
       Ft                 =       axial tension stress
       Fv, Fvy, Fvz =             shear stress. Second subscript refers to the associated axis.
       fy                 =       yield stress
       UCax               =       axial unity check (tension or compression)
       UCvy,vz            =       shear unity check
       UCvmax             =       shear resultant unity check for tubes
       UCby, bz           =       pure bending unity check
       UCB                =       combined axial compression and bending buckle check




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        UCY             =          combined axial and bending yield check
        UCCSR           =          upper bound member buckling check




4.1.4       AISC WSD Allowable Stresses and Unity Checks

The equations defined in the following section assume units of Kips and inches.



4.1.4.1          Allowable Stress Increase


Working stress design codes permit allowable stresses to be increased above those appropriate to Ordinary
conditions for other conditions. The percentage increase in allowable stresses to be applied to the allowable
stresses quoted herein for different loadcase types are:

                                        Loadcase                 axial/                 shear
                                          type                   bending

                                   Ordinary                         0.0                    0.0

                                   Extreme                        33.33                   33.33

                                   Earthquake                     33.33                   33.33




4.1.4.2          Axial Tension Checks

     Clause/(Eqn)                                              Commentary                                      Code   Message


                            Limiting slenderness ratio

          B7                  If                  kL                                                              A
                                                     ≤ 300
                                                   r
                              else if             kL       ............ ............ ...................          B     SLRW
                                                     > 300
                                                   r

            D1
                             Allowable stress
                                                Ft = 0.6fy




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4.1.4.3          Axial Compression Checks

     Clause/(Eqn)                                              Commentary                                   Code   Message



                           Limiting slenderness ratio

           B7                                    L      ............ ............ ...................               SLRF
                                                k > 200
                                                 r

                           Allowable stress

                           Tubular members

                                              Qa = 1.0       Qs = 1.0


          B5.2b               If                 D 13000 ............ ............ ...................              DTRF
                                                   >
                                                 t   fy
                              else if           3300        D 13000
                                                        <     <
                                                  fy        t   fy
        (A-B5-9)              then                                         t                                   D
                                               Falim = 0.4 f y + 662
                                                                           D

            E2                else if          D 3300
                                                   ≤
                                                t      fy
                              then             Falim = 0.6 f y                                                 C




                                                                                                                       Cont...




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4.1.4.3 Axial Compression Checks continued
     Clause/(Eqn)                                                  Commentary                                           Code   Message


                            I section

                              Web                      f = α(f a + | f by | + |

                                                       α = 1.0 for ordinary loadcases
                                                         = 0.75 for extreme and earthquake

                                                  h           253
        Table B5.1            If                       ≤
        &(A-B5-8)                                tw           f / 0.6

                               (The value of 253 satisfies the requirements of A-B5-8 so that
                               be ≤ b)
                              then               Qa = 1.0
        (A-B5-10)
                                                  h           253
                                                       >
                              else if             tw          f/ 0.6

                                                            253 t w               3     
                                                 he =               1 - 44.             
        (A-B5-8)              then                             f           (h/ t w ) f 
                                                                                         
                                                              (h- h e) t w
                                                 Qa = 1 -
        (A-B5-10)                                                  Aw
                                         if      h e ≤ 0.0          ............ ............ ...................
                            Flange                                                                                              WBIC
                              If                                                 h
                                                fabricated and                     > 70
                                                                                 t
        A-B5.2a
                             then
                                                             4.05
                                                 kc =
                                                            (h/t )0.46
                             else                k c = 1.0
                                                 b            95
                                                       ≤
        Table B5.1           If                  tf          f y / kc
                             then                Qs = 1.0

                                                       95          b  195
                                                             mark < ≤
        A-B5.2.a             else if                               tf
                                                      f y/kc          f y/kc

                                                                     b
        (A-B5-3)             then                Qs = 1.293 - 0.00309  f y / k c
                                                                      
                                                                      tf 
                             else if              b           195
                                                       >
                                                  tf          f y / kc

        (A-B5-4)                                                               kc
                                                                       [f                  ]
                             then                Qs = 26200
                                                                            y (b/ t f )
                                                                                       2




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4.1.4.3 Axial Compression Checks continued
     Clause/(Eqn)                                                 Commentary                                      Code   Message



                            Fabricated Box and Rolled Hollow sections

                                                      f = α (f a + | f by | + | f bz |)
                                             α         =          1.0 for ordinary loadcases
                                                       =          0.75 for extreme and earthquake
                                             t′        = tw       for fabricated box
                                                       = t        for rolled hollow box
                          Web
   Table B5.1               If                h      253
   & (A-B5-7)                                    ≤
                                              t′   f/ 0.527
                            (The value of 253 satisfies the requirements of A-B5-7 so that
                            be ≤ b)
   (A-B5-10)                then              Qaw = 1.0

                            else if           h      253
                                                 >
                                              t′   f/ 0.527

   (A-B5-7)                 then                         253 t′     50.3 
                                              he =              1 -      
                                                           f  (h/t) f 

   (A-B5-10)                                                   2(h- h e) t ′
                                              Qaw = 1 -
                                                            Aw
                                      if      h e ≤ 0.0 ............ ............ ....................                   WBIC
                             Flange
                                              b'       = b - 2tw        for fabricated box
                                                       = b - 4t         for rolled hollow box

   Table B5.1                                     b′     253
                            If                       ≤
   &(A-B5-7)
                                                  t′   f/ 0.527
                            (The value of 253 satisfies the requirements of A-B5-7 so that
                            be ≤ b)
                            then              Qa        = Qaw
                                                                    *
                            else if               b′     253
                                                     >
                                                  t′   f/ 0.527

   (A-B5-7)                 then                          253 t ′             3      
                                                  be =            1 - 50.            
                                                            f             (b′/t ′) f 

   (A-B5-10)                                                   2(b′- be) t ′
                                                  Qa = Qaw -
                                      if          b e ≤ 0.0 ............f ............ ....................
                                                                     A
                                                                                                                          FLIC




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4.1.4.3 Axial Compression Checks continued
     Clause/(Eqn)                                              Commentary                                   Code   Message


                            All section types


        A-B5.2.c                                            2π 2 E
                                                Cc ′ =
                                                           Qs Q a f y
                               If                 kL
                                                     ≤ Cc′
                                                   r


       (A-B5-11)               then                        (kL/r )2                                        D
                                                     QsQa 1 -       2 f y
                                                           2 Cc ′ 
                                                Fa =
                                                     5 3(k L / r ) (kL/r )3
                                                      +           -      3
                                                     3 8 Cc ′       8Cc′
                               else if            kL
                                                     ≥ Cc′
                                                   r

       (A-B5-12)               then                      12π 2 E                                             E
                                                Fa =               2
                                                          kL 
                                                       23    
                                                          r 
                           Tubular section

      A-B5.2.b                 If               Fa > Falim

                               then             Fa = Falim                                                   G




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4.1.4.4         Bending Checks

     Clause/(Eqn)                                              Commentary                                   Code   Message


                            Tubular section


                              If            3300           D 13000
                                                      <      <
                                                 fy        t   fy
           (A-B5-9)           then                                           t                                L
                                            Fbt = Fbc = 0.4 f y +662
                                                                             D
                              else if       D 3300
                                               <
                                             t     fy
           (F3-1)             then                                                                            A
                                            Fbt = Fbc = 0.66 f y

                            I section

                             Major axis

           (F1)               If             b        65
                                                  ≤
                                            tf        fy
           (F1-2)             and                     76 b f
                                          L ULCF≤
                                                        fy

                              and                  20000 b f
                                          L ULCF≤
                                                        df y
           (F1-1)             then          Fbt = Fbc = 0.66f y                                               A


           F1.2               else if        65      b   95
                                                    < ≤
                                                 f y tf f y/k

           (F1-4)             then                                        b                                 D
                                            Fbt = Fbc = f y 0.79 - 0.002                 f y/kc 
                                                                         2 tf                   

                              If                  95      b  195
                                                         < <
                                                 f y / kc t  f y / kc

           (A-B5-3)           then                                       b                                I
                                            Fbc = 0.6 f y 1.293 - 0.00309  f y / k c
                                                                                                       
                                                                                                        
                                                                         t                           
           (F1-5)             and           Fbt = 0.6f y




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4.1.4.4 Bending Checks continued
     Clause/(Eqn)                                               Commentary                                  Code   Message




                                 Else if       b   195
                                                 ≥
                                               t   f y / kc

              (A-B5-4)           then                         26200 k c                                     J
                                               Fbc = 0.6 f y            
                                                              f (b/t )2 
                                                              y         
              (F1-5)             and           Fbt = 0.6 f y


                                 If                         76 bf              20000 bf t f
                                               L ULCF>                  or >
                                                              fy                  df y
                                              b         95
                                 and               ≤
                                              tf       f y/kc
              (F1-5)             then
                                               Fbt = 0.6 f y


                                 If                102000 Cb L ULCF 510000 Cb
                                                            ≤      ≤
                                                      fy       rT      fy

                                                              L 
                                                                     2
              (F1-6)             then                                                                         O
                                                            fy  
                                                                
                                                       2 -     rT  
                                                Fbc =                   fy
                                                         3 1530000 Cb 
                                                                      
                                                       
                                                                      
                                                                       
                                 If
                                                 LULCF > 510000 Cb
                                                    rt         fy
                                                                                                             P
              (F1-7)             then                      170000 Cb
                                                   Fbc =            2
                                                          L
                                                           
                                                           rT                                              Q
              (F1-8)                                     12000 Cb bf t f
                                                   Fbc =
                                                               Ld

                                  Fbc = max [((F1 - 5) or (F1 - 7)) and (F1 - 8)]

              F1.3                                 Fbc = min (Fbc ,0.6)                                      N




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4.1.4.4 Bending Checks continued

     Clause/(Eqn)                                               Commentary                                        Code     Message




              G2                 If             h         760 ............ ............ ...................
                                                      >                                                                  PEWB/
                                                tw         Fbc                                                           PEFL
                                                                                                                         depending on
                                                                                                                         major minor
                                                                A w  h - 760 
              (G2-1)             then                                                                                    axis
                                               Fbc = 1 - 0.0005                Fbc R e
                                                     
                                                                Af  t
                                                                           Fbc 
                                                                                
                                       It is assumed that
                                       Re =         1.0
                                       Aw =         area of web at section under investigation
                                       Af =         area of compression flange under investigation
                                       (F1-6), (F1-7), (F1-8) and (G2-1) are repeated
                                       for combined stress buckle unity check using Cb′
                                       See Section 4.1.4.9 for Cb and Cb′

                                 Minor axis
                                 If             b         65
                                                     ≤
                                                tf         fy
              (F2-1)             then          Fbt = Fbc = 0.75f y                                                   B


                                 else if       65   b   95
                                                   < ≤
                                                f y tf f y/k
              (F2-3)             then                                      b                                     E
                                               Fbt = Fbc =f y 1.075 - 0.005  f y 
                                                                             
                                                                            tf   
                                 else if              95      b  195
                                                             < <
                                                     f y / kc tf f y / kc
                                                                             b  fy 
                                               Fbc = 0.6 f y 1.293 - 0.00309 
              (A-B5-3)           then                                                                                I
                                                                              
                                                             
                                                                             tf  kc 
                                                                                       
              (F1-5)             and           Fbt =0.6 f y


                                 else if       b          195
                                                     ≥
                                               tf         f y / kc
              (A-B5-4)           then                            26200 k c                                           J
                                              Fbc = 0.6 f y
                                                                 f y (b/ t f )
                                                                              2

              (F1-5)              and         Fbt = 0.6 f y




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4.1.4.4 Bending Checks continued
     Clause/(Eqn)                                              Commentary                                             Code   Message



                                 Fabricated Box and Rolled Hollow sections
                 F3.1

                 (F3-2)          If             b′ 190
                                                   ≤
                                                t′     fy
                                 and            d ≤6 b
                                 and            tf ≤ 2 tw
                                                                    M1  b
                                 and            L ULCF≤1950 + 1200     
                                                                    M2  f y
                                                               b
                                                LULCF>= 1200 
                                 but
                                                               f 
                                                                y
                 (F3-1)          then                                                                                   A
                                                Fbt = Fbc = 0.66 f y
                                                b′ and t′ as defined for axial compression
                                                depending upon axis under consideration.

                                 else if         b′    253
                                                    ≤
                                                 t′ f b′ / 0.527

                 (F3-3)          then           Fbt = Fbc = 0.6 f y                                                     F

                                                f b′ =f b                 for ordinary loadcases

                                                f b′ = 0.75 f b           for earthquake and extreme


                 (A-B5-7)                              253 t       50.3                                               K
                                                be =           1 -         
                                                         f      (b/t) f b′ 
                                 If             b e ≤ 0.0         ............ ............ ...................                 FLIB


                 A-B5.2d         Modified bending allowables for post-buckled section.

                                                     Sc
                                                Fbc =   0.6 f y
                                                     Sz
                                                     St
                                                Fbt = 0.6 f y
                                                     Sz
                                 where Sc, St           are the section modulii for extreme
                                                        compression and tension fibres
                                           Sz           is the pre-buckled section modulus



                                                                                                                                 Cont...




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4.1.4.4 Bending Checks continued

     Clause/(Eqn)                                              Commentary                                             Code   Message




                                                L                  2π 2 E
                                 If            k         <
                                                 r equiv             fy

                                                                     (
                                                               k (L/r )equiv 
                                                                            2
                                                                                        )
                                                           1-         2
                                                                              f y
                                                          
                                                                  2 Cc       
                                                                              
       (E2-1)                    then           Fbc =
                                                        +
                                                                 (
                                                      5 3 k (L/r )equiv k (L/r )equiv
                                                                        -
                                                                                  ) ( 3
                                                                                                       )                S
                                                      3      8 Cc             8 C3 c




       (C-F3-1)                  where           L        5.1 LSx
                                                   =
                                                  r equiv    JI y

       (E2-2)                    else                         12π 2 E                                                   T
                                                Fbc =                         2
                                                           L 
                                                        23 k   
                                                           r 
                                                                equiv 


                                                  Fbc = min (Fbc ,0.6)


       G2                        If                h       760        ............ ............ ...................
                                                       >                                                                      PEWB
                                                  tw        Fbc

                                 then                             A w  h 760 
                                                    Fbc = 1 - 0005  -         Fbc R e
                                                          
                                                                  Af  t Fbc 
                                                                              

                               Solid Rectangle

       (F1-5)                  Major axis
                                                  Fbc = Fbt = 0.60 Fy                                                   R


       (F2-1)                  Minor axis
                                                  Fbc = Fbt = 0.75 Fy                                                   B




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4.1.4.5          Shear Checks

     Clause/(Eqn)                                               Commentary                                            Code   Message


            F4                 Tube and Solid Rectangle


            (F4-1)                                  Fv = 0.4 f y                                                        Y
            (3.2.4.-1)
                            I Beam



                                                 Fvz = 0.4 f y                                                          Y


                               If                                      380
                                                 (d- 2 t f ) / t w ≤
                                                                         fy
            (F4-1)             then              Fvy = 0.4 f y


            (F4-2)             else                               fy                                                 Y/B
                                                 Fvy = min  0.4,     Cv 
                                                                 2.89 

                               where                          45000 K v
                                                 Cv =
                                                         f y ((d- 2 t f ) / t w )
                                                                                 2




                               If                Cv > 0.8

                               then                          190              Kv
                                                 Cv =
                                                         (d- 2 t f ) / t w    fy
                               where             K v = 5.34

                               If                d- 2 t f             14000               ............ ............            WBSF
                                                            >
                                                    tw            f y (f y + 16.5)


                            Fabricated Box and Rolled Hollow Section


                                                 h  380
                               If                ≤
                                                t    fy
            (F4-1)             then             Fv = 0.4 f y                                                            Y



                                                                                                                                 Cont...



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4.1.4.5 Shear Checks continued
     Clause/(Eqn)                                              Commentary                                                Code   Message




             (F4-2)             else                             fy                                                    Y/B
                                                 Fv = min  0.4,     Cv 
                                                                2.89 
                                where                     45000 K v
                                                  Cv =
                                                           f y (h /t )
                                                                      2



                                If                Cv > 0.8

                                then                      190 K v
                                                   Cv =
                                                          h /t f y
                                                   K v = 5.34

                                If                  h       14000                   .......................... .......
                                                      >                                                                            WBSF
                                                    t   f y (f y + 16.5)
                                 where

                                                                                             h             t
                                                    fabricated box             Qy        d-2tf             tw
                                                                               Qz        b-2tw             tf
                                                    rolled hollow box          Qy        d-4t              t
                                                                               Qz        b-4t              t




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4.1.4.6            Unity Checks

     Clause/(Eqn)                                              Commentary                                                     Code   Message


                              All section types
                              Axial
           E                                       f a for compressive
                                            UCax =        fa
                                                   Fa
           D1                                      f a for tensile
                                            UCax =        fa
                                                   Ft
                              All section types except tubes

                              Shear
           F4                                      f vy
                                            UCvy =
                                                   Fvy
                                                   f vz
                                            UCvz =
                                                   Fvz
                                If          UCvy or UCvz > 1.0
                                                                                                                  ......                SHYF
                                and         the associated allowable stress = shear yield

                                If
                                            UCvy or UCvz > 1.0
                                                                                                                    .......             SHBF
                               and          the associated allowable stress = shear buckle

                                If          UCvy < 1.0

           C-F4                 and          h > 260       ............ ............ ...................                                WBHP
                                             t
                              Tubular Sections only

                                                   f vy
                                            UCvy =
                                                   Fvy
                                                   f vz
                                            UCvz =
                                                   Fvz
                                                      f vmax
                                            UCvmax =
                                                        Fv
                                If                                                             ............ ............                SHYF
                                           UCvy or UCvz or UCvmax > 1.0

                              All section types
               F              Pure Bending
                                                        f by
                                            UCby =
                                                        Fbcy
                                                        f bz
                                            UCbz =
                                                        Fbcz




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4.1.4.7         Combined Stress Unity Checks

     Clause/(Eqn)                                              Commentary                                   Code   Message



                              All section types

                              Axial compression and bending buckle check

                                       UCB = UCB1 + UCB2 + UCB3

                                where           UCB1 = UCAX

                                                                 Cmyf by
                                                UCB 2 =
                                                            (1 -f a / Fe′y )Fbcy
                                                                  Cmz f bz
       (H1-1)                                   UCB 3 =
                                                            (1 - f a / Fe′z ) Fbcz
                                            See Section 4.1.4.10 for Cm computation

                                              Fe′ = 1.0 Fe for ordinary loadcases
                                                  = 1.33 Fe for extreme/earthquake

                                                     12 π 2 E
                                             Fe =
                                                    23 (kL/r )2

                              All section types except tubes
                              For axial tension and bending buckle check

                              For reporting purposes

                                          UCB, UCB1, UCB2 and UCB3 are reported



                              Tubular Sections only
                              For axial tension and bending buckle check

                              For reporting purposes

                                            UCB, UCB1 and UCB2 are reported
                                            where UCB2, = UCB2 + UCB3




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4.1.4.8         Combined Axial and Bending Yield Unity Check

     Clause/(Eqn)                                              Commentary                                   Code   Message



                              All section types


       (H1-2)                 For axial compression


                                                         f a + f by + f bz
                                             UCY =
                                                        α f y Fby Fbz
                                            where fby , fbz are compressive bending stresses

       (H2-1)                                     α = 0.6                for ordinary loadcases
                                                    = 0.8                for extreme or earthquake


                              For axial tension

                                                        f a + f by + f bz
                                             UCY =
                                                        Ft Fby Fbz
                                            where fby , fbz are tensile bending stresses




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4.1.4.9         Cb - Bending Coefficient

   Clause/(Eqn)                                                  Commentary                                       Message

                           The pure bending coefficient, Cb, is only calculated by the program when
                           LULCF=L. Cb is used in the evaluation of the major axis pure bending
                           allowable stress and is calculated as follows:

                         (1)      If LULCF < L (member length); Cb conservatively defaults to unity.

                                  And if the worst unity check exceeds unity (ie the beam fails the code
                                                                                                                 CONS
                                  check) a message is given in the Unity Check Report.

                         (2)      If LULCF > L; Cb defaults to unity and hand checking/assessment is             HAND
                                  recommended.

                         (3)      If LULCF=L and the beam is subject to transverse load and the
                                  maximum bending moment occurs within the beam span;
                                  Cb = 1.0.




                         (4)      If LULCF=L and the beam is not subject to transverse load or is subject
                                  to transverse load with the maximum moment at an end and the peak
                                  span moment Mp, at the point of maximum free moment Md, is less
                                  than that given by interpolation between end moments then;




                                                                                    2
                                                      M1 + 0.3  M1  ≤ 2.3
                                     Cb = 1.75 - 1.05              
                                                      M2        M2 
                                    where M1 and M2 are positive for beam sagging.
                                    M1 is the end moment with smaller magnitude
                                    M2 is the end moment with larger magnitude




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4.1.4.9 Cb - Bending Coefficient continued
     Clause/(Eqn)                                                    Commentary                                   Message

                            (5)      If the beam is subject to transverse load and the maximum is at an
                                     end with the peak span moment (Mp) greater than that given by
                                     interpolation between end moments, Cb as calculated in (4) is
                                     unconservative. The SSRC guide (Ref. 17) points out that in such
                                     cases is is conservative to substitute a straight line moment
                                     diagram external to the actual one.

                                     An equivalent uniform moment for the external moment diagram
                                     may be calculated as:




                                               M max +       1  Md    M max = M max
                                     M eq =            Md =  +
                                                                      
                                                             Cb M max 
                                                                                   *
                                                Cb                                Cb

                                                       1         1             1
                                    where
                                                         *
                                                             =      + M max ≥
                                                      C  b       Cb   Md      2.3
                                                       Cb = as for (4)

                                     In this case BEAMST adopts Cb* instead of Cb

                            (6)      The bending coefficient Cb′ deduced by the program and used in
                                     the evaluation of the major axis allowable bending stress for the
                                     combined axial and bending buckle unity check is calculated as
                                     follows:

                                     If the beam is part of a braced frame (Kz ≤ 1.0); Cb′ = 1.0

                                     If the beam is part of sway frame: Cb′ = Cb or Cb* as for (1) to (5)
                                     above




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4.1.4.10 Cmy , Cmz - Amplification Reduction Factors

     Clause/(Eqn)                                                    Commentary                                      Message

                            The amplification reduction factor, Cm, is only calculated by the program
                            when LULCF = L. Cm is used in the combined axial and bending buckle unity
                            check and is calculated as follows:

                            (1)      If LUNBR < L (member length); Cm conservatively defaults to unity.             CONS
                                     If the worst unity checks exceeds one a message is given in the Unity
                                     Check Report.

                            (2)      If LUNBR > L; Cm defaults to unity and hand checking/assessment is             HAND
                                     recommended.

                            The following calculations are performed by the program only if
                            LUNBR = L.

                            (3)      If the beam is part of a sway frame (K>1.0);
                                     Cm = 1 - (0.18fa/Fe′)
                                     In this case BEAMST adopts a constant value of Cm = 0.85

                            (4)      If the beam is subject to transverse load and the maximum bending
                                     moment (Mmax) occurs within the beam span;
                                     Cm = 1.0 (or 0.85 if API)

                            (5)      If the maximum moment (Mmax) occurs at a beam end and the peak
                                     span moment (Mp) is less than that given by interpolation between end
                                     moments;
                                     Cm = 0.6 + 0.4 (M1/M2) ≥ 0.4
                                     where M1, M2 are positive for beam sagging
                                     M1 is the end moment with smaller magnitude
                                     M2 is the end moment with greater magnitude

                            (6)      If the maximum moment (Mmax) occurs at a beam end and the peak
                                     span moment (Mp) is greater than that given by interpolation between
                                     end moments then Cm as calculated in Section 4.1.4.10 (5) is
                                     unconservative. Using a substitute straight line moment diagram
                                     external to the actual one (as in (5) for Cb) an equivalent uniform
                                     moment for the external linear moment diagram may be calculated as
                                     follows:


                                                                                                                      Cont...




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4.1.4.10 Cmy , Cmz - Amplification Reduction Factors continued


                                                                         Md )           *
                              M eq = Cm M max + M d = ( Cm +                   M max = Cm M max
                                                                         M max
                              where           *               M d ) ≥ 0.4
                                            Cm = Cm + (
                                                              M max
                                           Cm =        as for (5) above

                                   In this case Cm* is used instead of Cm in BEAMST

                            (7)      In steps (1) to (6), if both the end moments are of the same sign and
                                     the peak span moment (Mp) is of the opposite sign, Cm is limited to a
                                     maximum of 0.85.




                            (8)      Steps (1) to (7) are repeated for both local bending planes.

                            (9)      If the beam is tubular and of circular section and the check is being
                                     performed against API RP2A (API ALLO check); Cm is limited to a
                                     maximum of 0.85.




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4.1.5       Spectral Loadcases and ‘Automatic Signed Expansion Procedures’

In response spectrum analysis using modal superposition (Ref. 12), the structure displacements and forces
calculated represent estimated maxima. Such estimated maxima are, in general, unsigned (positive).

For the purpose of checking members to AISC WSD, a series of worst static-spectral possible loadcases must be
generated from the member unsigned spectral and signed static end forces.

The signs applied to the spectral end forces when generating a series of worst cases depends upon the unity
check being considered and details of the signs adopted/deduced are given in this section.

In BEAMST it is assumed that unity checks can be performed by considering the combination of static and
dynamic conditions to be purely a static condition.



4.1.5.1         Torsional Effects


The maximum torsional spectral load contribution at each beam section position is deduced in a similar manner
to the axial load contribution in 4.1.5.2.



4.1.5.2    Axial Unity Check and the Axial Component of Combined Stress Buckle and
Yield Unity Checks


The maximum axial spectral load contribution at each beam section position is calculated by assuming that the
spectral axial load distribution is linear with both member end loads having the same sign. The sign adopted for
these member spectral end loads is normally assumed to be of the same sign as the static axial load (if it exists).
In cases where the static loadcase is tensile it is possible that reversing the sign of the spectral case may produce
a net compressive load and, hence, a more onerous utilisation (since buckling may become a problem). Under
these conditions, the checks are repeated with the spectral axial stresses reversed with respect to the static case,
and the combination producing the highest utilisation of both conditions is reported. The sign adopted may be
ascertained from the utilisation code reported.

As in all checks performed by BEAMST, zero axial stress is treated as compressive (-ve sign, ASAS
convention).


4.1.5.3         Local Axes Shear Unity Checks and Maximum Shear Unity Check for Tubular
Sections


In order to be able to generate mid-member stresses an equivalent member spectral loading is required.
BEAMST assumes that the spectral loading consists of a linearly varying inertia loading on the member acting in
a rigid fashion (ie the load consists of that due to pure translation and rotation of the member). This inertia
loading is calculated by ‘balancing’ it against the member signed spectral end forces (shears and moments).




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For each local bending plane there are sixteen unique signed spectral end force (shears and moments)
expansions/cases of which eight are symmetric, but of opposite sign, to the remaining eight. Each of these
sixteen signed spectral expansions is denoted by a single alphabetic letter code in BEAMST in the range A-P as
shown in Figure 4.5. For spectral loadcases only eight of the sixteen possible expansions need theoretically be
considered but for static-spectral summations all sixteen have to be taken into account.

The Shear Unity Checks are maximised by adopting the static-spectral signed expansion which maximises the
total acting shear at each beam section position. For tubular sections the combination of static-spectral
expansions which maximises the resultant acting shear on the cross section and the Maximum Shear Unity
Check.

For a linearly varying inertia load it can be deduced a priori that the following spectral expansions are critical for
the Shear Unity Checks for static-spectral summation.

                          beam section position (α)                        local axes spectral expansions

                                         0 < α < 1/3                                         E or L

                                         1/3 < α < 2/3                                       D or M

                                         2/3 < α < 1                                         B or O



4.1.5.4 Local Axes Pure Bending Unity Checks and Bending Components of Combined
Stresses Yield Unity Check

For bending unity checks and unity check bending components it is necessary to determine the spectral
expansion which maximises the ratio of acting to allowable stress as opposed to simply maximising the acting
bending stress. In general this is necessary because the bending allowable may be a function of Cb which itself is
a function of the signs and relative magnitudes of the member total end forces.

BEAMST investigates each of the sixteen signed spectral expansions shown in Figure 4.5 for both of the local
axes bending planes for each beam section position being considered and reports the critical expansions at each
section. For tubular sections being checked to AISC WSD where it is necessary to calculate bending resultants
at each beam section the spectral expansions which maximise the ratio of local axes bending stress to allowable
are determined (as these local axes acting bending stresses are the ones which also maximise the acting bending
resultants and hence maximise the yield unity check components).

For static-spectral summation it is theoretically necessary to investigate all sixteen spectral expansions for the
worst cases but for loadcases composed of expanded spectral contributions only, the following generalisations
can be made:

(i).     The acting bending stress at each beam section position is maximised by adopting the spectral expansion
         defined by end moments of the same sign and end shears of opposite signs.

(ii).    Where the allowable stress is a function of Cb, the allowable will be minimised by adopting the expansion
         with spectral end moments of the same sign as this minimises Cb.


These two generalisations taken together imply spectral expansions A or P (Figure 4.5)



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4.1.5.5         Unity Check Report for Shear, Pure Bending and Yield Unity Checks


The Unity Check Report for a spectral or a static-spectral summation comprises four separate reports:

(i).     Highest Shear Unity Checks

(ii).    Highest Pure Bending Unity Checks

(iii).   Highest Yield Unity Checks

(iv).    Highest Buckle Unity Checks


The unity checks of direct interest to the user when checking against a design code are the shear checks in the
Highest Shear Unity Checks, the pure bend checks in the Highest Pure Bending Unity Checks etc. For the
Highest Shear, Pure Bending and Yield Reports, the worst unity check at each beam section position is reported
together with the spectral expansions in the local Y and Z which maximise the respective checks (as described in
4.1.5.1-4.1.5.4 above) appended to the loadcase number. In addition to the unity checks of direct interest in each
report all remaining unity checks are calculated for the spectral expansions quoted and are reported. This allows
users to obtain an overall picture of stress state in the beam at the section under consideration for the spectral
expansions cited. The combined buckle unity checks in these reports and the Highest Buckle Unity Check
Report are explained in 4.1.5.6 below.


4.1.5.6         Combined Stress Buckle Unity Check


As for the pure bending and yield unity check it is necessary to determine which spectral expansions maximise
the bending components of the buckle unity check defined by ratio of ‘equivalent uniform bending’ stress to
minimum allowable. This is necessary because the amplification-reduction factor Cm used to convert maximum
acting bending stress to an equivalent uniform bending stress is a function of the signs and relative magnitudes
of the member total end forces (moments).

BEAMST investigates all sixteen spectral expansions determining for each expansion the maximum bending
stress and minimum allowable stress occurring anywhere along the beam and the buckle unity check bending
component for the bending plane being considered. Over all sixteen expansions, those which maximise the
bending components in each of the local bending planes are used in the final buckle check and are reported in the
Highest Buckle Unity Check Report.

An example of the report generated for combined static and dynamic loadcases is given in Figure 4.6.




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                                                                 end1                          end2
                                  Spectral
                                  Expansion
                                                            shear       moment         shear       moment


                                        A                    +            +            -                +

                                        B                    +            +            -                -

                                        C                    +            +            +                +

                                        D                    +            +            +                -

                                        E                    +            -            -                +

                                        F                    +            -            -                -

                                        G                    +            -            +                +

                                        H                    +            -            +                -

                                        I                    -            +            -                +

                                        J                    -            +            -                -

                                        K                    -            +            +                +

                                        L                    -            +            +                -

                                        M                    -            -            -                +

                                        N                    -            -            -                -

                                        O                    -            -            +                +

                                        P                    -            -            +                -




     Figure 4.5 Automatic signed Spectral Expansion codes for Member Checks and the respective signs
                                      applied for bending in the local Y-Y/Z-Z planes


Notes

1.   Beam end spectral torque signs are chosen to be identical with their respective static components in static-
     spectral loadcases.

2.   Beam end spectral torque signs adopted for evaluation of spectral stresses at intermediate beam section
     positions are chosen to be identical with their respective static stress components at the section under
     consideration.




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                                                                                                          ..................................................................................................................................




                                                                                                                                                                                                                                                BEAMST User Manual
  Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.
                                                                                                           . ELEMENT    601 . NODES   6110   6130 . GROUP      6 . MEMBER UNITY CHECK REPORT                   UNITS (N   ,MM )      UNCK
                                                                                                           ....................................................... -------------------------                   -----                 ====
                                                                                                                          /-------------ALLOWABLE STRESSES--------------/              /--------UNITY CHECKS---------/ COMBINED /
                                                                                                            LOAD   SECTION/ CODE    AXIAL    SHEAR      -- BENDING --   / CB CMY CMZ / AXIAL SHEAR SHEAR PURE-BEND /UNITY CHECK/ MESSAGES
                                                                                                            CASE   NO POSN/                             Y           Z   /BEND          /         Y     Z     Y     Z /BUCKL.YIELD/
                                                                                                                          /                                             /              /                             /           /
                                                                                                              10    1 0.00/T.AYBN   280.00,   186.67,   350.00,   280.00/2.30 0.40 0.40/ 0.06 0.03 0.00 0.01 0.11 / 0.06 0.18 /
                                                                                                              10    2 0.25/T.AYBN   280.00,   186.67,   350.00,   280.00/2.30 0.40 0.40/ 0.06 0.03 0.00 0.01 0.05 / 0.03 0.12 /
                                                                                                              10    3 0.50/T.AYBN   280.00,   186.67,   350.00,   280.00/2.30 0.40 0.40/ 0.06 0.02 0.00 0.00 0.00 / 0.00 0.06 /
                                                                                                              10    4 0.75/T.AYBN   280.00,   186.67,   350.00,   280.00/2.30 0.40 0.40/ 0.06 0.02 0.00 0.00 0.04 / 0.02 0.10 /
                                                                                                              10    5 1.00/T.AYBN   280.00,   186.67,   350.00,   280.00/2.30 0.40 0.40/ 0.06 0.02 0.00 0.01 0.08 / 0.04 0.15 /
                                                                                                              10          /                                             /              /                   BUCKLE CSR/ 0.06      /
                                                                                                                          /                                             /              /                             /           /
                                                                                                                   -----------------HIGHEST SHEAR UNITY CHECKS-------------PLUS---------ASSOCIATED UNITY CHECKS--------------------
                                                                                                              11AI 1 0.00/T.AYBN    280.00,   186.67,   350.00,   280.00/3.07 0.40 0.40/ 0.06 0.03 0.00 0.02 0.11 / 0.06 0.19 /
                                                                                                              11EL 2 0.25/T.AYBN    280.00,   186.67,   350.00,   280.00/3.07 0.42 0.40/ 0.06 0.03 0.00 0.01 0.05 / 0.06 0.13 /
                                                                                                              11MD 3 0.50/T.AYBN    280.00,   186.67,   350.00,   280.00/3.07 0.40 0.40/ 0.06 0.02 0.00 0.00 0.00 / 0.06 0.07 /
                                                                                                              11OB 4 0.75/T.AYBN    280.00,   186.67,   350.00,   280.00/3.07 0.42 0.40/ 0.06 0.02 0.00 0.00 0.04 / 0.06 0.11 /
                                                                                                              11CA 5 1.00/T.AYBN    280.00,   186.67,   350.00,   280.00/3.07 0.42 0.40/ 0.06 0.02 0.00 0.01 0.08 / 0.06 0.16 /
                                                                                                                          /                                             /              /                             /           /
                                                                                                                   ---------------HIGHEST PURE-BEND UNITY CHECKS-----------PLUS---------ASSOCIATED UNITY CHECKS--------------------
                                                                                                              11AE 1 0.00/T.AYBN    280.00,   186.67,   350.00,   280.00/3.07 0.42 0.40/ 0.06 0.03 0.00 0.02 0.11 / 0.06 0.19 /
                                                                                                              11AP 2 0.25/T.AYBN    280.00,   186.67,   350.00,   280.00/3.07 0.42 0.40/ 0.06 0.03 0.00 0.01 0.05 / 0.06 0.13 /
                                                                                                              11AP 3 0.50/T.AYBN    280.00,   186.67,   350.00,   280.00/3.07 0.42 0.40/ 0.06 0.02 0.00 0.00 0.00 / 0.06 0.07 /
                                                                                                              11PA 4 0.75/T.AYBN    280.00,   186.67,   350.00,   280.00/3.07 0.40 0.40/ 0.06 0.02 0.00 0.00 0.04 / 0.06 0.11 /
                                                                                                              11BA 5 1.00/T.AYBN    280.00,   186.67,   350.00,   280.00/3.07 0.42 0.40/ 0.06 0.02 0.00 0.01 0.08 / 0.06 0.16 /
                                                                                                                          /                                             /              /                             /           /
                                                                                                                   ---------HIGHEST COMBINED STRESS YIELD UNITY CHECKS-----PLUS---------ASSOCIATED UNITY CHECKS--------------------
                                                                                                              11AE 1 0.00/T.AYBN    280.00,   186.67,   350.00,   280.00/3.07 0.42 0.40/ 0.06 0.03 0.00 0.02 0.11 / 0.06 0.19 /
                                                                                                              11AP 2 0.25/T.AYBN    280.00,   186.67,   350.00,   280.00/3.07 0.42 0.40/ 0.06 0.03 0.00 0.01 0.05 / 0.06 0.13 /
                                                                                                              11AP 3 0.50/T.AYBN    280.00,   186.67,   350.00,   280.00/3.07 0.42 0.40/ 0.06 0.02 0.00 0.00 0.00 / 0.06 0.07 /
                                                                                                              11PA 4 0.75/T.AYBN    280.00,   186.67,   350.00,   280.00/3.07 0.40 0.40/ 0.06 0.02 0.00 0.00 0.04 / 0.06 0.11 /
                                                                                                              11BA 5 1.00/T.AYBN    280.00,   186.67,   350.00,   280.00/3.07 0.42 0.40/ 0.06 0.02 0.00 0.01 0.08 / 0.06 0.16 /
                                                                                                           ..................................................................................................................................
                                                                                                           . ELEMENT    601 . NODES   6110   6130 . GROUP      6 . MEMBER UNITY CHECK REPORT                   UNITS (N   ,MM )      UNCK
                                                                                                           ....................................................... -------------------------                   -----                 ====
                                                                                                                   -----------------------------------HIGHEST COMBINED STRESS BUCKLE UNITY CHECK-----------------------------------




                                                                                                                                                                                                                                                   AISC Member Checks
                                                                                                                          /-----MIN. ALLOWABLE COMPRESSIVE STRESSES-----/    /-----MAX. ACTING STRESSES-----/                    /
                                                                                                            LOAD   SECTION/ CODE    AXIAL    BEND-Y    BEND-Z     FEY   / CMY/   AXIAL     BEND-Y    BEND-Z /----BUCKLE CHECK----/ MESSAGES
                                                                                                            CASE   NO POSN/          POSN    POSN-Y    POSN-Z     FEZ   / CMZ/    POSN     POSN-Y    POSN-Z / AX. BENDY BENDZ UCK/
                                                                                                              11AE        /C.C-BO   135.31,   350.00,   233.19,   136.91/0.42/     0.00C,     6.34,    29.94/ 0.00 0.01 0.05 0.06/
                                                                                                              11AE        /           1.00,     0.00,     0.00, 2146.97/0.40/      0.00 ,     0.00,     0.00/                    /
                                                                                                                   ----------------------------------------------------------------------------------------------------------------
                                                                                                                          /                                             /              /                             /           /
                                                                                                                                                                                                                      -------------
Page 4-38




                                                                                                                                                                                                                MAXIMA 0.06 0.19
                                                                                                                                                                                                                 CASES    11   11
                                                                                                                                                                                                                 CASES    11   10

                                                                                                                                                           Figure 4.6 Spectral Expansion Report
BEAMST User Manual                                                                           AISC LRFD Member Checks




4.2 AISC Load and Resistance Factor Design Member Check


4.2.1       Overview

The AISC LRFD MEMB header command in BEAMST is used to request member stress checks to AISC LRFD
design recommendations, second and third editions (Ref. 23, Ref. 25), for tubular, I-shaped and hollow
rectangular section types.

The AISC specification is written in terms of member yield strengths, so a YIELd command must be used to
specify the yield strength.

Members may be selected for processing by elements and/or groups. The member section dimensions must be
specified (if not specified in the structural analysis) using DESI commands. Further commands are available for
defining topological characteristics of the members (EFFE, UNBR and ULCF) and specifying members that are
classified as ‘secondary’ (SECO).

The SECT command may be used to define intermediate points along a member at which member forces are to
be evaluated, checked and reported. These are in addition to results automatically printed at the member end
points and positions of any step change in cross-section properties. Alternatively the SEARch command may be
used which requests that moments and stresses are to be evaluated at specified locations along the beam but to be
reported only if they give a maximum force, stress or utilisation. These extra locations are in addition to those
selected using the SECT command.

The AISC LRFD standard utilises limit state checks with resistance coefficients to achieve the desired level of
safety. In keeping with this principle, applied loads must be multiplied by appropriate factors, as defined in the
code of practice (Section C, Loads), to develop the design load case combinations necessary for processing.
Where non-linear pile analysis is undertaken (using SPLINTER) the design loads must be applied to the pile
model to account for the increased non-linearity this introduces. In situations where a non-linear pile analysis
has not been carried out, the design loads may be produced using the COMB or CMBV commands utilising the
required load factors.

The selection of output reports is made using the PRIN command with the appropriate parameters for the
required reports. The PRIN command is also used to request the various summary reports available. Two
summary reports are available.

Summary report 1 is requested with the SUM1 subcommand and details the loadcase producing the highest unity
check value for each element.

Summary report 3 is requested with the PRIN SUM3 command and consists of the highest unity check for each
selected loadcase for each element selected.

A complete list of the command set available for the AISC LRFD MEMB code checks is given in Table 4.3
and described in detail in Section 3.4. An example data file is given in Figure 4.7.




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           Command                                                Description                           Usage     Note
     AISC LRFD MEMB                   AISC allowable stress header command                                C

     UNIT                             Units of length and force                                           C         1
     YIEL                             Yield stress
     GROU                             Groups to be reported
                                                                                                          C         2
     ELEM                             Elements to be reported
     SECT                             Sections to be reported
     SEAR                             Search other sections in addition to those requested on the
                                      SECT command for maximum forces and stresses
     SECO                             Secondary members
     DESI                             Defines design section properties                                   C         3
     PROF                             Section profiles for use in design
     EFFE                             Effective lengths/factors
     CB                               Pure bending Cb coefficient
     CMY/CMZ                          Amplification reduction factors Cmy/Cmz
     UNBR                             Unbraced lengths of element
     ULCF                             Unbraced length of compression flange
     CASE                             Basic loadcases to be reported
                                                                                                          C         4
     COMB                             Define a combined loadcase for processing
     CMBV                             Define a combined loadcase for processing
     SELE                             Select/redefine a combined/basic loadcase title
     SPEC                             Basic loadcases from response spectrum analysis
     RENU                             Renumber a ‘basic loadcase’
     PRIN                             Reports to be printed
     TEXT                             Text or comment command
     TITL                             Redefine global title
     END                              Terminates Command data block                                       C


Usage
C         Compulsory command, but see notes below where applicable

Notes

1.   See Sections 3.4 and A.12.

2.   At least one GROUP or ELEM command must be included

3.   Compulsory for non-tubulars unless Sections have been used in the preceding analyses for all elements to
     be processed.

4.   At least one CASE, COMB or CMBV command must be included


                                         Table 4.3 AISC LRFD MEMB Commands




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       SYSTEM DATA AREA 100000
       TEXT BEAMST USER MANUAL EXAMPLE STRUCTURE T0847
       JOB POST
       PROJECT MANU
       COMPONENT PILE DECA
       OPTION GOON
       END
       AISC LRFD ED2 MEMB
       *
       * Select all elements using the GROUP command except
       * elements 991 and 992 - dummy elements
       *
       GROUP ALL
       NOT ELEMENT 991 992
       UNIT KN M
       *
       * Define section properties for some elements that
       * used areas and inertia values in the ASAS run
       *
       UNITS MM
       DESI RHS 900.0 400.0 40.0 ELEMENT 851 TO 854 861
       :                                  931 TO 942
       UNITS M
       *
       * Examine two load cases including jacket loading
       *
       SELE 10 Extreme Wave 1 + Dead Loads + Topside Loads
       COMB 10 1.35 1 1.1 3 1.1 4
       SELE 11 Extreme Wave 2 + Dead Loads + Topside Loads
       COMB 11 1.35 2 1.1 3 1.1 4
       *
       * Yield Value Constant for all elements
       *
       YIELD 3.5E05 ELEM ALL
       *
       * Main deck beams use effective length
       * coefficient of 1.0
       * Deck columns use effective length coeff of 1.2
       * Note that the element definition overrides the
       * group definition irrespective of order
       *
       EFFE 0.8 ELEM 851 To 854
       EFFE 1.0 GROU ALL
       *
       * Unbraced lengths need redefining
       * assumes no lateral restraint from deck plating
       *
       UNBR FACT 1.0 2.0 ELEM 701 704
       UNBR FACT 2.0 1.0 ELEM 706 707
       UNBR FACT 2.0     ELEM 702 703
       UNBR LENG 4.875 19.5 ELEM 711 713
       UNBR LENG 9.75 19.5 ELEM 712
       *
       * Override program computed moment amplification RF
       *
       CMZ 0.85 ELEM 711 712 713
       CMZ 0.85 ELEM 701 TO 704
       CMY 0.85 ELEM 702 703
       CMY 0.85 ELEM 706 707
       *
       * Check mid-span and quarter point sections
       *
       SECT 0.25 0.5 0.75 ELEM ALL
       *
       * Ask explicitly for all reports
       *
       PRIN XCHK PROP UNCK FORC STRE SUNI N MM SUM1 SUM3 BOTH
       END
       STOP

                                    Figure 4.7 Example AISC LRFD MEMB data file




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4.2.2       AISC LRFD Unity Check Report

The detailed unity check report is presented on an element by element basis. The header line displays the
element number, the associated node numbers, the element group number and the units in use. The results are
printed for each of the selected positions (or sections) on the element for each loadcase in turn. The first
columns of the report define the loadcase, section number and position as a ratio of the elements length together
with the section dimensions, slenderness ratios and the moment amplification reduction factors, cmy and cmz.

Following the section information is an alphanumeric descriptor (CODE) that indicates the derivation of each of
the design strengths that have been computed for this section. These descriptors are of the form:

                T.XVYZ or C.XVYZ

T or C defines whether the member is in tension or compression, XVYZ are individual alpha codes which relate
to the axial(X), shear(V), and bending(Y,Z) design strengths. These alpha codes specify the design code clause
or equation used to evaluate the design strengths and are defined in Table 4.4.




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         A     B7                                        axial tension - B7 satisfied
         B     B7                                        axial tension - B7 violated
         C                                               axial compression - Fcr indeterminate (Qa or Qs <0)
  X      D     (E2-2)                                    axial compression
         E     (E2-3)                                    axial compression
         A     (F2-1)                                    shear yield
  V      B     (F2-2)                                    shear buckle - FBI, WF, BOX, RHS
         C     (F2-3)                                    elastic buckling stress - FBI, WF, BOX, RHS
         A     (A-F1-1)                                  Major - FBI, WF, BOX, RHS LTB
         B     (A-F1-2)                                  Major - FBI, WF, BOX, RHS LTB
         C     (A-F1-4)                                  Major - FBI, WF, BOX, RHS LTB
         D     (A-F1-1)                                  Major - FBI, WF, BOX, RHS FLB, TUB
         E     (A-F1-3)                                  Major - FBI, WF, BOX, RHS FLB, TUB
  Y      F     (A-F1-4)                                  Major - FBI, WF, BOX, RHS FLB, TUB
         G     (A-F1-1)                                  Major - FBI, WF, BOX, RHS WLB
  Z      H     (A-F1-3)                                  Major - FBI, WF, BOX, RHS WLB
          J    (A-G2-1)                                  Major - FBI, WF, BOX, RHS Slender web tension flange yield
         K     (A-G2-2)                                  Major - FBI, WF, BOX, RHS Slender web flange local
                                                         buckling
         L     (A-F1-1)                                  Minor - FBI, WF, BOX, RHS
         M     (A-F1-3)                                  Minor - FBI, WF, BOX, RHS
         N     (A-F1-4)                                  Minor - FBI, WF, BOX, RHS




                                              Table 4.4 Strength alphabetic codes


For example, the unity check CODE combination

                C.DALA

indicates that the member is in compression and that the following clause/equations were used to derive the
allowable stresses:

       Axial             -    D =       (E2-1)                   axial compression - (E2-2) satisfied
       Shear             -    A =       (F2-1)                   shear yield
       Bending Y         -    L =       (A-F1-3)                 Minor - FBI, WF, BOX, RHS
       Bending Z         -    A =       (A-F1-1)                 Major - FBI, WF, BOX, RHS Lateral Torsional Buckle




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The next two columns present the acting axial force, shear and bending moments pertaining to the given
loadcase, and these are followed by the nominal strengths and associated parameters for axial, shear and bending
loads and their respective utilisations.

The final columns of the table, headed Message, flag all lines of results where any of the checks have failed.
These messages may be summarised as follows.

       FAIL          -            Member has a utilisation exceeding unity or fails parameter limits (flagged with
                                  THKF, DTRF, SLRF)

       PNT9          -            Unity check value exceeds 0.9

       SLRF          -            Slenderness ratio greater than limiting value

                                                         13000
       DTRF          -            D/t ratio exceeds                 (ksi units)
                                                            fy

       SHYF          -            Shear yield failure

       SHBF          -            Shear buckling failure

       HOVT          -            Web requires stiffening

       WBIC          -            Reduced web width calculation is required, this is not currently undertaken by the
                                  program

        HAND         -            Member is part of sway frame (k1.0)
                                  Manual check required for combined interaction check


The format of the detailed unity check report is shown in Figure 4.8. Examples of the summary reports available
are given in Figure 4.9.




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                                                                                                                                                               MEMBER UNITY CHECK REPORT                         STRESS UNITS (KN     ,M   )     UNCK
                                                                                                          ELEMENT       1   GROUP        1                     -------------------------                          OTHER UNITS (KN     ,M   )
                                                                                                          NODE1         1   NODE2       31
                                                                                                                                                           /--ACTING FORCES--/---------NOMINAL STRENGTHS---------/-----UNITY CHECK-----/
                                                                                                          LOAD   SECT/DPTH DIA/ BREADTH/KL/R(Y)/ CMY/ CODE /   AXIAL   SHEARM/   AXIAL   EULERY   SHEARY   SHEARZ/AXIAL SHRY SHRZ/YIELD/MESS
                                                                                                          CASE   POSN/ THICKN / THICKF /KL/R(Z)/ CMZ/ CB /     BENDY    BENDZ/     FCR   EULERZ    BENDY    BENDZ/      BNDY BNDZ/     /




                                                                                                                                       D               B                       cmy T.XVYZ      Fa         Vm           Fc/Ft         fey         Vy            Vz   UCax
                                                                                                             UCvy UCvz      UCy
                                                                                                                                     t/tw              tf                       cmz   cb            Fby          Fbz           Fcr         fez           Mny         Mnz
                                                                                                             UCby UCbz




                                                                                                                                                                                                                                                                              AISC LRFD Member Checks
                                                                                                                                                                                                                                            CSR/ UCc /


                                                                                                             (2 lines per element section position, plus 1 line for the CSR)



                                                                                                                                                                       Figure 4.8 Detailed Member Check Report
Page 4-46
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                                                                                                                                                          MEMBER UNITY CHECK SUMMARY REPORT NO. 1         STRESS UNITS (KN ,M      )     SUM1
                                                                                                                                                          ---------------------------------------          OTHER UNITS (KN ,M      )
                                                                                                                                                               /--ACTING FORCES--/---------NOMINAL STRENGTHS---------/-----UNITY   CHECK-----/
                                                                                                            ELEM   POSN/DPTH DIA/   BREADTH/KL/R(Y)/ CMY/ CODE /   AXIAL   SHEARM/   AXIAL   EULERY   SHEARY   SHEARZ/AXIAL SHRY   SHRZ/YIELD/MESS
                                                                                                            LOAD       / THICKN /   THICKF /KL/R(Z)/ CMZ/ CB /     BENDY    BENDZ/     FCR   EULERZ    BENDY    BENDZ/      BNDY   BNDZ/     /
                                                                                                               2   1.00/   0.700/          / 41.58/0.40/C.DADD/ 2730.99    133.41/ 9746.14 48789.00 3206.27 3206.27/ 0.33 0.00     0.05/ 0.63/
                                                                                                               1       /   0.020/          / 41.58/1.00/ 1.00/ 711.02        0.00/ 9746.14 48789.00 2312.67 2312.67/        0.34   0.00/     /
                                                                                                               3   1.00/   0.700/          / 41.58/0.40/T.AADD/ 3735.42    111.65/ 9746.14 48789.00 3206.27 3206.27/ 0.39 0.00     0.04/ 0.64/
                                                                                                               1       /   0.020/          / 41.58/1.00/ 1.00/ 598.86        0.00/ 9746.14 48789.00 2312.67 2312.67/        0.29   0.00/     /
                                                                                                               4   0.00/   0.700/          / 41.58/0.40/T.AADD/ 2730.99     82.52/ 9746.14 48789.00 3206.27 3206.27/ 0.28 0.00     0.03/ 0.48/
                                                                                                               1       /   0.020/          / 41.58/1.00/ 1.00/ 456.52        0.00/ 9746.14 48789.00 2312.67 2312.67/        0.22   0.00/     /
                                                                                                               5   1.00/   1.200/          / 23.89/0.72/C.DAEE/4.12D+03 3.79D+01/1.44D+04 2.06D+05 4.46D+03 4.46D+03/ 0.34 0.00    0.01/ 0.44/
                                                                                                               1       /   0.016/          / 23.89/1.00/ 1.00/5.46D+02 0.00D+00/1.44D+04 2.06D+05 5.31D+03 5.31D+03/        0.11   0.00/     /
                                                                                                               6   0.00/   2.000/          / 20.08/0.40/T.AAFF/5.52D+03 1.49D+02/9.70D+03 2.45D+05 3.75D+03 3.75D+03/ 0.49 0.00    0.04/ 0.69/
                                                                                                               1       /   0.008/          / 20.08/1.00/ 1.00/1.34D+03 0.00D+00/9.70D+03 2.45D+05 6.55D+03 6.55D+03/        0.23   0.00/     /
                                                                                                               7   1.00/   2.000/          / 20.08/0.40/C.DAFF/7.84D+03 1.70D+02/9.70D+03 2.45D+05 3.75D+03 3.75D+03/ 0.95 0.00    0.05/ 1.18/FAIL
                                                                                                               1       /   0.008/          / 20.08/1.00/ 1.00/1.51D+03 0.00D+00/9.70D+03 2.45D+05 6.55D+03 6.55D+03/        0.26   0.00/     /




                                                                                                                                                           MEMBER UNITY CHECK SUMMARY REPORT NO. 3                                      SUM3
                                                                                                          AISC LRFD(1ST.ED. SEP. 1986)                     ---------------------------------------
                                                                                                                                                    CHECK FLAG      T/C - TENSION/COMPRESSION AXIAL M - MOMENT Y - YIELD S - SHEAR B - BUCKLE
                                                                                                           ELEM    NODE1   NODE2   GROUP   WORST   LOAD   ELEM ------------UNITY CHECKS FOR REQUESTED LOAD CASES---------------------------------




                                                                                                                                                                                                                                                        AISC LRFD Member Checks
                                                                                                                                           UN CK   CASE   POSN CASES    1
                                                                                                              2       2       4       1    0.63Y      1   1.00      0.63Y
                                                                                                              3       5       3       2    0.64Y      1   1.00      0.64Y
                                                                                                              4       6       4       2    0.48Y      1   0.00      0.48Y
                                                                                                              5       3       4       3    0.44Y      1   1.00      0.44Y
                                                                                                              6       2       3       4    0.69Y      1   0.00      0.69Y
                                                                                                              7       4       5       4    1.18Y      1   1.00      1.18Y
Page 4-47




                                                                                                                                                            Figure 4.9 Example AISC LRFD Summary Reports 1 and 3
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  4.2.3        Nomenclature


  4.2.3.1           Definition of Symbols

  (a)      Rolled Sections




  (b)      Welded Sections




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  4.2.3.2              Dimensional

           Ag                    = Gross cross sectional area
           Aw                    = Area of web
           Ay, Az                = Shear area for y and z axis
           d                     = Full nominal depth of rolled or fabricated sections
           b                     = Actual width of box flange plates, I flange effective width
           h                     = Clear distance between flanges
           hc                    = Assumed web depth for stability
           D                     = Tube outer diameter
           t                     = Tube thickness or thickness of rolled hollow section
           tw                    = Web plate thickness
           tf                    = Flange plate thickness
           J                     = Torsion constant
           I y, I z              = Moment of inertia about y and z axis
           Zy, Zz                = Plastic modulus about y and z axis
           Sy, Sz                = Elastic section modulus about y and z axis
           k, ky, kz             = Effective length factors. Subscript refers to the associated axis. No subscript
                                      refers to either axis, as appropriate
           L, Ly, Lz             = Unbraced member length. Subscript refers to the associated axis. No subscript
                                      refers to either axis, as appropriate
           LULCF                 = Unstiffened length of the compression flange
           r, ry, rz             = Radii of gyration. Subscript refers to the associated axis. No subscript
                                      refers to either axis, as appropriate
           rT                    = Torsional radius of gyration



  4.2.3.3              Acting Forces and Stresses

           fa                    = Axial force
           fby, fbz              = Bending moment about y and z axis
           fvy, fvz              = Sheas force for y and z axis
           Fa                    = Axial stress




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  4.2.3.4             Strengths and Utilisations

           Fey, Fez              = Euler strength for y and z axis
           Pn                    = Nominal axial strength
           Mny, Mnz              = Nominal flexural strength about y and z axis
           Vy, Vz                = Nominal shear strength for y and z axis
           Mr                    = Limiting buckling moment
           Mp                    = Plastic bending moment
           Fcr                   = Critical stress
           UCax                  = Axial unity check (tension or compression)
           UCvy, UCvz            = Shear unity check for y and z axis
           UCby, UCbz            = Pure bending unity check about y and z axis
           UCcb                  = Combined axial and bending interaction check




  4.2.3.5             Parameters

           E                     = Youngs modulus
           G                     = Shear Modulus
           Cb                    = Bending coefficient
           Cmy, Cmz              = Amplification reduction factors for y and z axis
           Fr                    = Compressive residual stress in flange                   = 10 ksi for rolled sections
                                                                                              16.5 ksi for welded sections
           Fy                    = Yield stress
           Qa                    = Reduction factor for slender stiffened compression elements
           Qs                    = Reduction fcator for slender unstiffened compression elements
           Q                     = Full reduction factor for slender compression elements
           øc                    = resistance factor for axial compression
           øt                    = resistance factor for axial tension
           øb                    = resistance factor for bending
           øv                    = resistance factor for shear




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  4.2.4        AISC LRFD MEMBER CHECKS

  The equations defined in the following section assume units of Kips and inches.



  4.2.4.1           AISC LRFD Partial Coefficients

         Clause/(Eqn)                                                  Commentary                                 Message


                                  All section types
                              Resistance factors
                 (D1-1)                        φt = 0.90

                 (E2-2)                        φc = 0.85

                 H1.2                          φb = 0.90
                 F2.2                          φv = 0.90

                                Load coefficients
                                BEAMST assumes the appropriate factors have already been applied
                                by the user




  4.2.4.2           Nominal Axial Tension Strength

         Clause/(Eqn)                                             Commentary                              Code    Message



                                All section types
                              Yielding on gross section
                                P n = F y Ag
    (D1-1)
                              Limiting slenderness ratio
                                          kL
                                 If          ≤ 300
    B7                                     r                                                             A

                                  If           kL                                                        B
                                                  > 300
                                                r                                                                SLRF




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  4.2.4.3           Nominal Axial Compressive Strength

         Clause/(Eqn)                                             Commentary                              Code    Message


                                All section types

                              Limiting slenderness ratio

    B7                             If            L                                                               SLRF
                                                k > 200
                                                 r

                                 Tubular members

                                                 Q a = 1.0
                                 If              D 13000
                                                     >
                                                 t       Fy                                                      DTRF
                                                 3300 D 13000
                                 Else If                < ≤
    (A-B5-13)                                      Fy      t     Fy
                                                         1100    2
                                                 Qs =          +
                                                             D   3
                                                       F y( )
                                                             t
                                   Else          Q s = 1.0


                                                                                                                        Cont...




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  4.2.4.3 Nominal Axial Compressive Strength continued
    Clause/(Eqn)              Commentary                                                                 Code   Message


                                 I section

                                 Web
                                                     h 253
    Table B5.1                    If                    ≤
                                                     tw   Fy
                                                     Q aw = 1.0

                                  If                 h 253
                                                        >
                                                     tw   Fa

    (A-B5-12)                                               326tw     57.2                
                                                     hc =         1 −                     
                                                              Fa  (h / tw ) Fa
                                                                                          
                                                                                           
    (A-B5-14)                                                      2(h − he )tw
                                                    Qaw = 1 −
                                                                       Aw

                                 Else
                                                     Qaw = 1.0


                                                                                                                     Cont...




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    Clause/(Eqn)              Commentary                                                                 Code   Message


                                 I section

                                 Rolled section flange
                                 If           b     95
    Table B5.1                                   ≤
                                              tf     Fy
                                                    Qs = 1.0
                                                     95      b 176
                                                         < <
                                 If                   Fy tf     Fy
                                                                         b
    (A-B5-5)
                                                    Qs = 1.415 - 0.00437( ) Fy
                                                                         tf
                                                    b 176
                                  If
                                                       ≥
                                                    tf     Fy
                                                               20000
                                                    Qs =
    (A-B5-6)                                                    b 2 
                                                               Fy   
                                                                tf  
                                                                      

                                 Fabricated section flange

                                             kc =
                                                   4                           0.35 ≤ k c ≤ 0.763
                                                    b
                                                               tf
    Table B5.1
                                                     b        109
                                  If                      <
                                                     tf     Fy
                                                            kc
                                                     Qs = 1.0
                                                      109      b    200
                                                             <    <
                                  If                    Fy     tf    Fy
    (A-B5-7)                                            kc           kc
                                                                         b Fy
                                                    Qs = 1.415 - 0.00381( )
                                                                         tf kc
                                                    b     200
                                                       ≥
                                  If                tf      Fy
    (A-B5-8)                                                kc
                                                          26200 k c
                                                    Qs =
                                                           b 2 
                                                          Fy   
                                                           tf  
                                                                  




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  4.2.4.3 Nominal Axial Compressive Strength continued
    Clause/(Eqn)              Commentary                                                                 Code   Message



                                 Fabricated Box and Rolled Hollow sections
                                 Web

                                                    t′ = t w         for fabricated box
                                                    t′ = t           for rolled hollow section

                                 If rolled hollow section or constant thickness box
                                                     h 238
                                                        ≤
    Table B5.1                   If                  t′   Fy
                                                     Qaw = 1.0

                                                     h 238
                                                       >
                                 If                  t′ F a

                                                           326 t ′     64.9 
                                                     he=           1 -      
    (A-B5-11)                                                Fa  (h/t ′) Fa 
                                                                  2(h- h e) t ′
                                                    Qaw = 1 -
    (A-B5-14)
                                                                      Aw
                                 Else               Qaw = 1.0

                                 If fabricated box with different thickness plates
                                                      h     253
                                  If                     <=
    Table B5.1
                                                      t'     Fy
                                                      Qaw = 1.0

                                                      h 253
                                  If                    >
                                                      t' F a
                                                             326 t'     57.2 
                                                      he=           1 -       
                                                               Fa  (h/t' ) Fa 
    (A-B5-12)
                                                                   2(h- h e) t'
                                                      Qaw = 1 -
                                                                        Aw
    (A-B5-14)
                                  Else                Qaw = 1.0




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  4.2.4.3 Nominal Axial Compressive Strength continued
    Clause/(Eqn)              Commentary                                                                 Code   Message


                                 Fabricated Box and Rolled Hollow sections

                                 Flange
                                                    t′ = t f         for fabricated box
                                                    t′ = t           for rolled hollow section

                                                    b 238
                                 If                    <
    Table B5.1                                      t′   Fy
                                                    Qa = Qaw

                                 If                  b 238
                                                       >
                                                     t′ F a

                                                            326 t ′     64.9 
                                                     be =           1 -      
    (A-B5-11)                                                 Fa  (b/t ′) Fa 
                                                                   2(b′-be) t ′
                                                     Qa = Qaw -
    (A-B5-14)                                                          Af
                                 Else               Qa = Qaw




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  4.2.4.3       Nominal Axial Compressive Strength continued

                                                                    Commentary                            Code    Message
    Clause/(Eqn)


                                 All section types

                                 Column slenderness parameter

                                              kL    Fy
    E2-4                               λc =
                                              rπ    E
                                    Q = Qa Qs

                                 Critical stress

                                  If           Q a or Q s ≤ 0

                                               F cr = 0.0                                                C

                                  If           λ c Q ≤ 1.5

    E2-2                                                   (
                                               F cr = Q 0.658
                                                                        Q λ c2
                                                                                 )F   y
                                                                                                         D

                                  If           λ c Q > 1.5
                                                       0.877                                             E
    E2-3                                       F cr=               Fy
                                                         λc
                                                               2


                                 Nominal Strength
                                               P n = Ag F cr
    (E2-1)




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  4.2.4.4           Bending Strength




                                   Compressive flange residual stress

    F1.3                            F r = 10
                                    F r = 16.5




  4.2.4.5           Major Axis Bending Strength


                                 All section types

                                   Plastic capacity

    F1.1                                         M p= FyZz



                                   The nominal flexural strength, Mn, is the lowest value
                                   obtained according to the limit states of
                                   Lateral Torsional Buckling
                                   Flange Local Buckling
                                   Web Local Buckling




                                                                                                                   Cont...




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  4.2.4.5 Major Axis Bending Strength continued
        Clause/(Eqn)                                              Commentary                              Code    Message


                                 I Sections

                                 Lateral Torsional Buckling

                                                                       Slenderness parameter
    Table A-F1.1                    λ = LULCF
                                             ry
                                             300                       Compact limit
    Table A-F1.1                    λp=
                                               Fy
    (F1-8)                                   π      EGJA               Beam buckling factor
                                     X1=
                                         Sx          2
                                                      2
    (F1-9)                               4 Cw  S z                   Beam buckling factor
                                     X2=           
                                          I y  GJ 
                                   Non compact limit



                                              X1     1 + 1 + X 2 (F y - F r )
                                                                             2
    Table A-F1.1                    λr =
                                            F y - Fr
                                   Compact section

                                   If        λ ≤λp

                                             M nltb = M p                                                A
    (A-F1-1)
                                   Non compact section

                                   If        λ p < λ ≤ λr

                                             M r = ( F y - Fr )Sz
    Table A-F1.1
                                                                              λ - λ p 
                                             M nltb = C b  M p - (M p - M r )         
                                                                               λ - λ  ≤ M p
                                                                                                         B
    (A-F1-2)                                              
                                                                              r p     
                                   Slender section

                                   If        λ > λr

                                                      Cb X 1 2             2       
                                             F cr =                    1+  X 1 X 2 
    Table A-F1.1                                            λ              2λ 
                                                                                 2



                                             M nltb = S z F cr ≤                                         C

    (A-F1-4)




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  4.2.4.5 Major Axis Bending Strength continued
        Clause/(Eqn)                                              Commentary                              Code    Message


                                 I Sections

                                 Flange Local Buckling
                                           b
    Table A-F1.1                    λ=                                 Slenderness parameter
                                           t
                                               65
    Table A-F1.1                    λp=                                Compact limit
                                                Fy
                                                141
                                    λr =
                                               F y - Fr                Non compact limit
    Table A-F1.1                                162
                                    λr =
                                                F y - Fr
                                                    kc
                                   Compact section

                                   If          λ ≤λp

                                               M nflb = M p                                              D
    (A-F1-1)
                                   Non compact section

                                   If          λ p < λ ≤ λr
                                                                           λ -λp                       E
    (A-F1-3)                                   M nflb = M p - (M p - M r )
                                                                          λ -λ 
                                                                                  
                                                                            r   p

                                   Slender section

                                   If          λ > λr
                                                     20000
                                           F cr =
                                                         λ2
    Table A-F1.1                                     26200 k c
                                           F cr =
                                                          λ2
                                                                                                         F
                                           M nflb = S z F cr ≤ M p
    (A-F1-4)


                                                                                                                      Cont...




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  4.2.4.5 Major Axis Bending Strength continued
        Clause/(Eqn)                                              Commentary                                  Code    Message


                                 I Sections

                                 Web Local Buckling

    Table A-F1.1                    λ = hc                             Slenderness parameter
                                           tw
                                                fa
                                   If                 ≤ 0.125
                                             φb Py
                                                      640  2.75 f a 
    Table B5.1                               λp=          1 -       
                                                              φb Py 
                                                       Fy                               Compact limit
                                   else

                                                      191         f  253
                                             λp=           2.33 - a  ≥
    Table B5.1                                                   φb Py 
                                                       Fy               Fy

                                             970           f  253
                                    λr =          1 - 0.74 a  ≥                         Non compact limit
    Table B5.1                                            φb Py 
                                              Fy                 Fy
                                   Compact section

                                   If        λ ≤λp

                                             M nwlb = M p                                                     G
    (A-F1-1)
                                   Non compact section

                                   If        λ p < λ ≤ λr

                                                                       λ -λp 
                                           M nwlb = M p - (M p - M r )                                      H
                                                                      λ -λ 
    (A-F1-3)                                                            r   p
                                   Slender section

                                   If        λ > λr

                                             If rolled section, hand check required.

    Appendix G                                                                                                       HAND
                                             If fabricated section, take smaller of tension flange
                                             yield (Mntfy) and flange local buckling (Mnflb), as
                                             defined below.

                                   If        λ > 260                   Stiffeners required

                                                                                                                     HOVT




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  4.2.4.6           Slender Web

        Clause/(Eqn)                                              Commentary                              Code    Message


                                 I Sections

                                 Tension flange yield

    G2                                                d tw
                                               ar =
                                                      bt f
                                                                      h c 970 
                                               R PG = 1 - 0.0005 a r  -          ≤ 1.0
    (A-G2-3)
                                                                      tw   F cr 
                                                                                
                                               Re = 1.0            Hybrid girder factor


                                               M ntfy = S z Re F y                                       J
    (A-G2-1)

                                 Flange local buckling

                                               M nflb = S z R PG R e F cr                                K
    (A-G2-2)




                                                                                                                      Cont...




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  4.2.4.6 Slender Web continued
        Clause/(Eqn)                                              Commentary                              Code    Message


                                 I Sections
                                 Fcr is computed as follows for the limit states of lateral torsional
                                 buckling and flange local buckling and the lower value used.

                                 Lateral torsional buckling

                                                                               Slenderness parameter
    (A-G2-7)                                 λ = LULCF
                                                      rT
                                                      300                      Compact limit
    (A-G2-8)                                 λp=
                                                       Fy
                                                      756                      Non compact limit
    (A-G2-9)                                 λr =
                                                    Fy
                                             C PG = 286000 C b
    (A-G2-10)

                                 Flange local buckling

                                                   b                           Slenderness parameter
    (A-G2-11)                                λ=
                                                  2t f
                                                    65                         Compact limit
    (A-G2-12)                                λp=
                                                     Fy
                                                   230                         Non compact limit
    (A-G2-13)                                λr =
                                                     Fy
                                             C PG = 26200 k c                    C b = 1.0
    (A-G2-14)

                                 Critical stress Fcr

                                   If        λ ≤λp

                                             F cr = F y
    (A-G2-4)
                                   If        λ p < λ ≤ λr

                                                                    λ - λ p 
                                             F cr = C b F y 1 - 0.5         
                                                                     λ - λ  ≤ F y
    (A-G2-5)
                                   If        λ > λr         
                                                                    r p     

                                                      C PG
                                             F cr =
    (A-G2-6)
                                                       λ2




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  4.2.4.7           Minor Axis Bending Strength

        Clause/(Eqn)                                              Commentary                              Code    Message


                                 I Sections

                                 Flange Local Buckling
                                                b
    Table A-F1.1                    λ = 0.5                            Slenderness parameter
                                               tf
                                              65
    Table A-F1.1                    λp=                                Compact limit
                                               Fy
                                                141
                                    λr =
                                               F y - Fr                Non compact limit
    Table A-F1.1
                                                162
                                    λr =
                                               F y - Fr
                                                    kc
                                   Plastic capacity
                                             M p= FyZy

                                   Compact section

                                   If        λ ≤λp

                                             M nflb = M p                                                L
    (A-F1-1)
                                   Non compact section

                                   If        λ p < λ ≤ λr
                                                                                                         M
                                                                         λ - λp 
    (A-F1-3)
                                             M nflb = M p - (M p - M r )
                                                                        λ -λ 
                                                                                 
                                                                         r     p
                                   Slender section

                                   If        λ > λr
                                                    20000
                                           F cr =
                                                         λ2
    Table A-F1.1                                    26200 k c
                                           F cr =
                                                          λ2
                                           M nflb = S z F cr ≤ M p                                       N
    (A-F1-4)




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  4.2.4.8           Bending Strength Box and RHS

        Clause/(Eqn)                                              Commentary                              Code    Message


                                 Fabricated Box and Rolled Hollow Sections

                                 Lateral Torsional Buckling

                                 Limiting Buckling Moment


    Table A-F1.1
                                               M r = F y S eff
                                   Seff is the effective section modulus with compression
                                   flange be

                                           L                           Slenderness parameter
    Table A-F1.1                    λ=
                                           r
                                   L, r, S and Mp relate to the axis under consideration


                                            3750 JA                    Compact limit
    Table A-F1.1                    λp=
                                               Mp
                                            57000 JA                   Non compact limit
    TAble A-F1.1                    λr =
                                                  Mr
                                   Compact section

                                   If          λ ≤λp
                                               M nltb = M p                                              A
    (F1-9)
                                   Non compact section

                                   If          λ p < λ ≤ λr

                                                                                λ - λ p 
                                               M nltb = C b  M p - (M p - M r )         
                                                                                 λ - λ  ≤ M p
    (A-F1-2)                                                
                                                                                r p                 B

                                   Slender section

                                   If          λ > λr

                                                      57000 C b JA
                                               F cr =
    Table A-F1.1                                             λS
                                               M nltb = S F cr
                                                                                                         C
    (A-F1-4)




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  4.2.4.8 Bending Strength Box and RHS continued
        Clause/(Eqn)                                              Commentary                              Code    Message


                                   Fabricated Box and Rolled Hollow Sections

                                  Flange Local Buckling

    Table A-F1.1                            b                           Slenderness parameter
                                     λ=
                                            t
                                    b and t relate to the axis under consideration


                                                190                     Compact limit
    Table A-F1.1                     λp=
                                               Fy
                                              238                       Non compact limit
    Table A-F1.1                     λr =
                                                 Fy
                                    Compact section

                                    If          λ ≤λp

                                                M nflb = M p
    (A-F1-1)                                                                                             D
                                    Non compact section

                                    If          λ p < λ ≤ λr

                                                M r = ( F y - F r ) S eff
    Table A-F1.1
                                                                            λ -λp 
                                                M nflb = M p - (M p - M r )                            E
    (A-F1-3)                                                               λ -λ 
                                                                            r p
                                    Slender section

                                    If          λ > λr

                                                       S eff
                                                F cr =       Fy
    Table A-F1.1                                        S
                                                M nflb = S F cr
                                                                                                         F
    (A-F1-4)




                                                                                                                      Cont...




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  4.2.4.8 Bending Strength Box and RHS continued
        Clause/(Eqn)                                              Commentary                                  Code    Message


                                 Fabricated Box and Rolled Hollow Sections

                                 Web Local Buckling

                                           h                           Slenderness parameter
    Table A-F1.1                    λ=
                                           t
                                   h and t relate to the axis under consideration

                                   If            fa
                                                       ≤ 0.125
                                               φb Py
                                                       640  2.75 f a 
    Table B5.1
                                               λp=         1 -       
                                                               φb Py                    Compact limit
                                   else                 Fy           

                                                       191         f  253
                                               λp=          2.33 - a  ≥
    Table B5.1                                                    φb Py 
                                                        Fy               Fy

                                               970           f  253                     Non compact limit
    Table B5.1                      λr =            1 - 0.74 a  ≥
                                                            φb Py 
                                                Fy                 Fy
                                   Compact section

                                   If          λ ≤λp

                                               M nwlb = M p
    (A-F1-1)
                                   Non compact section

                                   If          λ p < λ ≤ λr

                                                                       λ -λp 
                                           M nwlb = M p - (M p - M r )
                                                                                                              G
                                                                              
                                                                      λ -λ 
                                                                            p
    (A-F1-3)                                                             r
                                   Slender section

                                   If          λ > λr

                                               Stiffeners required.                                           H
                                                                                                                     HOVT




                                                                                                                          Cont...




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  4.2.4.9           Bending Strength Tubes

        Clause/(Eqn)                                              Commentary                              Code    Message


                                 Tubular members

                                 Flange Local Buckling

                                         D                             Slenderness parameter
    Table A-F1.1                    λ=
                                         t
                                          2070                         Compact limit
    Table A-F1.1                    λp=
                                           Fy
                                         8970                          Non compact limit
    Table A-F1.1                    λr =
                                           Fy
                                   Compact section

                                   If        λ ≤λp

                                             Mn= M p
    (A-F1-1)                                                                                             D
                                   Non compact section

                                   If        λ p < λ ≤ λr

                                                 600       
                                             Mn=     + F y S
    Table A-F1.1
                                                 λ                                                     E
                                   Slender section

                                   If        λ > λr

                                                      9570
                                             F cr =
    Table A-F1.1                                         λ
                                             M n = S F cr
    (A-F1-4)                                                                                             F

                                   If               l3000
                                             λ>
                                                      Fy                                                         DTRF




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  4.2.4.10 Shear

        Clause/(Eqn)                                                    Commentary                        Code    Message


                                 I Sections

                                 Shear z

    (F2-1)                                   V z = 0.6 Az F y
                                                                                                         A
                                 Shear y
                                 Web plate buckling coefficient is taken assuming that no
                                 stiffeners are required i.e. k = 5

                                              h        418
                                   If             ≤
                                             tw         Fy
                                             V y = 0.6 A y F y
    (F2-1)                                                                                               A
                                              418          h            523
                                   If
                                                       <        ≤
                                                  Fy       tw            Fy
                                                                         418
                                                                          Fy
    (F2-2)                                   V y = 0.6 A y F y                                           B
                                                                          h
                                   If                                     tw
                                              h        523
                                                  >
                                             tw         Fy
    (F2-3)                                             132000 A y                                        C
                                             Vy=                    2
                                                           h
                                                            
                                                            tw 

                                                                                                                      Cont...




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  4.2.4.10 Shear continued
        Clause/(Eqn)                                                   Commentary                            Code    Message


                                    Fabricated Box and Rolled Hollow Sections




                                                 h        418
                                       If             ≤
                                                 tw     Fy
                                                 V y = 0.6 A y F y
    (F2-1)                                      418           h        523
                                                          <        ≤                                         A
                                       If         Fy          tw            Fy
                                                                            418
                                     If                                      Fy
                                              V y = 0.6 A y F y
    (F2-2)                                                                   h
                                                                                                             B
                                                  h        523              tw
                                                      >
                                                 tw        Fy
                                                          132000 A y
                                                 Vy=                    2
    (F2-3)                                                     h                                           C
                                     where                      
                                                                tw 
                                                                                                h       t
                                                          fabricated box            Vy       d-2tf      tw
                                                                                    Vz       b-2tw      tf
                                                          rolled hollow box         Vy       d-4t       t
                                                                                    Vz       b-4t       t




                                   Tubular members


                                                 V y = V z = 0.6 A y F y
                                                                                                             A
    (F2-1)




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  4.2.4.11 Unity Checks

         Clause/(Eqn)                                              Commentary                             Code    Message



                                 All section types
                                 Axial
    E2                                                        fa
                                               U C ax =                for f a compressive
                                                           φ c Pn
    D1                                                        fa
                                               U C ax =               for f a tensile
                                                           φ t Pn
                                 All section types except tubes

                                 Shear
                                                        f vy
                                                UCvy =
    F2                                                 φ v Vy
                                                        f vz
                                                UCvz =
                                                       φ v Vz
                                   If          UCvy or UCvz > 1.0
                                   and          the associated allowable stress = shear yield
                                                                                                                 SHYF
                                   If          UCvy or UCvz > 1.0
                                   and         the associated allowable stress = shear buckle
                                                                                                                 SHBF
                                 Tubular Sections only


                                                        f vy
                                               UCvy =
                                                      φ v Vy
                                                       f vz
                                               UCvz =
                                                      φ v Vz
                                   If         UCvy or UCvz > 1.0
                                                                                                                 SHYF
                                 All section types
                                 Pure Bending
                                                              f by
                                               UCby =
                                                           φ b M ny
                                                              f bz
    F1                                          UCbz =
                                                           φ b M nz




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  4.2.4.12 Combined Stress Unity Checks

        Clause/(Eqn)                                              Commentary                              Code    Message



                                All section types

                                 Axial compression and bending check
                                 This check is strictly only valid if the member is part of a non
                                 sway frame, i.e. k < 1.0, since second order moments are ignored.
                                 If part of a sway frame a hand check is recommended.

                                                                                                                 HAND
                                     If          k y > 1.0 or k z > 1.0

                                                         C my
    (H1-3)                                       B1 y =        ≥ 1.
                                                        1- fa
                                                           Fey
    (H1-3)                                               C mz ≥ 1.0
                                                 B1 z =
                                                        1- f a
                                                           Fez

    (H1-2)                                       M uy = B1y f by                   M uz = B1z f bz


                                     If            f a ≥ 0.2
                                                 φ c Pn

    (H1-1a)                                                   f a + 8  M uy + M uz 
                                                                                        
                                                 UCcb =
                                                            φ c Pn 9  φ b M ny φ b M nz 
                                                                                        
                                     If            f a < 0.2
                                                 φ c Pn

    (H1-1b)                                                    f a +  M uy + M uz 
                                                                                         
                                                 UCcb =
                                                            2 φ c P n  φ b M ny φ b M nz 
                                                                                         




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  4.2.4.12 Combined Stress Unity Checks continued
        Clause/(Eqn)                                              Commentary                              Code    Message



                                All section types

                                 Axial tension and bending check


                                     If           f a ≥ 0.2
                                                 φ t Pn

    (H1-1a)                                                 f a + 8  f by + f bz 
                                                                                       
                                                 UCcb =
                                                           φ t Pn 9  φ b M ny φ b M nz 
                                                                                       
                                     If            f a < 0.2
                                                 φ t Pn

                                                             f a + f by + f bz 
                                                                                       
                                                 UCcb =
                                                           2φ t P n  φ b M ny φ b M nz 
    (H1-1b)
                                                                                       




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  4.2.4.13 Cb - Bending Coefficient

       Clause/(Eqn)                                                 Commentary                                  Message

                              The pure bending coefficient, Cb, is only calculated by the program when
                              LULCF=L. Cb is used in the evaluation of the major axis pure bending
                              allowable stress and is calculated as follows:

                            (1)      If LULCF < L (member length); Cb conservatively defaults to unity.

                            (2)      If LULCF > L; Cb defaults to unity and hand checking/assessment is
                                     recommended.

                            (3)      If LULCF=L and the beam is subject to transverse load and the
                                     maximum bending moment occurs within the beam span;
                                     Cb = 1.0.




                            (4)      If LULCF=L and the beam is not subject to transverse load or is subject
                                     to transverse load with the maximum moment at an end and the peak
                                     span moment Mp, at the point of maximum free moment Md, is less
                                     than that given by interpolation between end moments then;




                                                                                       2
                                                          M1 + 0.3  M1  ≤ 2.3
                                        C b = 1.75 - 1.05              
                                                          M2        M2 
                                       where M1 and M2 are positive for beam sagging.
                                       M1 is the end moment with smaller magnitude
                                       M2 is the end moment with larger magnitude




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  4.2.4.13 Cb - Bending Coefficient continued
        Clause/(Eqn)                                                  Commentary                                Message

                               (5)      If the beam is subject to transverse load and the maximum is at an
                                        end with the peak span moment (Mp) greater than that given by
                                        interpolation between end moments, Cb as calculated in (4) is
                                        unconservative. The SSRC guide (Ref. 17) points out that in such
                                        cases is is conservative to substitute a straight line moment
                                        diagram external to the actual one.

                                        An equivalent uniform moment for the external moment diagram
                                        may be calculated as:




                                            M max +       1  Md 
                                   M eq =           Md =  +
                                                                    M max = M max
                                                                    
                                                          Cb M max 
                                                                                *
                                             Cb                                Cb

                                  where              1        1             1
                                                      *
                                                          =      + M max ≥
                                                    C b       Cb   Md      2.3
                                                     Cb = as for (4)

                                        In this case BEAMST adopts Cb* instead of Cb

                               (6)      The bending coefficient Cb′ deduced by the program and used in
                                        the evaluation of the major axis allowable bending stress for the
                                        combined axial and bending buckle unity check is calculated as
                                        follows:

                                        If the beam is part of a braced frame (Kz ≤ 1.0); Cb′ = 1.0

                                        If the beam is part of sway frame: Cb′ = Cb or Cb* as for (1) to (5)
                                        above




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  4.2.4.14 Cmy , Cmz - Amplification Reduction Factors

        Clause/(Eqn)                                                    Commentary                                 Message

                               The amplification reduction factor, Cm, is only calculated by the program
                               when LULCF = L. Cm is used in the combined axial and bending buckle unity
                               check and is calculated as follows:

                               (1)      If LUNBR < L; Cm conservatively defaults to unity.

                               (2)      If LUNBR > L; Cm defaults to unity and hand checking/assessment is
                                        recommended.

                               The following calculations are performed by the program only if
                               LUNBR = L.

                               (3)      If the beam is part of a sway frame;
                                        Cm = 1 - (0.18fa/Fe′)
                                        In this case BEAMST adopts a constant value of Cm = 0.85

                               (4)      If the beam is subject to transverse load and the maximum bending
                                        moment (Mmax) occurs within the beam span;
                                        Cm = 1.0 (or 0.85 if API)

                               (5)      If the maximum moment (Mmax) occurs at a beam end and the peak
                                        span moment (Mp) is less than that given by interpolation between end
                                        moments;
                                        Cm = 0.6 + 0.4 (M1/M2) ≥ 0.4
                                        where M1, M2 are positive for beam sagging
                                        M1 is the end moment with smaller magnitude
                                        M2 is the end moment with greater magnitude

                               (6)      If the maximum moment (Mmax) occurs at a beam end and the peak
                                        span moment (Mp) is greater than that given by interpolation between
                                        end moments then Cm as calculated in Section 4.1.4.9 (5) is
                                        unconservative. Using a substitute straight line moment diagram
                                        external to the actual one (as in (5) for Cb) an equivalent uniform
                                        moment for the external linear moment diagram may be calculated as
                                        follows:


                                                                                                                   Cont...




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  4.2.4.14 Cmy , Cmz - Amplification Reduction Factors continued


                                                                             Md )           *
                                 M eq = Cm M max + M d = ( Cm +                    M max = Cm M max
                                                                             M max
                                  where                          M d ) ≥ 0.4
                                                  *
                                               Cm = Cm + (
                                                                 M max
                                               Cm =       as for (5) above

                                       In this case Cm* is used instead of Cm in BEAMST

                               (7)      In steps (1) to (6), if both the end moments are of the same sign and
                                        the peak span moment (Mp) is of the opposite sign, Cm is limited to a
                                        maximum of 0.85.




                               (8)      Steps (1) to (7) are repeated for both local bending planes.

                               (9)      If the beam is tubular and of circular section and the check is being
                                        performed against API RP2A (API ALLO check); Cm is limited to a
                                        maximum of 0.85.




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  4.2.5        AISC LRFD MEMBER CHECKS - 3rd Edition

  The equations defined in the following section assume units of Kips and inches.



  4.2.5.1           AISC LRFD Partial Coefficients

         Clause/(Eqn)                                                  Commentary                                 Message


                                  All section types
                              Resistance factors
                 (D1-1)                        φt = 0.90

                 (E2-1)                        φc = 0.85

                 H1.2                          φb = 0.90
                 F2.2                          φv = 0.90

                                Load coefficients
                                BEAMST assumes the appropriate factors have already been applied
                                by the user




  4.2.5.2           Nominal Axial Tension Strength

         Clause/(Eqn)                                             Commentary                              Code    Message



                                All section types
                              Yielding on gross section
    (D1-1)                      P n = F y Ag

                              Limiting slenderness ratio
                                  If           kL                                                        A
    B7                                            ≤ 300
                                  If
                                                r
                                                                                                         B
                                               kL
                                                  > 300                                                          SLRF
                                                r




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  4.2.5.3           Nominal Axial Compressive Strength

         Clause/(Eqn)                                             Commentary                              Code    Message


                                All section types

                              Limiting slenderness ratio

    B7                             If            L                                                               SLRF
                                                k > 200
                                                 r

                                 Tubular members
                                                 Q a = 1.0
                                                 D 0.45E
                                                   >
                                   If            t   Fy                                                          DTRF
                                                 0.11E     D 0.45E
                                                           <  ≤
    (A-B5-13)                      Else If         Fy      t      Fy
                                                       0.038E 2
                                                 Qs =           +
                                                           D      3
                                                       F y( )
                                                            t
                                   Else
                                                 Q s = 1.0


                                                                                                                        Cont...




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  4.2.5.3 Nominal Axial Compressive Strength continued
    Clause/(Eqn)              Commentary                                                                 Code   Message


                                 I section

                                 Web
    Table B5.1                                        h        E
                                  If                    ≤ 1.49
                                                     tw        Fy

                                                     Qaw = 1.0

                                 If                   h        E
                                                        > 1.49
                                                     tw        Fa


    (A-B5-12)                                                        E        0.34    E 
                                                    he = 1.91t            1 −            
                                                                     Fa    (h / t w ) Fa 

    (A-B5-14)                                                       2(h − he )t w
                                                     Qaw = 1 −
                                                                        Aw


                                 Else                Qaw = 1.0



                                                                                                                     Cont...




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    Clause/(Eqn)              Commentary                                                                 Code   Message


                                 I section

                                 Rolled section flange
    Table B5.1                   If           b         E
                                                 ≤ 0.56
                                              tf        Fy
                                                    Qs = 1.0

                                 If                            E         b                E
                                                    0.56            <         < 1.03
                                                               Fy        tf               Fy
                                                                      b Fy
    (A-B5-5)                                        Qs = 1.415 - 0.74( )
                                                                      tf E
                                                     b                  E
                                  If                      ≥ 1.03
                                                     tf            Fy
                                                               0.69 E
                                                    Qs =
                                                                b 2
    (A-B5-6)                                                  F y   
                                                                tf  
                                                                      
                                 Fabricated section flange
                                                    4
                                             kc =                                  0.35 ≤ k c ≤ 0.76
                                                     h
                                                               tw
                                  If                 b        0.64 E
                                                          <
    Table B5.1                                       tf            Fy
                                                                   kc
                                                     Qs = 1.0
                                                     0.64 E             b         1.17 E
                                  If                                <         <
                                                          Fy            tf           Fy
                                                          kc                         kc
                                                                       b   Fy
    (A-B5-7)                                         Qs = 1.415 - 0.65( )
                                                                       tf kc E
                                  If                 b                       E
                                                          ≥ 1.17
                                                     tf         F y kc
                                                          0.90 E k c
                                                    Qs =
    (A-B5-8)                                               b 2 
                                                          Fy   
                                                           tf  
                                                                  




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  4.2.5.3 Nominal Axial Compressive Strength continued
    Clause/(Eqn)              Commentary                                                                 Code   Message



                                 Fabricated Box and Rolled Hollow sections
                                 Web

                                                    t′ = t w         for fabricated box
                                                    t′ = t           for rolled hollow section

                                 If rolled hollow section or constant thickness box


                                 If                  h         E
    Table B5.1                                          ≤ 1.40
                                                     t′        Fy
                                                     Qaw = 1.0

                                 If                  h         E
                                                        > 1.40
                                                     t′        Fa
                                                                     E  0.38 E 
    (A-B5-11)                                        h e =1.91 t        1 -        
                                                                     Fa  (h/t′) Fa 
                                                                   2(h- h e) t ′
                                                    Qaw = 1 -
    (A-B5-14)                                                         Aw
                                 Else               Qaw = 1.0

                                 If fabricated box with different thickness plates

                                  If                  h         E
                                                         ≤ 1.49
    Table B5.1
                                                      t′        Fy
                                                      Qaw = 1.0

                                  If                  h         E
                                                         > 1.49
                                                      t′        Fa
                                                                      E  0.34 E 
                                                      h e =1.91 t        1 -        
    (A-B5-12)                                                         Fa  (h/t′) Fa 

                                                                    2(h- h e
                                                      Qaw = 1 -
    (A-B5-14)                                                           Aw
                                  Else                Qaw = 1.0




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  4.2.5.3 Nominal Axial Compressive Strength continued
    Clause/(Eqn)              Commentary                                                                 Code   Message


                                 Fabricated Box and Rolled Hollow sections

                                 Flange
                                                    t′ = t f         for fabricated box
                                                    t′ = t           for rolled hollow section

                                                    b         E
                                 If                    < 1.40
    Table B5.1                                      t′        Fy
                                                    Qa = Qaw

                                 If                  b         E
                                                        > 1.40
                                                     t′        Fa

                                                                      E  0.38 E 
                                                     b e =1.91 t′        1 -        
    (A-B5-11)                                                         Fa  (b/t′) Fa 

                                                                    2(b′-be) t ′
    (A-B5-14)                                        Qa = Qaw -
                                                                        Af
                                 Else               Qa = Qaw




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  4.2.5.3 Nominal Axial Compressive Strength continued

  Clause/(Eqn)                                                        Commentary                         Code   Message


                                 All section types

                                 Column slenderness parameter
                                              kL     Fy
                                       λc =
  E2-4                                        rπ     E

                                       Q = Qa Qs


                                 Critical stress

                                  If               Qa or Qs ≤ 0


                                                   F cr = 0.0                                           C

                                  If               λ c Q <= 1.5


  (A-B5-15)
                                                             (
                                                   Fcr = Q 0. 658Qλc Fy
                                                                          2
                                                                              )                         D

                                  If               λc Q > 1.5

                                                           0.877                                        E
  (A-B5-16)                                        Fcr =         2   Fy
                                                            λc
                                 Nominal Strength
  (E2-1)                                           Pn = Ag Fcr




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  4.2.5.4           Bending Strength




                                   Compressive flange residual stress

    F1.3                            F r = 10ksi (69 MPa)
                                    F r = 16.5ksi (114 MPa)




  4.2.5.5           Major Axis Bending Strength


                                 All section types

                                   Plastic capacity

                                                 M p = F y Zz ≤ M y
    F1.1
                                                 M y = Fy S


                                   The nominal flexural strength, Mn, is the lowest value
                                   obtained according to the limit states of
                                   Yielding
                                   Lateral Torsional Buckling
                                   Flange Local Buckling
                                   Web Local Buckling



                                                                                                                   Cont...




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  4.2.5.5 Major Axis Bending Strength continued
        Clause/(Eqn)                                              Commentary                              Code    Message


                                 I Sections

                                 Lateral Torsional Buckling

                                                                       Slenderness parameter
    Table A-F1.1                    λ = LULCF
                                             ry
                                                       E               Compact limit
    Table A-F1.1
                                    λ p = 1.76
                                                     Fy
    (F1-8)                                   π      EGJA               Beam buckling factor
                                     X1=
                                         Sx           2
                                                      2
    (F1-9)                               4 Cw  S z                   Beam buckling factor
                                     X2=           
                                          I y  GJ 
                                   Non compact limit



                                              X1     1 + 1 + X 2 (F y - F r )
                                                                             2
    Table A-F1.1                    λr =
                                            F y - Fr
                                   Compact section

                                   If        λ ≤λp

                                             M nltb = M p                                                A
    (A-F1-1)
                                   Non compact section

                                   If        λ p < λ ≤ λr

                                             M r = ( F y - Fr )Sz
    Table A-F1.1
                                                                              λ - λ p 
                                             M nltb = C b  M p - (M p - M r )          
                                                                               λ - λ  ≤ M p
                                                                                                         B
    (A-F1-2)                                              
                                                                               r     p 
                                   Slender section

                                   If        λ > λr

                                                      Cb X 1 2             2       
                                             F cr =                    1+  X 1 X 2 
    Table A-F1.1                                            λ              2λ 
                                                                                 2



                                                                                                         C
                                             M nltb = S z F cr ≤ M p
    (A-F1-4)




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  4.2.5.5 Major Axis Bending Strength continued
        Clause/(Eqn)                                               Commentary                             Code    Message


                                 I Sections

                                 Flange Local Buckling

    Table A-F1.1                           b                           Slenderness parameter
                                    λ=
                                           t
    Table A-F1.1                                      E                Compact limit
                                    λ p = 0.38
                                               Fy
                                                  E
                                    λ r = 0.83                         Non compact limit
    Table A-F1.1                               F y - Fr
                                                               E
                                    λ r = 0.95
                                                     ( F y - F r )/ k c
                                   Compact section

                                   If          λ ≤λp

                                               M nflb = M p                                              D
    (A-F1-1)
                                   Non compact section

                                   If          λ p < λ ≤ λr
                                                                           λ -λp 
                                               M nflb = M p - (M p - M r )
                                                                                                         E
                                                                                  
    (A-F1-3)                                                              λ -λ 
                                                                           r p
                                   Slender section

                                   If          λ > λr

                                                           E
                                           F cr = 0.69
                                                          λ2
    Table A-F1.1                                    0.90E k c
                                           F cr =
                                                        λ2
                                                                                                         F
                                           M nflb = S z F cr ≤ M p
    (A-F1-4)


                                                                                                                      Cont...




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  4.2.5.5 Major Axis Bending Strength continued
        Clause/(Eqn)                                              Commentary                              Code    Message


                                 I Sections

                                 Web Local Buckling

                                    λ = hc                             Slenderness parameter
    Table A-F1.1                           tw
                                   Compact limit
                                                fa
                                   If                 ≤ 0.125
                                             φb Py
    Table B5.1                                          E  2.75 f a 
                                             λ p = 3.76   1 -        
                                   else                 Fy
                                                               φb Py 
                                                                      
                                                        E          f        E
                                             λ p = 1.12    2.33 - a  ≥ 1.49
                                                          
                                                        Fy             
                                                                  φb Py      Fy
    Table B5.1
                                   Non compact limit


                                                     E           f         E
    Table B5.1                      λ r = 5.70          1 - 0.74 a  ≥ 1.49
                                                     Fy
                                                                φb Py 
                                                                            Fy
                                   Compact section

                                   If        λ ≤λp

                                             M nwlb = M p                                                G
    (A-F1-1)
                                   Non compact section

                                   If        λ p < λ ≤ λr
                                                                         λ -λp 
                                             M nwlb = M p - (M p - M r )
                                                                        λ -λ 
                                                                                                        H
    (A-F1-3)                                                             r p
                                   Slender section

                                   If        λ > λr

                                             If rolled section, hand check required.

    Appendix G                                                                                                   HAND
                                             If fabricated section, take smaller of tension flange
                                             yield (Mntfy) and flange local buckling (Mnflb), as
                                             defined below.

                                   If        λ > 260                   Stiffeners required                       HOVT




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  4.2.5.6           Slender Web

        Clause/(Eqn)                                              Commentary                              Code    Message


                                 I Sections

                                 Tension flange yield
                                                      d tw
    G2                                         ar =
                                                      bt f
                                                                             hc          
    (A-G2-3)                                   R PG = 1 -
                                                                  ar         - 5.70 E  ≤ 1.0
                                                             1200 - 300 a r  t w
                                                                                    f cr 
                                                                                          
                                               Re = 1.0                   Hybrid girder factor


                                               M ntfy = S z Re F y                                       J
    (A-G2-1)

                                 Flange local buckling

                                               M nflb = S z R PG Re F cr                                 K
    (A-G2-2)




                                                                                                                      Cont...




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  4.2.5.6 Slender Web continued
        Clause/(Eqn)                                                Commentary                            Code    Message


                                 I Sections
                                 Fcr is computed as follows for the limit states of lateral torsional
                                 buckling and flange local buckling and the lower value used.
                                 Lateral torsional buckling


    (A-G2-7)                                 λ = LULCF                         Slenderness parameter
                                                      rT
                                                                E              Compact limit
    (A-G2-8)                                 λ p = 1.76
                                                               Fy
                                                               E               Non compact limit
    (A-G2-9)                                 λ r = 4.44
                                                        Fy
                                             C PG = 286000 C b (ksi units)
    (A-G2-10)
                                                  = 1970000 C b (MPa units)
                                 Flange local buckling

                                                     b                         Slenderness parameter
    (A-G2-11)                                λ=
                                                    2t f
                                                               E               Compact limit
    (A-G2-12)                                λ p = 0.38
                                                        Fy
                                                           E          Non compact limit
    (A-G2-13)                                λ r = 1.35
                                                        F y / kc
                                             C PG = 26200 k c (ksi units)    C b = 1.0
    (A-G2-14)
                                                    = 180650 K c (MPa units)
                                 Critical stress Fcr

                                   If        λ ≤λp

                                             F cr = F y
    (A-G2-4)
                                   If        λ p < λ ≤ λr
                                                                    λ - λ p 
                                             F cr = C b F y 1 - 0.5         
                                                                     λ - λ  ≤ F y
    (A-G2-5)                                                
                                                                    r p     
                                   If
                                             λ > λr
                                                      C PG
                                             F cr =
    (A-G2-6)
                                                       λ2




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  4.2.5.7           Minor Axis Bending Strength

        Clause/(Eqn)                                              Commentary                              Code    Message


                                 I Sections

                                 Flange Local Buckling

                                                b                                 Slenderness parameter
    Table A-F1.1                    λ = 0.5
                                                tf
    Table A-F1.1                                       E                          Compact limit
                                    λ p = 0.38
                                                      Fy
                                                         E
                                    λ r = 0.83
    Table A-F1.1                                      F y - Fr                    Non compact limit

                                                              E
                                    λ r = 0.95
                                                      ( F y - F r )/ K c
                                   Plastic capacity

                                             M p= FyZy

                                   Compact section

                                   If        λ ≤λp

                                             M nflb = M p                                                 L
    (A-F1-1)
                                   Non compact section

                                   If        λ p < λ ≤ λr
                                                                         λ -λp                          M
                                             M nflb = M p - (M p - M r )
                                                                        λ -λ 
                                                                                
    (A-F1-3)                                                             r p
                                   Slender section

                                   If        λ > λr
                                                     0.69E
                                           F cr =
                                                       λ2
    Table A-F1.1                                     0.90 Ek c
                                           F cr =
                                                        λ2
                                           M nflb = S z F cr ≤ M p                                        N
    (A-F1-4)




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  4.2.5.8           Bending Strength Box and RHS

        Clause/(Eqn)                                              Commentary                              Code    Message


                                 Fabricated Box and Rolled Hollow Sections

                                 Lateral Torsional Buckling

                                 Limiting Buckling Moment


    Table A-F1.1
                                               M r = F y S eff
                                   Seff is the effective section modulus with compression
                                   flange be

                                           L                           Slenderness parameter
    Table A-F1.1                    λ=
                                           r
                                   L, r, S and Mp relate to the axis under consideration

                                            0.13E JA
    Table A-F1.1                    λp=                                Compact limit
                                                  Mp

                                            2.0E JA                    Non compact limit
    TAble A-F1.1                    λr =
                                                 Mr
                                   Compact section
                                   If          λ ≤λp
                                               M nltb = M p                                              A
    (F1-9)
                                   Non compact section

                                   If          λ p < λ ≤ λr

                                                                                λ - λ p 
    (A-F1-2)                                   M nltb = C b  M p - (M p - M r )          
                                                                                 λ - λ  ≤ M p
                                                                                                         B
                                                            
                                                                                 r     p 
                                   Slender section

                                   If          λ > λr

                                                      2.0E C b JA
                                               F cr =
    Table A-F1.1                                           λS
                                               M nltb = S F cr
                                                                                                         C
    (A-F1-4)


                                                                                                                      Cont...




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  4.2.5.8 Bending Strength Box and RHS continued
        Clause/(Eqn)                                              Commentary                              Code    Message


                                   Fabricated Box and Rolled Hollow Sections

                                  Flange Local Buckling

    Table A-F1.1                            b                           Slenderness parameter
                                     λ=
                                            t
                                    b and t relate to the axis under consideration


                                                         E              Compact limit
    Table A-F1.1
                                     λ p = 1.12
                                                         Fy
                                                         E              Non compact limit
    Table A-F1.1
                                     λ r = 1.40
                                                         Fy
                                    Compact section

                                    If          λ ≤λp

                                                M nflb = M p
    (A-F1-1)                                                                                             D
                                    Non compact section

                                    If          λ p < λ ≤ λr

                                                M r = ( F y - F r ) S eff
    Table A-F1.1
                                                                            λ -λp 
                                                M nflb = M p - (M p - M r )
                                                                           λ -λ 
                                                                                                        E
    (A-F1-3)                                                                 r   p

                                    Slender section

                                    If          λ > λr

                                                       S eff
                                                F cr =       Fy
    Table A-F1.1                                        S
                                                M nflb = S F cr
                                                                                                         F
    (A-F1-4)




                                                                                                                      Cont...




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  4.2.5.8 Bending Strength Box and RHS continued

        Clause/(Eqn)                                              Commentary                              Code    Message


                                 Fabricated Box and Rolled Hollow Sections

                                 Web Local Buckling

                                           h                           Slenderness parameter
    Table A-F1.1                    λ=
                                           t
                                   h and t relate to the axis under consideration
                                   Compact limit
                                   If            fa
                                                       ≤ 0.125
                                               φb Py
    Table B5.1
                                                          E  2.75 f a 
                                               λ p = 3.76   1 -        
                                   else
                                                          Fy
                                                                 φb Py 
                                                                        
                                                          E          f        E
                                               λ p = 1.12    2.33 - a  ≥ 1.49
    Table B5.1                                              
                                                          Fy             
                                                                    φb Py      Fy
                                   Non compact limit
                                                       E           f         E
    Table B5.1                      λ r = 5.70            1 - 0.74 a  ≥ 1.49
                                                         
                                                       Fy               
                                                                   φb Py      Fy
                                   Compact section

                                   If          λ ≤λp

                                               M nwlb = M p
    (A-F1-1)
                                   Non compact section

                                   If          λ p < λ ≤ λr
                                                                           λ -λp 
                                               M nwlb = M p - (M p - M r )
                                                                          λ -λ 
                                                                                                        G
    (A-F1-3)                                                               r p
                                   Slender section

                                   If          λ > λr

                                               Stiffeners required.                                      H
                                                                                                                 HOVT




                                                                                                                      Cont...




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  4.2.5.9           Bending Strength Tubes

        Clause/(Eqn)                                              Commentary                              Code    Message


                                 Tubular members

                                 Flange Local Buckling

                                         D                             Slenderness parameter
    Table A-F1.1                    λ=
                                         t
                                          0.071E                       Compact limit
    Table A-F1.1                    λp=
                                            Fy
                                         0.31E                         Non compact limit
    Table A-F1.1                    λr =
                                           Fy
                                   Compact section

                                   If        λ ≤λp

                                             Mn= M p
    (A-F1-1)                                                                                             D
                                   Non compact section

                                   If        λ p < λ ≤ λr

                                                 0.021E       
                                             Mn=        + F y S
    Table A-F1.1
                                                 λ                                                     E
                                   Slender section

                                   If        λ > λr

                                                      0.33E
                                             F cr =
    Table A-F1.1                                          λ
                                             M n = S F cr
    (A-F1-4)                                                                                             F

                                   If               0.45E
                                             λ>
                                                      Fy                                                         DTRF




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  4.2.5.10 Shear

        Clause/(Eqn)                                                  Commentary                          Code    Message


                                 I Sections

                                 Shear z

    (F2-1)                                   V z = 0.6 Az F y
                                                                                                         A
                                 Shear y
                                 Web plate buckling coefficient is taken assuming that no
                                 stiffeners are required i.e. k = 5

                                              h                  E
                                   If             ≤ 2.45
                                             tw           Fy
    (F2-1)
                                             V y = 0.6 A y F y
                                                                                                         A
                                   If                   E            h             E
                                             2.45           <             ≤ 3.07
                                                       Fy            tw            Fy

                                                                          2.45 E / F y
    (F2-2)                                   V y = 0.6 A y F y                                           B
                                                                              h /tw
                                   If         h                  E
                                                  > 3.07
                                             tw            Fy
                                                     4.52 EA y
    (F2-3)                                   Vy=                 2                                       C
                                                        h
                                                         
                                                         tw 


                                                                                                                      Cont...




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  4.2.5.10 Shear continued

        Clause/(Eqn)                                                   Commentary                            Code    Message



                                  Fabricated Box and Rolled Hollow Sections



                                  The shear term is computed for each axis using the appropriate
                                  terms for the axis under consideration

                                                h                  E
                                     If             ≤ 2.45
                                               tw               Fy
    (F2-1)                                     V y = 0.6 A y F y
                                                                                                             A
                                     If                   E            h             E
                                               2.45           <            ≤ 3.07
                                                         Fy        tw               Fy

                                                                           2.45 E / F y
    (F2-2)                                     V y = 0.6 A y F y                                             B
                                                                               h/ t w
                                     If         h                  E
                                                    > 3.07
                                               tw           Fy
                                                       4.52E A y
    (F2-3)                                     Vy=                 2                                         C
                                                          h
                                   where                   
                                                           tw 
                                                                                              h         t
                                                      fabricated box                Vy     d-2tf        tw
                                                                                    Vz     b-2tw        tf
                                                      rolled hollow box             Vy     d-4t         t
                                                                                    Vz     b-4t         t




                                 Tubular members


                                               V y = V z = 0.6 A y F y
                                                                                                             A
    (F2-1)




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  4.2.5.11 Unity Checks

         Clause/(Eqn)                                              Commentary                             Code    Message



                                 All section types
                                 Axial
    E2                                                        fa
                                               U C ax =                for f a compressive
                                                           φ c Pn
    D1                                                        fa
                                               U C ax =                for f a tensile
                                                            φ t Pn
                                 All section types except tubes

                                 Shear
                                                        f vy
                                                UCvy =
    F2
                                                       φ v Vy
                                                        f vz
                                                UCvz =
                                                       φ v Vz
                                   If          UCvy or UCvz > 1.0
                                                                                                                 SHYF
                                   and         the associated allowable stress = shear yield

                                   If
                                               UCvy or UCvz > 1.0                                                SHBF
                                   and         the associated allowable stress = shear buckle

                                 Tubular Sections only


                                                        f vy
                                               UCvy =
                                                      φ v Vy
                                                       f vz
                                               UCvz =
                                                      φ v Vz
                                   If         UCvy or UCvz > 1.0                                                 SHYF+


                                 All section types
                                 Pure Bending
                                                              f by
                                               UCby =
                                                           φ b M ny
                                                              f bz
    F1                                          UCbz =
                                                           φ b M nz




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  4.2.5.12 Combined Stress Unity Checks

        Clause/(Eqn)                                              Commentary                              Code    Message



                                All section types

                                 Axial compression and bending check
                                 This check is strictly only valid if the member is part of a non
                                 sway frame, i.e. k < 1.0, since second order moments are ignored.
                                 If part of a sway frame a hand check is recommended.

                                                                                                                 HAND
                                     If          k y > 1.0 or k z > 1.0
                                                           C my
    (C1-2)                                       B1 y =          ≥ 1.0
                                                          1- fa
                                                             Fey
    (C1-2)                                                 C mz ≥ 1.0
                                                 B1 z =
                                                          1- f a
                                                            Fez

    (C1-1)                                       M uy = B1y f by                   M uz = B1z f bz


                                     If            f a ≥ 0.2
                                                 φ c Pn

    (H1-1a)                                                   f a + 8  M uy + M uz 
                                                                                        
                                                 UCcb =
                                                            φ c Pn 9  φ b M ny φ b M nz 
                                                                                        
                                     If            f a < 0.2
                                                 φ c Pn

    (H1-1b)                                                    f a +  M uy + M uz 
                                                                                         
                                                 UCcb =
                                                            2 φ c P n  φ b M ny φ b M nz 
                                                                                         




                                                                                                                      Cont...




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  4.2.5.12 Combined Stress Unity Checks continued

        Clause/(Eqn)                                              Commentary                              Code     Message



                                All section types

                                 Axial tension and bending check


                                     If           f a ≥ 0.2
                                                 φ t Pn

    (H1-1a)                                                 f a + 8  f by + f bz 
                                                                                       
                                                 UCcb =
                                                           φ t Pn 9  φ b M ny φ b M nz 
                                                                                       
                                     If            f a < 0.2
                                                 φ t Pn

                                                             f a + f by + f bz 
                                                                                       
                                                 UCcb =
                                                           2φ t P n  φ b M ny φ b M nz 
    (H1-1b)
                                                                                       




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  4.2.5.13 Cb - Bending Coefficient

       Clause/(Eqn)                                                 Commentary                                   Message

                              The pure bending coefficient, Cb, is only calculated by the program when
                              LULCF=L. Cb is used in the evaluation of the major axis pure bending
                              allowable stress and is calculated as follows:

                            (1)      If LULCF < L (member length); Cb conservatively defaults to unity.

                            (2)      If LULCF > L; Cb defaults to unity and hand checking/assessment is
                                     recommended.

                            (3)      If LULCF=L and the beam is subject to transverse load and the
                                     maximum bending moment occurs within the beam span;
                                     Cb = 1.0.




                            (4)      If LULCF=L and the beam is not subject to transverse load or is subject
                                     to transverse load with the maximum moment at an end and the peak
                                     span moment Mp, at the point of maximum free moment Md, is less
                                     than that given by interpolation between end moments then;




                                                                                       2
                                                          M1 + 0.3  M1  ≤ 2.3
                                        C b = 1.75 - 1.05              
                                                          M2        M2 

                                       where M1 and M2 are positive for beam sagging.
                                       M1 is the end moment with smaller magnitude
                                       M2 is the end moment with larger magnitude




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  4.2.5.13 Cb - Bending Coefficient continued

        Clause/(Eqn)                                                    Commentary                               Message

                               (5)      If the beam is subject to transverse load and the maximum is at an
                                        end with the peak span moment (Mp) greater than that given by
                                        interpolation between end moments, Cb as calculated in (4) is
                                        unconservative. The SSRC guide (Ref. 17) points out that in such
                                        cases is is conservative to substitute a straight line moment
                                        diagram external to the actual one.
                                        An equivalent uniform moment for the external moment diagram
                                        may be calculated as:




                                                  M max +       1  Md 
                                        M eq =            Md =  +
                                                                          M max = M max
                                                                          
                                                                Cb M max 
                                                                                      *
                                                   Cb                                Cb

                                        where             1         1             1
                                                            *
                                                                =      + M max ≥
                                                          C b       Cb   Md      2.3
                                                          Cb = as for (4)




                                        In this case BEAMST adopts Cb* instead of Cb

                               (6)      The bending coefficient Cb′ deduced by the program and used in
                                        the evaluation of the major axis allowable bending stress for the
                                        combined axial and bending buckle unity check is calculated as
                                        follows:

                                        If the beam is part of a braced frame (Kz ≤ 1.0); Cb′ = 1.0

                                        If the beam is part of sway frame: Cb′ = Cb or Cb* as for (1) to (5)
                                        above




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  4.2.5.14 Cmy , Cmz - Amplification Reduction Factors

        Clause/(Eqn)                                                    Commentary                                 Message

                               The amplification reduction factor, Cm, is only calculated by the program
                               when LULCF = L. Cm is used in the combined axial and bending buckle unity
                               check and is calculated as follows:

                               (1)      If LUNBR < L; Cm conservatively defaults to unity.

                               (2)      If LUNBR > L; Cm defaults to unity and hand checking/assessment is
                                        recommended.

                               The following calculations are performed by the program only if
                               LUNBR = L.

                               (3)      If the beam is part of a sway frame;
                                        Cm = 1 - (0.18fa/Fe′)
                                        In this case BEAMST adopts a constant value of Cm = 0.85

                               (4)      If the beam is subject to transverse load and the maximum bending
                                        moment (Mmax) occurs within the beam span;
                                        Cm = 1.0 (or 0.85 if API)

                               (5)      If the maximum moment (Mmax) occurs at a beam end and the peak
                                        span moment (Mp) is less than that given by interpolation between end
                                        moments;
                                        Cm = 0.6 + 0.4 (M1/M2) ≥ 0.4
                                        where M1, M2 are positive for beam sagging
                                        M1 is the end moment with smaller magnitude
                                        M2 is the end moment with greater magnitude

                               (6)      If the maximum moment (Mmax) occurs at a beam end and the peak
                                        span moment (Mp) is greater than that given by interpolation between
                                        end moments then Cm as calculated in Section 4.1.4.9 (5) is
                                        unconservative. Using a substitute straight line moment diagram
                                        external to the actual one (as in (5) for Cb) an equivalent uniform
                                        moment for the external linear moment diagram may be calculated as
                                        follows:


                                                                                                                   Cont...




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  4.2.5.14 Cmy , Cmz - Amplification Reduction Factors continued


                                                                             Md )           *
                                 M eq = Cm M max + M d = ( Cm +                    M max = Cm M max
                                                                             M max
                                 where                           M d ) ≥ 0.4
                                                  *
                                               Cm = Cm + (
                                                                 M max
                                               Cm =       as for (5) above

                                       In this case Cm* is used instead of Cm in BEAMST

                               (7)      In steps (1) to (6), if both the end moments are of the same sign and
                                        the peak span moment (Mp) is of the opposite sign, Cm is limited to a
                                        maximum of 0.85.




                               (8)      Steps (1) to (7) are repeated for both local bending planes.

                               (9)      If the beam is tubular and of circular section and the check is being
                                        performed against API RP2A (API ALLO check); Cm is limited to a
                                        maximum of 0.85.




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5.     API Code Check

The API command data block is used to request member and joint checking to the API WSD standard (Ref. 2)
and API LRFD standard (Ref. 3) for tubular sections.




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5.1 API Working Stress Design Allowable Member Stress Check (API WSD ALLO)


5.1.1       Overview

The API WSD ALLO header command in BEAMST is used to request member stress checks to API Working
Stress Design recommendations (Ref. 2).                  The strength requirements of API WSD 21st ed (Ref. 26), as
applicable to BEAMST, are the same as those of API WSD 20th ed (Ref. 2). Hence the equations for API 20th
ed given in Section 5 of this manual also apply to API 21st ed.

The API WSD ALLOwable Command exists as a derivative of the AISC allowable stress check data described
in Section 4.2. The stress check follows an identical path to the AISC check except for TUBE elements or other
beam types that have been assigned circular tubular sections in the structural analysis. For such elements the
code checks are performed to the American Petroleum Institute supported design recommendation API RP2A,
which refers to the AISC specification (Ref. 1), but amplifies the clauses particular to tubular members.
Unstiffened tubular local buckling, allowable stresses taking into account inelastic shell buckling, member
buckling and yield strength and unity checks are all performed to the API recommendations as detailed in
Section 5.6.4. Amplification-reduction factors, Cmy and Cmz, are restricted to a maximum of 0.85 unless these
values are user defined. TUBE element effective shear areas are rigidly restricted to one half of the cross-section
area.

The API specification is written in terms of member yield strengths, so a YIELd command must be used to
specify the yield strength. The units of the yield strength must be those of the UNIT command (Section 3.4).

Members may be selected for processing by elements and/or groups. The member section types must be
specified (if not specified in the structural analysis) using DESI commands. Further commands are available for
defining topological characteristic of the members (EFFE, UNBR and ULCF) and specifying members that are
classified as ‘secondary’ (SECO).

Loadcases from the preceding structural analysis may be selected for processing using the CASE command
and/or new loadcases formed from combinations of existing loadcases using the COMB and CMBV commands.
The AISC/API permitted one third increase in allowable stresses for wind extreme loading may be requested on
a loadcase basis using the EXTR command. For seismic conditions, API permits a higher increase in basic
allowable stresses for strength assessment taking member allowable actions to the point of first yield. This may
be requested on a loadcase basis using the QUAK command.

The SECT command may be used to define intermediate points along a member at which member forces are to
be evaluated, checked and reported. These are in addition to results automatically printed at the member end
points and positions of any step change in cross-section properties. For the code checks it is necessary to ensure
the maximum acting bending moment and stresses are evaluated. Since this may not occur at one of the
‘selected’ locations, BEAMST has a SEARch command which causes the moments and stresses to be evaluated
at every L/4 and L/6 (L = beam length) for prismatic and stepped beams respectively. These extra locations are
in addition to those selected and the results at these locations are only presented if they give the maximum
moments or stresses.



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The selection of output reports is made using the PRIN command with the appropriate parameters for the
required reports. The PRIN command is also used to request the various summary reports available and to set
exceedence values for the unity checks. Four summary reports are available.

Summary report 1 is requested with the SUM1 subcommand and gives the highest local buckling, global
buckling and yield unity check values for each element.

Summary report 2 is requested with the PRIN SUM2 command and gives the highest buckle check and all unity
checks at the section with the highest yield combined stress unity check for each element.

Summary report 3 is requested with the PRIN SUM3 command and consists of the highest unity check for each
selected loadcase for each element selected.

Summary report 4 is selected with the PRIN SUM4 command and provides the three worst unity checks for each
selected group, together with the distribution of unity check values. The distribution provides information on the
number of unity checks exceeding an upper limit (default 1.0), less than a lower limit (default 0.5), and the
number in the mid-range.

A complete list of the command set available for the API code checks is given in Table 5.9 and described in
detail in Section 3.4. An example data file is given in Figure 5.20.




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        Command                                                Description                                 Usage     Note
     API WSD ALLO                  API allowable stress header command                                          C

     UNIT                          Units of length and force                                                    C    1
     YIEL                          Yield stress
     GROU                          Groups to be reported
                                                                                                                C    2
     ELEM                          Elements to be reported
     SECT                          Sections to be reported
     SEAR                          Search for maximum forces and stresses
     SECO                          Secondary members
     DESI                          Defines design section properties                                            C    3
     PROF                          Section profiles for use in design
     EFFE                          Effective lengths/factors
     CB                            Pure bending Cb coefficient
     CMY/CMZ                       Amplification reduction factors Cmy/Cmz
     UNBR                          Unbraced lengths of element
     ULCF                          Unbraced length of compression flange
     CASE                          Basic loadcases to be reported
     COMB                          Define a combined loadcase for processing                                    C    4
     CMBV                          Define a combined loadcase for processing
     SELE                          Select/redefine a combined/basic loadcase title
     SPEC                          Basic loadcases from response spectrum analysis
     HARM                          Loadcases originating from harmonic steady state
                                   response analysis
     RENU                          Renumber a ‘basic loadcase’
     EXTR                          Loadcases allowing 33% overstress
     QUAK                          Loadcases with earthquake permitted overstress
     PRIN                          Reports to be printed
     TEXT                          Text or comment command
     TITL                          Redefine global title
     END                           Terminates Command data block                                            C


Usage
C       Compulsory command, but see notes below where applicable.

Notes

1.   See Sections 3.4 and A.12.

2.   At least one GROUP or ELEM command must be included.

3.   Compulsory for non-tubular elements unless Sections have been used in the preceding analyses for all
     elements to be processed.

4.   At least one CASE, COMB or CMBV command must be included.

                                             Table 5.1 API WSD ALLO Commands



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       SYSTEM DATA AREA 100000
       TEXT BEAMST USER MANUAL EXAMPLE STRUCTURE T0847
       JOB POST
       PROJECT MANU
       COMPONENT PILE JACA
       OPTION GOON
       END
       API ED20 ALLO
       *
       * Horizontal plan bracing level -50 m
       *
       GROU 1
       UNIT KN M
       *
       * Change tubular dimensions for one element
       *
       DESI TUB 1.0 0.05 ELEM 131
       *
       * Examine two wave cases
       *
       SELE 10 Extreme Wave 1 + Dead Loads + Topside Loads
       COMB 10 1.0 1 1.0 3 1.0 4
       SELE 11 Extreme Wave 2 + Dead Loads + Topside Loads
       COMB 11 1.0 2 1.0 3 1.0 4
       *
       * Indicate that these loadcases are extreme events
       *
       EXTR 10 11
       *
       * Yield Value Constant for all elements
       *
       YIELD 3.5E05 ELEM ALL
       *
       * Main plan bracing members use effective length
       * coefficient of 0.8
       * Note that the element definition overrides the
       * group definition irrespective of order
       *
       EFFE 0.8 ELEM 105 106
       EFFE 0.8 ELEM 101 TO 104
       EFFE 0.8 ELEM 107 TO 110
       EFFE 1.0 GROU 1
       *
       * Out of plane unbraced lengths need redefining
       *
       UNBR FACT 2.0 1.0 ELEM 105 106
       UNBR LENG 15.0 7.5 ELEM 102 103
       *
       * Override program computed moment amplification RF
       *
       CMY 0.85 ELEM 102 103 105 106
       CMZ 0.85 ELEM 102 103 105 106
       *
       * Check mid-span sections
       *
       SECT 0.5 ELEM ALL
       *
       * Ask explicitly for all reports
       *
       PRIN XCHK PROP UNCK FORC STRE SUNI N MM SUM1 SUM2 SUM3 SUM4 BOTH
       END
       STOP
                                     Figure 5.1 Example of API WSD ALLO data file




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5.1.2       API Allowable Unity Check Report

The unity check report is presented on an element by element basis. The header line displays the element
number, the associated node numbers, the element group number and the units in use. The results are printed for
each of the selected positions (or sections) on the element for each loadcase in turn. The first columns of the
report define the loadcase, section number and position as a ratio of the elements length.

The allowable stresses for axial, shear and bending (in local Y and Z axes) stresses are presented in the next
columns of the report. These are preceded by an alpha numeric descriptor (CODE) that indicates the derivation
of each of the allowable stresses. These descriptors are of the form:

                T.XVYZ or C.XVYZ

T or C defines whether the member is in tension or compression, XVYZ are individual alpha codes which relate
to the axial(X), shear(V), and bending(Y,Z) allowable stresses. These alpha codes specify the design code
clause or equation used to evaluate the allowable stresses and are defined in Table 5.10.

   Stress       Code       Clause                                Description
                  A        AISC B7                               axial tension - B7 satisfied
                  B        AISC B7                               axial tension - B7 violated
                  C        (3.2.2-1)                             axial compression - kL/r < Cc
                   E       (3.2.2-2)                             axial compression - kL/r ≥ Cc

                  B        AISC (F4-2)                           shear buckle
     V            Y        AISC (F4-1)                           shear yield
                  U                                              user defined allowable

                                                                 bending         D 1500
                  C        (3.2.3-1a)                                              ≤
                                                                                 t   fy
                  G        (3.2.2-1b)                            bending       1500 D 3000
                                                                                      < <
                                                                                fy  t   fy
                  H        (3.2.2-1c)                            bending       3000 D
                                                                                   < < 300
                                                                                fy  t
     Y
     Z




                                        Table 5.2 Allowable Stress alphabetic codes


For example, the unity check CODE combination

                C.CYCC




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indicates that the member is in compression and that the following clause/equations were used to derive the
allowable stresses:
      Axial              -    C =       (3.2.2-1)                axial compression - kL/r<Cc
       Shear             -    Y =       AISC (F4-1)              shear yield
                                                                               D 1500
       Bending           -    C =       (3.2.3-1a)               bending         ≤
                                                                               t   fy

The last two characters are always the same for tubular members.

The final columns of the table, header messages, flag all lines of results where any of the checks have failed.
These messages may be summarised as follows

       FAIL          -            Code check failure for this member

       ***           -            Unity check value exceeds unity

       **            -            Unity check value exceeds 0.9

       THKF          -            Wall thickness less than ¼ inch

        DTRF         -            D/t ratio exceeds 300

        YIEL         -            Yield stress greater than 60 ksi

        SLRF         -            Slenderness ratio greater than 200 for a compression member

        SLRW         -            Slenderness ratio greater than 300 for a tension member

        SHYF         -            Shear yielding failure


The format of the detailed unity check report is shown in Figure 5.2 . Examples of the summary reports
available are given in Figure 5.3.




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                                                                                                                                                                                                                                                                  BEAMST User Manual
                                                                                                            ..................................................................................................................................
                                                                                                            . ELEMENT    602 . NODES   6130   6150 . GROUP      6 . MEMBER UNITY CHECK REPORT                   UNITS (N   ,MM )      UNCK
                                                                                                            ....................................................... -------------------------                   -----                 ====
                                                                                                                           /-------------ALLOWABLE STRESSES-------------/         /--------UNITY CHECKS----------/ COMBINED /
                                                                                                            LOAD    SECTION/ CODE    AXIAL    SHEAR   TORSION   BENDING / CMY CMZ /AXIAL   SHEAR   PURE-BEND RSLT/UNITY CHECK/ MESSAGES
                                                                                                            CASE    NO POSN/                                            /         /      FLEX TORS   Y    Z BEND/BUCKL.YIELD/
                                                                                                                           /                                            /         /                              /           /



                                                                                                                                  T.XVYZ       Fa or Ft          Fv            Fvt         Fb     Cmy   Cmz   UCax UCvmax UCTOR UCby UCbz   UCY2 UCCB   UCY

                                                                                                                                                                                                                                       BUCKLE CSR/ UCCSR      /

                                                                                                            (1 line per element section position, plus 1 line for the buckle CSR)



                                                                                                                                                                                     Figure 5.2 Detailed Member Check Report




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                                                                                                            API RP2A(20TH.ED. JUL. 1993)                             MEMBER UNITY CHECK SUMMARY REPORT NO. 1                                           SUM1




                                                                                                                                                                                                                                                                   BEAMST User Manual
                                                                                                            AISC    ( 9TH.ED. JUN. 1989)                             =======================================                                           ==== ====

                                                                                                              ELEM        MAX. LOAD        UNITY COMPONENT VALUES      MAX. LOAD   UNITY COMPONENT VALUES    ELEM KLY/RY KLZ/RZ      NEXT HIGH /
                                                                                                               NO.       BUCKLE CASE       ----------------------     YIELD CASE   ----------------------    POSN ------ ------     YIELD LOAD / MESSAGES
                                                                                                                          CHECK              AXIAL BEND-Y BEND-Z      CHECK          AXIAL BEND-Y BEND-Z                            CHECK CASE / --------
                                                                                                                    1      0.17    8          0.10      0.07          0.28C    6      0.06      0.21         0.00    41.0    41.0   0.27C    8 /
                                                                                                                    2      0.25    8          0.09      0.16          0.46C    8      0.08      0.38         0.90    41.3    41.3   0.42C    5 /
                                                                                                                    3      0.07    5          0.00      0.07          0.22T    8      0.06      0.16         0.90    41.3    41.3   0.21T    8 /
                                                                                                                    4      0.14    5          0.00      0.14          0.39T    5      0.06      0.33         0.90    41.3    41.3   0.36T    8 /
                                                                                                                    5      0.57    5          0.13      0.45          0.90C    5      0.10      0.79         1.00    62.5    62.5   0.83C    8 /
                                                                                                                    6      0.20    5          0.00      0.20          0.97T    8      0.57      0.40         1.00   102.0   102.0   0.92T    8 /
                                                                                                                    7      1.72    8          0.67      1.05          1.29C    5      0.28      1.01         0.00   103.8   103.8   1.26C    8 / FAIL




                                                                                                            API RP2A(20TH.ED. JUL. 1993)                             MEMBER UNITY CHECK SUMMARY REPORT NO. 3                                           SUM3
                                                                                                            AISC    ( 9TH.ED. JUN. 1989)                             =======================================                                           ==== ====

                                                                                                              ELEM       NODE1   NODE2      GROUP   WORST   LOAD    ELEM ------------UNITY CHECKS FOR    REQUESTED LOAD CASES---------------------------------
                                                                                                                                                    UN CK   CASE    POSN CASES     5      6       7          8
                                                                                                                    1        1         3        1   0.28Y      6    0.00       0.26 C 0.28 C 0.10 C      0.27 C
                                                                                                                    2        2         4        1   0.46Y      8    0.90       0.42 C 0.26 C 0.42 C      0.46 C
                                                                                                                    3        5         3        2   0.22Y      8    0.90       0.21 T 0.20 T 0.13 T      0.22 T
                                                                                                                    4        6         4        2   0.39Y      5    0.90       0.39 T 0.31 T 0.30 T      0.36 T
                                                                                                                    5        3         4        3   0.90Y      5    1.00       0.90 C 0.81 C 0.49 C      0.83 C
                                                                                                                    6        2         3        4   0.97Y      8    1.00       0.89 T 0.88 T 0.49 T      0.97 T
                                                                                                                    7        4         5        4   1.72B      8               1.32 B 1.22 B 0.90 B      1.72 B




                                                                                                            API RP2A(20TH.ED. JUL. 1993)                             MEMBER UNITY CHECK SUMMARY REPORT NO. 4                                           SUM4
                                                                                                            AISC    ( 9TH.ED. JUN. 1989)                             =======================================                                           ==== ====




                                                                                                                                                                                                                                                                       API Member Checks
                                                                                                                                              THREE WORST UNITY CHECKS
                                                                                                                                              ------------------------                                         NUMBERS OF ELEMENTS IN EACH GROUP
                                                                                                                        ----------FIRST------- ---------SECOND-------           ----------THIRD-------       ----------- Y I E L D --- --- B U C K L E ------
                                                                                                            GROUP         ELEM     UNITY LOAD / ELEM       UNITY LOAD         / ELEM       UNITY LOAD    /   TOTAL    GE     GE     LT     GE     GE      LT
                                                                                                                                   CHECK CASE /            CHECK CASE         /            CHECK CASE    /           1.00   0.50   0.50   1.00   0.50    0.50
                                                                                                                1            2     0.46C     8 /     2     0.42C     5        /      2     0.42C     7   /       2       0      0      2      0      0       2
                                                                                                                4            7     1.72B     8 /     7     1.32B     5        /      7     1.29C     5   /       2       1      1      0      1      0       1
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                                                                                                                3            5     0.90C     5 /     5     0.83C     8        /      5     0.81C     6   /       1       0      1      0      0      1       0
                                                                                                                2            4     0.39T     5 /     4     0.36T     8        /      4     0.33T     5   /       2       0      0      2      0      0       2



                                                                                                                                                                        Figure 5.3 Example of API Allowable Summary Reports
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5.1.3           Nomenclature


5.1.3.1             Dimensional




D          =        tube outside diameter
t          =        thickness
k          =        effective length factor
L          =        unbraced length of member
r          =        radius of gyration


5.1.3.2             Acting Section Forces and Stresses


N          =        axial force
Nely,z =            Euler force in y or z direction
My,z        =       bending moment about y or z
fa         =        axial stress
fby,fbz =           bending stresses about y and z
fv          =       maximum shear stress
fvm         =       von Mises stress
Mo         =        maximum free bending moment from all sections examined along member




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5.1.3.3           Allowable Stresses and Unity Checks



            fy          =       yield stress
            Fxe         =       elastic local buckling stress
            Fxc         =       inelastic local buckling stress
            Fa          =       allowable axial compressive stress
            Ft          =       allowable axial tensile stress
            Fb          =       allowable bending stress
            Fv          =       allowable flexural shear stress
            Fvt         =       allowable torsional shear stress
            Fe          =       euler stress divided by a factor of safety
            UCax        =       axial unity check
            UCvmax =            flexural shear unity check
            UCTOR       =       torsional shear unity check
            UCby        =       pure bending check about y axis
            UCbz        =       pure bending check about z axis
            UCCB        =       combined axial compression and bending buckle check
            UCY         =       combined axial and bending yield unity check member
            UCCSR       =       upper bound member buckling unity check


5.1.3.4           Parameters



            E               =    Youngs modulus
            Cmy,Cmz         =    moment amplification reduction factors. See 4.1.4.10




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5.1.4       API Allowable Stresses and Unity Checks


5.1.4.1         API Allowable Stress Increase


Working stress design codes permit allowable stresses to be increased above those appropriate to Ordinary
conditions for other conditions. The percentage increase in allowable stresses to be applied to the allowable
stresses quoted herein for different loadcase types are:

                                                                              API
                                           type                  axial/                 shear
                                                                 bending

                                   Ordinary                         0.0                    0.0

                                   Extreme                        33.33                   33.33

                                   Earthquake                     70.00                   44.34



The following section describes the computations undertaken for tubular sections only (with two exceptions, see
below). For non-tubular members being checked to API reference should be made to Section 4.1.4, Allowable
Stresses and Unity Checks for the AISC code. Note that the combined Unity Checks for non-tubular members
utilise modified parameters based upon API recommendations. See Notes 1 and 2 in Section 5.6.4.7.




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5.1.4.2         Tension

     Clause/(Eqn)                                               Commentary                                                          Code   Message




              (3.2.1-1)      Allowable Stress                                                                                              SLRW
                                            Ft = 0.6fy


                             Limiting slenderness ratio
                                If           kL       ............................ ............. .....................                A
                                                ≤ 300
                                              r
             AISC B7            If           kL       ............................ ............. .....................                 B
                                                > 300
                                              r


5.1.4.3         Compression

     Clause/(Eqn)                                               Commentary                                                          Code   Message




             AISC B7            If              L               .............. ............. ............. ......................            SLRF
                                             k > 200
                                                r
             3.2.2b             If           D                  .............. ............. ............. ......................            DTRF
                                                 > 300
                                              t
             C3.2               If                1             .............. ............. ............. ......................            THKF
                                             t < in
                                                  4
             C3.2               If           f y > 60 ksi       .............. ............. ............. ......................            YIEL


                                If           D
                                                ≤ 60
                                             t
             (3.2.2-4)                       Fxc = f y

                                If                   D
                                            60 <       < 300
                                                     t
             (3.2.2-4)                                              D 
                                            Fxc = f y 1.64 - 0.23 4   
                                                      
                                                                     t  
                                                                           
             (3.2.2-3)                              0.6 Et
                                            Fxe =
                                                       D
                                             1
             3.2.2b                         fy = min(Fxc , Fxe)




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5.1.4.3 Compression continued
     Clause/(Eqn)                                              Commentary                               Code   Message




         3.2.2a                                          2π 2 E
                                            Cc =
                                                          fy
                                 If          kL
                                                < Cc
                                              r
                                                    (kL/r )2                                            C
                                                    1-       2  f y
         (3.2.2-1)                                     2 Cc 
                                             Fa =
                                                  5 3(kL / r ) (kL/r )3
                                                   +           -     3
                                                  3 8 Cc         8 Cc
                                 If          kL
                                                 ≥C c
                                              r
         (3.2.2-2)                                 12π 2 E                                                E
                                             Fa =
                                                  23(k L /r )2


5.1.4.4         Bending

     Clause/(Eqn)                                              Commentary                               Code   Message




       (3.2.3-1a)               If          D 1500                                                         C
                                               ≤
                                             t    fy
                                            Fb = 0.75 f y

                                If          1500         D 3000                                            G
                                                    <      <
                                              fy         t   fy

      (3.2.3-1b)                                             f y D
                                            Fb = 0.84 - 1.74
                                                               Et 
                                                                     fy
                                                                  
                                If          3000         D                                                 H
                                                     <     < 300
                                              fy         t

       (3.2.3-1c)                                             f y D
                                             Fb = 0.72 - 0.58
                                                                Et 
                                                                      fy
                                                                   



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5.1.4.5           Shear

     Clause/(Eqn)                                              Commentary                                         Code       Message




                                  Beam Shear

        (3.2.4-2)                              Fv = 0.4 f y                                                           Y

                                  Torsional Shear
        (3.2.4-4)                              Fvt = 0.4f y



5.1.4.6           Unity Checks

     Clause/(Eqn)            Code                                        Commentary                                          Message




                                         Axial
          3.2.2                                                       fa
                                                           UCax =        f a compressive
                                                                      Fa
          3.2.1                                                       fa
                                                           UCax =        f a tensile
                                                                      Ft
                                         Shear
         3.2.4a                                                    f vmax
                                                           UCvmax =
                                                                     Fv
                                          If              UCvmax > 1.0 .............. ............. ............. ........    SHYF


         3.2.4b                                                          f vt
                                                           UCTOR =
                                                                         Fvt
                                         Pure Bending

          3.2.3                                                       f by
                                                           UCby =
                                                                       F
                                                                      f bz
                                                           UCbz =
                                                                       F
                                                                         (f 2 + f 2 )
                                                                            by    bz
                                                          UCY 2 =
                                                                                Fb




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5.1.4.7         Combined Stresses

     Clause/(Eqn)                                              Commentary                                   Code   Message




                              Axial compression and bending buckle check

                                                                           2                            2
                                              Cmyf by   Cmzf bz 
                                                           1      +             1     
      (3.3.1-4)                        f a +  ( 1 -(f a / Fey) )   ( 1 -(f a / Fez) ) 
                                 UCCB=
                                       Fa                          Fb
                                             = UCB1 + UCB 2
                                               1
                                              Fe =        1.0 Fe         for ordinary loadcases
                                                    =     1.33 Fe        for extreme/earthquake
                                                    =     1.7 Fe         for earthquake

                                 where                12π 2 E
                                               Fe =
                                                     23(kL/r)2
                                                     1
                                If            f a > Fe
                                              UCB = 99.99 indicating elastic buckling
                               Note If non-tubular members are checked to API
                                                         1
                               the computed values of Fe above are utilised in the
                               appropriate AISC check. See 4.1.4.7.

                               For axial tension and bending buckle check
                                             UCB1 is set = 0.0

                               Combined axial and bending yield check

                                                              2      2
                                                     f a + (f by + f bz )
                                              UCY =
      (3.3.1-2)
                                                    αfy         Fb
                                                  = UCY1 + UCY 2
                              where fby , fbz are compressive or tensile bending stresses
                              as appropriate to the axial stress.
                                              α = 0.6 for ordinary loadcases
                                                   = 0.8 for extreme
                                                   = 1.02 for earthquake
                                Note If non-tubular members are checked to API the computed
                                value of α above is utilised in the appropriate AISC check.




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5.1.4.7 Combined Stresses continued

     Clause/(Eqn)                                              Commentary                               Code   Message




                              Buckle CSR check

                                                     UCCSR

                                This uses the same equation (3.3.1-4) as the axial compression
                                and bending buckle check but utilises the maximum stresses and
                                the minimum member properties occurring along the member in
                                order to compute an upper bound buckle check. It should be
                                noted that this check often results in high utilisation ratios which
                                may not occur in practice, but indicates a need to undertake a
                                more rigorous hand analysis of the member.




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5.1.5       Spectral Loadcases

In response spectrum analysis using modal superposition (Ref. 12) the structure displacements and forces
calculated represent estimated maxima and are, in general, unsigned (positive).

For the purpose of checking members to API a series of worst case static-spectral loadcase permutations must be
generated from the member unsigned spectral and signed static end forces.

The signs applied to the spectral end forces when generating a series of worst cases depends upon the unity
check being considered and details of the signs adopted/deduced are given in this section.

In BEAMST it is assumed that unity checks can be performed by considering the combination of static and
dynamic conditions to be purely a static condition.



5.1.5.1         Torsional Effects


The maximum torsional spectral load contribution at each beam section position is deduced in a similar manner
to the axial load contribution in 5.1.5.2.



5.1.5.2    Axial Unity Check and the Axial Component of Combined Stress Buckle and
Yield Unity Checks


The maximum axial spectral load contribution at each beam section position is calculated by assuming that the
spectral axial load distribution is linear with both member end loads having the same sign. The sign adopted for
these member spectral end loads is normally assumed to be of the same sign as the static axial load (if it exists).
In cases where the static loadcase is tensile it is possible that reversing the sign of the spectral case may produce
a net compressive load and, hence, a more onerous utilisation (since buckling may become a problem). Under
these conditions, the checks are repeated with the spectral axial stresses reversed with respect to the static case,
and the combination producing the highest utilisation of both conditions is reported. The sign adopted may be
ascertained from the utilisation code reported.

As in all checks performed by BEAMST, zero axial stress is treated as compressive (-ve sign, ASAS
convention).


5.1.5.3         Local Axes Shear Unity Checks and Maximum Shear Unity Check for Tubular
Sections


In order to be able to generate mid-member stresses an equivalent member spectral loading is required.
BEAMST assumes that the spectral loading consists of a linearly varying inertia loading on the member acting in
a rigid fashion (ie the load consists of that due to pure translation and rotation of the member). This inertia
loading is calculated by ‘balancing’ it against the member signed spectral end forces (shears and moments).




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For each local bending plane there are sixteen unique signed spectral end force (shears and moments)
expansions/cases of which eight are symmetric, but of opposite sign, to the remaining eight. Each of these
sixteen signed spectral expansions is denoted by a single alphabetic letter code in BEAMST in the range A-P as
shown in Figure 5.4. For spectral loadcases only eight of the sixteen possible expansions need theoretically be
considered but for static-spectral summations all sixteen have to be taken into account.

The Shear Unity Checks are maximised by adopting the static-spectral signed expansion which maximises the
total acting shear at each beam section position. For tubular sections the combination of static-spectral
expansions which maximises the resultant acting shear on the cross section and the Maximum Shear Unity
Check.

For a linearly varying inertia load it can be deduced a priori that the following spectral expansions are critical for
the Shear Unity Checks for static-spectral summation.

                          beam section position (α)                        local axes spectral expansions

                                         0 < α < 1/3                                         E or L

                                         1/3 < α < 2/3                                       D or M

                                         2/3 < α < 1                                         B or O




5.1.5.4     Local Axes Pure Bending Unity Checks and Bending Components of Combined
Stresses Yield Unity Check


For bending unity checks and unity check bending components it is necessary to determine the spectral
expansion which maximises the ratio of acting to allowable stress as opposed to simply maximising the acting
bending stress. In general this is necessary because the bending allowable may be a function of Cb which itself
is a function of the signs and relative magnitudes of the member total end forces.

BEAMST investigates each of the sixteen signed spectral expansions shown in Figure 5.4 for both of the local
axes bending planes for each beam section position being considered and reports the critical expansions at each
section. For tubular sections being checked to AISC where it is necessary to calculate bending resultants at each
beam section the spectral expansions which maximise the ratio of local axes bending stress to allowable are
determined (as these local axes acting bending stresses are the ones which also maximise the acting bending
resultants and hence maximise the yield unity check components).

For static-spectral summation it is theoretically necessary to investigate all sixteen spectral expansions for the
worst cases but for loadcases composed of expanded spectral contributions only, the following generalisations
can be made:

(i).     The acting bending stress at each beam section position is maximised by adopting the spectral expansion
         defined by end moments of the same sign and end shears of opposite signs.

(ii).    Where the allowable stress is a function of Cb, the allowable will be minimised by adopting the expansion
         with spectral end moments of the same sign as this minimises Cb.




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These two generalisations taken together infer spectral expansions A or P (Figure 5.4)


5.1.5.5         Unity Check Report for Shear, Pure Bending and Yield Unity Checks


The Unity Check Report for a spectral or a static-spectral summation comprises four separate reports:

       Highest Shear Unity Checks

       Highest Pure Bending Unity Checks

       Highest Yield Unity Checks

       Highest Buckle Unity Checks


The unity checks of direct interest to the user when checking against a design code are the shear checks in the
Highest Shear Unity Checks, the pure bend checks in the Highest Pure Bending Unity Checks etc. For the
Highest Shear, Pure Bending and Yield Reports, the worst unity check at each beam section position is reported
together with the spectral expansions in the local Y and Z which maximise the respective checks (as described in
5.1.5.1-5.1.5.4 above) appended to the loadcase number. In addition to the unity checks of direct interest in each
report all remaining unity checks are calculated for the spectral expansions quoted and are reported. This allows
users to obtain an overall picture of stress state in the beam at the section under consideration for the spectral
expansions cited. The combined buckle unity checks in these reports and the Highest Buckle Unity Check
Report are explained in 5.1.5.6 below.


5.1.5.6         Combined Stress Buckle Unity Check


As for the pure bending and yield unity check it is necessary to determine which spectral expansions maximise
the bending components of the buckle unity check defined by ratio of ‘equivalent uniform bending’ stress to
minimum allowable. This is necessary because the amplification-reduction factor Cm used to convert maximum
acting bending stress to an equivalent uniform bending stress is a function of the signs and relative magnitudes
of the member total end forces (moments).

BEAMST investigates all sixteen spectral expansions determining for each expansion the maximum bending
stress and minimum allowable stress occurring anywhere along the beam and the buckle unity check bending
component for the bending plane being considered. Over all sixteen expansions, those which maximise the
bending components in each of the local bending planes are used in the final buckle check and are reported in the
Highest Buckle Unity Check Report.

An example of the report generated for combined static and dynamic loadcases is given in Figure 5.5.




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                                                                 end1                         end2
                                  Spectral
                                  Expansion
                                                            shear       moment        shear       moment


                                        A                    +            +            -                +

                                        B                    +            +            -                -

                                        C                    +            +            +                +

                                        D                    +            +            +                -

                                        E                    +            -            -                +

                                        F                    +            -            -                -

                                        G                    +            -            +                +

                                        H                    +            -            +                -

                                        I                    -            +            -                +

                                        J                    -            +            -                -

                                        K                    -            +            +                +

                                        L                    -            +            +                -

                                        M                    -            -            -                +

                                        N                    -            -            -                -

                                        O                    -            -            +                +

                                        P                    -            -            +                -




     Figure 5.4 Automatic signed Spectral Expansion codes for Member Checks and the respective signs
                                      applied for bending in the local Y-Y/Z-Z planes


Notes

1.    Beam end spectral torque signs are chosen to be identical with their respective static components in static-
      spectral loadcases.

2.    Beam end spectral torque signs adopted for evaluation of spectral stresses at intermediate beam section
      positions are chosen to be identical with their respective static stress components at the section under
      consideration.




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   Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.   .................................................................................................................................




                                                                                                                                                                                                                                                BEAMST User Manual
                                                                                                           . ELEMENT    101 . NODES   1110   1120 . GROUP      1 . MEMBER UNITY CHECK REPORT                   UNITS (N   ,MM )      UNCK
                                                                                                           ....................................................... -------------------------                   -----                 ====
                                                                                                                          /-------------ALLOWABLE STRESSES--------------/         /--------UNITY CHECKS----------/ COMBINED /
                                                                                                            LOAD   SECTION/ CODE    AXIAL     SHEAR   TORSION   BENDING / CMY CMZ /AXIAL   SHEAR   PURE-BEND RSLT/UNITY CHECK/ MESSAGES
                                                                                                            CASE   NO POSN/                                             /         /      FLEX TORS   Y    Z BEND/BUCKL.YIELD/
                                                                                                                          /                                             /         /                              /           /
                                                                                                              10    1 0.00/C.CYCC   254.15,   186.67,   186.67,   344.61/0.61 0.40/ 0.06 0.03 0.00 0.06 0.19 0.20/ 0.15 0.25 /
                                                                                                              10    2 0.50/C.CYCC   254.15,   186.67,   186.67,   344.61/0.61 0.40/ 0.06 0.02 0.00 0.03 0.00 0.03/ 0.08 0.08 /
                                                                                                              10    3 1.00/C.CYCC   254.15,   186.67,   186.67,   344.61/0.61 0.40/ 0.06 0.01 0.00 0.04 0.10 0.10/ 0.11 0.16 /
                                                                                                              10          /                                             /         /                    BUCKLE CSR/ 0.15      /
                                                                                                                          /                                             /         /                              /           /
                                                                                                                   -----------------HIGHEST SHEAR UNITY CHECKS-------------PLUS---------ASSOCIATED UNITY CHECKS--------------------
                                                                                                              11AI 1 0.00/T.AYCC    357.00,   140.00,   202.07,   439.38/0.82 0.85/ 0.05 0.03 0.00 0.04 0.16 0.16/ 0.13 0.21 /
                                                                                                              11MD 2 0.50/T.AYCC    357.00,   140.00,   202.07,   439.38/0.40 0.60/ 0.05 0.04 0.00 0.01 0.08 0.08/ 0.10 0.12 /
                                                                                                              11CA 3 1.00/T.AYCC    357.00,   140.00,   202.07,   439.38/0.85 0.85/ 0.05 0.01 0.00 0.02 0.08 0.08/ 0.16 0.13 /
                                                                                                                          /                                             /         /                              /           /
                                                                                                                   ---------------HIGHEST PURE-BEND UNITY CHECKS-----------PLUS---------ASSOCIATED UNITY CHECKS--------------------
                                                                                                              11AE 1 0.00/T.AYCC    357.00,   140.00,   202.07,   439.38/0.85 0.41/ 0.05 0.03 0.00 0.04 0.17 0.17/ 0.08 0.22 /
                                                                                                              11AP 2 0.50/T.AYCC    357.00,   140.00,   202.07,   439.38/0.85 0.85/ 0.05 0.02 0.00 0.04 0.18 0.19/ 0.16 0.23 /
                                                                                                              11BA 3 1.00/T.AYCC    357.00,   140.00,   202.07,   439.38/0.76 0.85/ 0.05 0.01 0.00 0.02 0.08 0.08/ 0.16 0.13 /
                                                                                                                          /                                             /         /                              /           /
                                                                                                                   ---------HIGHEST COMBINED STRESS YIELD UNITY CHECKS-----PLUS---------ASSOCIATED UNITY CHECKS--------------------
                                                                                                              11AE 1 0.00/T.AYCC    357.00,   140.00,   202.07,   439.38/0.85 0.41/ 0.05 0.03 0.00 0.04 0.17 0.17/ 0.08 0.22 /
                                                                                                              11AP 2 0.50/T.AYCC    357.00,   140.00,   202.07,   439.38/0.85 0.85/ 0.05 0.02 0.00 0.04 0.18 0.19/ 0.16 0.23 /
                                                                                                              11BA 3 1.00/T.AYCC    357.00,   140.00,   202.07,   439.38/0.76 0.85/ 0.05 0.01 0.00 0.02 0.08 0.08/ 0.16 0.13 /

                                                                                                           ..................................................................................................................................
                                                                                                           . ELEMENT    101 . NODES   1110   1120 . GROUP      1 . MEMBER UNITY CHECK REPORT                   UNITS (N   ,MM )      UNCK
                                                                                                           ....................................................... -------------------------                   -----                 ====
                                                                                                                   -----------------------------------HIGHEST COMBINED STRESS BUCKLE UNITY CHECK-----------------------------------
                                                                                                                          /-----MIN. ALLOWABLE COMPRESSIVE STRESSES-----/    /-----MAX. ACTING STRESSES-----/                /
                                                                                                            LOAD   SECTION/ CODE    AXIAL    BEND-Y    BEND-Z     FEY   / CMY/   AXIAL     BEND-Y    BEND-Z /--BUCKLE CHECK--/ MESSAGES
                                                                                                            CASE   NO POSN/          POSN    POSN-Y    POSN-Z     FEZ   / CMZ/    POSN     POSN-Y    POSN-Z /AXIAL BEND UNCK /




                                                                                                                                                                                                                                                    API Member Checks
                                                                                                              11AP        /C.C-CC   324.04,   439.38,   439.38, 2060.28/0.85/      0.00C,    16.62,    80.50/ 0.00 0.16 0.16 /
                                                                                                              11AP        /           1.00,     0.00,     0.00, 2060.28/0.85/      0.00 ,     0.50,     0.50/                /
                                                                                                                   ----------------------------------------------------------------------------------------------------------------
                                                                                                                          /                                             /              /                             /           /
                                                                                                                                                                                                                 -------------
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                                                                                                                                                                                                           MAXIMA 0.16 0.25
                                                                                                                                                                                                            CASES    11   10

                                                                                                                                                           Figure 5.5 Spectral Expansion Report
BEAMST User Manual                                                                      API Nominal Load Joint Checks




     5.2 API Nominal Load Check (API WSD JOIN)


     5.2.1        Overview

     The API WSD JOIN command requests that a joint check be performed. The check differs from the
     punching shear check as defined in revision 2 of the 21st edition of the API’s RP 2A-WSD Clause 4.3
     or later editions, this superceeds earlier NOMI or PUNC checks required for earlier versions.

     The joints may consist of TUBE elements and/or other beam types that have been assigned tubular
     sections in the structural analysis.

     Joints for the API check post-processing are selected using the JOINt command in BEAMST which
     specifies the node numbers at joint positions. All joints are assumed ‘simple’. Elements may be
     excluded from the joint punching shear check using the SECOndary command.

     Joints are automatically classed as a combination of K, T or Y depending on the loading applied. A
     maximum of 5 types per brace member is permitted; results are produced for each brace forming the
     joint.

     1.    The chord member is the member with the greatest outside diameter.

     2.    If two or more potential chord members have equal diameters; BEAMST will consider the two
           with the largest wall thicknesses and for each loadcase selected will check the one most heavily
           stressed against all brace members.

     3.    In the case of two or more potential chord members with equal diameters and wall thicknesses, the
           first two encountered as shown in the Cross Check Report will be considered.

     4.    If the CHORd command is used to specify a chord member, this alone will be considered. If two
           chords are specified, the most heavily stressed chord will be checked against all brace members for
           each loadcase selected.

     5.    All members not selected as chord members are treated as brace members (unless defined as
           secondary), with each brace-chord pair being checked.


     A joint is formed of a maximum of 3 nodes connected by valid chord members. These nodes must
     form a straight line and must be within a distance of D/4. This process is performed automatically,
     however, if required can be specified manually using the CHOR command.

     All valid members that form the joing are allocated to a number of planes. A tolerance of +/- 15° exists
     to identify braces belonging to the same plane. Each member in each plane is then assessed to obtain
     unity factors for axial and bending forces in addition to an interaction ratio to account for the
     combination of such forces.




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BEAMST User Manual                                                                      API Nominal Load Joint Checks


     Beamst automatically decides on the type of joint by assessing the balancing axial force in each valid
     brace member forming the joint. Firstly any load paths that form a K joint are assessed; it can be the
     case that in a traditional KT Joint shape that this will result in 2 K joints with different gaps between
     members.

     All forces that transfer acrross the joint to an opposite brace will form X Joints; again it is possible that
     multiple X Joint load paths co-exist within one joint; in this case these will be calculated with the
     appropriate offsets. Finally, any shear that exists in a jont will be accounted for by the provision of a Y
     joint type. The final joint capacity will be calculated using the proportion of axial load that is allocated
     to each of the joint types.

     BEAMST will only check selected joints in which two or more incident members are tubular and of
     circular section. All other selected joints are automatically bypassed.

     The user may override these classifications using the TYPE and CHOR commands. Interpolated joint
     classifications may be defined using the TYPE command. For K joints a gap dimension appropriate to
     the joint may be specified in the TYPE command. A default gap dimension may be specified using the
     GAPD command.

     The detailed joint check report provides information on joint geometric parameters, type, acting chord
     and brace stresses, punching shear, Qf and Qu factors, punching shear allowable(s), and unity checks.
     This may be requested using the PRINt UNCK command. The maximum unity check is flagged for
     ease of reference. When an interpolatory joint type classification is being employed two sets of
     punching shear allowables are reported, one for each joint classification type and these pertain to joints
     classified as 100% of the respective joint types.

     Summary report 3 comprises the highest unity check for each selected loadcase for each joint.

     Summary report 4 comprises the three worst unity checks for each selected joint, together with the
     distribution of unity check values. This distribution provides information on the number of unity
     checks exceeding an upper limit (default 1.0), less than a lower limit (default 0.5), and the number in
     the mid range.

     BEAMST commands applicable to the API punching stress command are given in Table 5.7 and are
     described in detail in Section 3.4. An example data file is given in Figure 5.15.




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BEAMST User Manual                                                                      API Nominal Load Joint Checks



            Command                                                 Description                          Usage    Note
          API WSD JOIN                  API joint check header command                                     C

          UNIT                          Units of length and force                                          C       1
          YIEL                          Yield stress

          JOIN                          Joint numbers to be reported
          TYPE                          Joint type and brace element definition
          CHOR                          Chord elements at a joint
          SECO                          Secondary members to be ignored in checks

          DESI                          Defines design section properties
          GAPD                          Define default gap dimension
          PROF                          Section profiles for use in design
          STUB                          Tubular member end stub dimensions

          CASE                          Basic loadcases
          COMB                          Define a combined loadcase for processing
                                                                                                           C       2
          CMBV                          Define a combined loadcase for processing
          SELE                          Select/redefine a combined/basic loadcase title
          SPEC                          Loadcases originating from response spectrum analysis
          RENU                          Renumber a basic loadcase
          QUAK                          Loadcases with earthquake permitted overstress
          EXTR                          Loadcase allowing extreme loading overstress

          PRIN                          Reports to be printed
          TEXT                          Text or comment command
          TITLE                         Redefine global title

          END                           Terminates command data block                                      C


     Usage
     C.         Compulsory command, but see notes below where applicable.

     Notes

     1.    See Sections 3.4 and A.12.

     2.    At least one CASE, COMB or CMBV command must be included

                                            Table 5.3 API WSD JOIN Commands




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BEAMST User Manual                                                                      API Nominal Load Joint Checks


              SYSTEM DATA AREA 100000
              TEXT BEAMST USER MANUAL EXAMPLE STRUCTURE T0847
              JOB POST
              PROJECT MANU
              COMPONENT PILE JACA
              OPTION GOON
              END
              API ED21 JOIN
              *
              * Investigate all joints in the model except where
              * only one element is connected
              *
              JOINT ALL
              NOT JOINTS 1315 1355 5110 5150
              *
              * Ignore dummy elements
              *
              SECONDARY ELEMENTS 801 802
              UNIT KN M
              *
              * Change tubular dimensions for one element
              *
              DESI TUB 1.0 0.05 ELEM 131
              *
              * Examine two wave cases
              *
              SELE 10 Extreme Wave 1 + Dead Loads + Topside Loads
              COMB 10 1.0 1 1.0 3 1.0 4
              SELE 11 Extreme Wave 2 + Dead Loads + Topside Loads
              COMB 11 1.0 2 1.0 3 1.0 4
              *
              * Indicate that these loadcases are extreme events
              *
              EXTR 10 11
              *
              * Yield Value Constant for all elements
              *
              YIELD 3.5E05 ELEM ALL
              *
              * Specify the chord elements for one of the joints
              *
              CHORD 1130 122 123
              *
              * Set some joints as being Y
              *
              TYPE.OF.JOINT 1130 Y 102
              TYPE.OF.JOINT 1130 Y 103
              *
              * Ask explicitly for all reports
              *
              PRIN XCHK UNCK SUNI N MM SUM3 BOTH SUM4 BOTH
              END
              STOP

                                        Figure 5.6 Example API WSD JOIN data file




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BEAMST User Manual                                                                      API Nominal Load Joint Checks




     5.2.2        API Nominal Load Check Reports

     The detailed JOINT check report provides information on joint geometric parameters, type, acting
     chord and brace loading, Qf, and Qu factors, nominal load allowables and unity checks. This may be
     requested using the PRINt UNCK command. The maximum unity check is flagged for ease of
     reference.

     Messages displayed in output reports or obtained from the database have the following meanings.

     FAIL                -          Unity check value exceeds unity

     PNT9                -          Unity check value exceeds 0.9

     NOCK                -          No check has been carried out, due to one of the following error messages

     BETA                -          * Beta value β is outside the valid API range

     THET                -          *Theta value θ is outside the valid API range

     GAMA                -          * Gamma value γ is outside the valid API range

     NOCY                -          Computed Py value is less than zero

     DIST                -          + The distance between work points exceeds D/4



     * Error message:
     + Warning message:




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BEAMST User Manual                                                                      API Nominal Load Joint Checks




     5.2.3          Nomenclature


     5.2.3.1               Dimensional




     D          =             chord outside diameter
     d          =             brace outside diameter
     R          =             chord radius
     T          =             chord thickness
     t          =             brace thickness
     γ          =             ratio between the chord radius and thickness R/T
     τ          =             ratio between the thickness of the brace and chord t/T
     θ          =             angle between brace and chord
     β          =             ratio between the diameter of the brace and chord d/D
     g          =             K joint gap



     5.2.3.2               Acting Forces and Stresses


                    P        =    brace axial force
                    Mip      =    brace in-plane bending moment
                    Mop      =    brace out-of-plane bending moment
                    faxc     =    chord axial stress component
                    fipc     =    chord in-plane bending stress
                    fopc     =    chord out-of-plane bending stress
                    fa       =    brace axial stress component
                    fip      =    brace in-plane bending stress




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BEAMST User Manual                                                                      API Nominal Load Joint Checks


                  fop      =      brace out-of-plane bending stress
                  fb       =      resultant brace bending stress


     5.2.3.3            Allowable Stresses and Unity Checks



                  fyc      =      chord yield stress
                  Pa       =      allowable axial force
                  Maip     =      allowable in-plane bending moment
                  Maop     =      allowable out-of-plane bending moment
                  UCax =          axial force unity check
                  UCip =          in-plane bending unity check
                  UCop =          out-of-plane bending unity check
                  UCBN =          combined bending unity check




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BEAMST User Manual                                                                      API Nominal Load Joint Checks




     5.2.4        API Allowable Nominal Loads and Unity Checks


     5.2.4.1           Basic Capacity

          Clause/(eqn)                                                 Commentary                             Message

         Table 4.3-1a                                               2
                                                           FycT
                                      Pa = µQuQf
                                                          1.6 sin θ
                                                                   2
                                                      FycT d
         Table 4.3-1b
                                      Ma = µQuQf
                                                     1.6 sin θ
                                      µ = 1.0 for ordinary loadcases
                                        = 11 / 3 for extreme loadcases
                                        = 1.6 for earthquake loadcases
                                      where multiple types are present

                                                  Axial load ∈ brace assigned for type
                                      Pa = ∑                                           x Pafortype
                                                        Total Axial load ∈ brace




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BEAMST User Manual                                                                      API Nominal Load Joint Checks




     5.2.4.2           Strength Factor Qu

          Clause/(eqn)                                               Commentary                               Message

           Table 4.3-1                for Ma calculations, all joint types:
                                      In-plane bending:

                                                     Qu = (5 + 0.7 γ ) β 1.2
                                      Out of plane bending:
                                                     Qu = 2.5 + (4.5 + 0.2γ ) β 2.6
                                       for Pa calculations, K joints:
                                                     Qu = (16 + 1.2γ ) β 1.2 Qg
                                                           but ≤ 40 β 1.2 Qg
                                       for Pa calculations, T/Y joints
                                       In axial tension:
                                                      Qu = 30 β
                                        In axial compression:
                                                      Qu = 2.8 + (20 + 0.8γ ) β 1.6
                                                            but ≤ 2.8 + 36 β 1.6
                                        for Pa calculations, X joints:
                                        In axial tension:
                                                      If β ≤ 0.9 : Qu = 23β
                                                             else : Qu = 20.7 + ( β - 0.9)(17γ - 220)
                                         In axial compression:
                                                      Qu = [2.8 + (12 + 0.1γ )β ]. Q B
                                          Notes and definitions of terms as per table 4.3-1




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     5.2.4.3           Chord Load Factor Qf

          Clause/(eqn)                                                 Commentary                               Message

                                                SF Pc      SF Mipb 
             Eqn 4.3-2             Qf = 1 + c1 
                                                Py  - C 2  Mp  - C 3 A
                                                                    
                                                                   
                                                                   2                  2
             Eqn 4.3-3             where           SF Pc   SF Mc 
                                               A= 
                                                          +
                                                                  
                                                                    
                                                   Py   Mp 
                                   and
                                               Mc = Mipb2 + Mops 2
                                  where SF = 1.6 for normal loading
                                            = 1.2 for extreme loading
                                                = 1.0 for earthquake loading




     5.2.4.4           Joints with Thickened Cans

          Clause/(eqn)                                                 Commentary                               Message

            Eqn 4.3-4               For braces that are not classified as forming a K Joint. and where the
                                    chord nominal thickness and effective length are provided via the
                                    CHORd’s EFFE command, Pa is multiplied by the following factor:
                                                                       2
                                     factor              Tn 
                                            r + (1 - r ) 
                                                         Tc 
                                     where Tn = nominal chord thickness
                                              Tc = chord thickness at joint. (can).
                                              If β ≤ 0.9
                                              r = Lc/2.5D
                                              If β > 0.9

                                              r=
                                                  (4 β - 3)Lc
                                                     1.5D
                                      where Lc = effective total length




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     5.2.4.5           Nominal Load Unity Checks

          Clause/(eqn)                                                Commentary                                                        Message
                                   Unity checks are calculated for each component of brace loading, ie
                                                             P
                                                      UCax =  
                                                              Pa  ax
                                                             M
                                                      UCip =  
                                                              M a ip
                                                            M
                                                     UCop =  
                                                             M a  op
                                                                                                                                       PNT9
                                                      If any UC > 0.9............................................................
                                                                                                                                       FAIL
                                                      If any UC > 1.0............................................................




     5.2.4.6           Combined Axial and Bending Unity Checks

          Clause/(eqn)                                                Commentary                                                        Message

            Eqn 4.3-5                                   2
                                    UC BN = UC AX +UC IP + UC op
                                     If   UCBN > 0.9             ............. .............. ............. ............ ...........    PNT9

                                     If   UCBN > 1.0             .............. ............. ............. ............. ..........    FAIL




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BEAMST User Manual                                                                      API Nominal Load Joint Checks




     5.2.5        Spectral Expansion for Joint Checks (API NOMI)

     In response spectrum analysis using modal superposition (Ref. 12) structure displacements and forces
     calculated represent estimated maxima. Such estimated maxima are, in general, unsigned (positive).

     For the purpose of checking joints to API, a series of worst static-spectral possible loadcases must be
     generated from the member unsigned spectral and signed static end forces.

     The signs applied to the spectral end forces when generating a series of worst cases depends upon the
     unity check being considered and details of the signs adopted/deduced are given in this section.

     In BEAMST it is assumed that unity checks can be performed by considering the combination of static
     and dynamic conditions to be purely a static condition. Any joint type identification dependant on
     axial load is carried out prior to any combinations with dynamic cases.

     There are eight possible unique combinations of signs, or ‘spectral expansions’, which can be applied
     to unsigned spectral axial and local bending stresses:

              2 - axial (tension and compression)
              x
              2 - local Y bending (hog and sag)
              x
              2 - local Z bending (hog and sag)


     and each is denoted by a single alphabetic letter code in BEAMST in the range R-Y as shown in Table
     5.8. The spectral expansion codes indicating the signs chosen by BEAMST for both the chord and
     brace member spectral stresses are appended to the loadcase number in the unity check report, the code
     for the chord member being appended first.

     Each of the 8 spectral expansions are applied to the dynamic chord forces before they are combined
     with the static forces the worst cases Qf factor for the joint to determine.

     If the dynamic axial force is not of a sufficient magnitude that it can change the combined brace axial
     forces direction then a single design is undertaken with the axial force assigned to each joint type being
     determined by the static cases proportions.

     If the magnitude is sufficient to change the axial force direction, a second analysis is performed; again
     the axial force is proportioned by the joint types determined with the static case. The unity checks are
     compared and the conservative case is selected. Because force directions are not available for the
     dynamic case the joint type assignments may be incorrect, hence it may be preferable to overide this
     function by using the TYPE command.

     An example of a spectral expansion report for joint checks is given in Figure 5.19.




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     BEAMST User Manual                                                                      API Hydrostatic Collapse Checks




5.3 API Hydrostatic Collapse Check (API WSD HYDR)


5.3.1       Overview

The API WSD HYDR header command is used to request that hydrostatic pressure, allowable stresses, member
actions, unity checks and combined stress hydrostatic collapse unity checks be performed to API
recommendations for TUBE elements, or other beam types that have been assigned tubular sections in the
structural analysis (Ref. 2).

Elements may be selected by ELEMent, GROUp and CASE/COMBine commands as in the POST and AISC
Command data blocks. Hydrostatic pressures, allowable stresses and collapse unity checks may be requested at
any user selected position along the element using the SECTion command in BEAMST.

The calculation of hydrostatic pressures requires a knowledge of each member position with respect to still water
level, tide height, wave height and length as well as details of the sea medium and various commands in
BEAMST exist to define these. First a reference frame has to be specified for the (sea) water axes and its origin
position in terms of the jacket reference frame defined (i.e. the global co-ordinate system used in the previous
ASAS analysis) using a MOVE command. (See Section 3.4 and Ref. 14). This command is optional and if
omitted the water and jacket frame origins are taken to coincide. Having defined the water axes origin, the
relative orientations of water and jacket axes must follow. For example the jacket axes may be inclined to the
water axes if the jacket is being considered in a semi-submerged position. In order to convert pressure heads to
hydrostatic pressure the coefficient of gravity in the vertical downwards (-Zwater) water direction is required. If
the components of this coefficient of gravity are specified in terms of the jacket axes then the water-jacket axes
orientation and the coefficient of gravity can be specified in a single operation. The GRAVity command in
BEAMST is available for this purpose and is compulsory for the API hydrostatic collapse check. The jacket and
water axes are now spatially fixed and the only remaining information required for calculation of water static
head is that of mean water level, sea bed level, density of seawater and tide height. This information is specified
using the compulsory ELEVation command.                      For completion a further command WAVE is available for
specification of wave height and period, for the inclusion of wave induced pressure components. This command
is optional and if omitted the static water head only is considered. For calculation of hydrostatic head to API
recommendations the wave length is required and this is computed automatically by BEAMST on the basis of
water depth and wave period using linear wave theory. Details of this procedure are given in Section 5.3.4.

All elements selected for hydrostatic collapse post-processing are assumed to be unflooded and unstiffened (i.e.
axial length of cylinder between stiffening rings, diaphragms or end connections is equal to the element length).
This unstiffened length may be defined explicitly using a ULCF command. This command allows ring stiffened
tubulars to be checked for hydrostatic pressure collapse between the stiffening rings.

The API design code provides safety factors for axial tensile, compressive and compressive hoop loading to be
used in calculating allowable stresses for different design conditions. The code permits the user some flexibility
in the choice of the safety factor for axial compressive loading, indeed the factors given for earthquake loading
are only suggested ones. BEAMST allows EXTReme and QUAK commands to be used for automatic selection
of default safety factors for design extreme environmental and earthquake (seismic) loading conditions




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     BEAMST User Manual                                                                      API Hydrostatic Collapse Checks


respectively. These default values are given in Section 5.3.4. If required the user can override these default
values in BEAMST using the SAFE command.

A detailed Unity Check Report incorporating beam section hydrostatic depth, member acting and allowable
stresses, membrane hoop and tension/compression - collapse interaction unity checks is available and may be
requested using the PRIN UNCK command.

The BEAMST commands applicable to the API hydrostatic collapse Command data are given in Table 5.11 and
are described in detail in Section 3.4. An example data file is given in Figure 5.24.

A summary report is also available. Summary report number 1 is requested using the SUM1 sub-command and
gives the highest unity check values for each element.




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      BEAMST User Manual                                                                     API Hydrostatic Collapse Checks


        Command                                                Description                               Usage      Note
     API WSD HYDR                   API hydrostatic collapse header command                                   C

     UNIT                           Units of length and force                                                 C     1
     YIEL                           Yield stress

     ELEV                           Water depth and density                                                   C
     MOVE                           Water axis origin in global structure axis system
     WAVE                           Wave height and period
     GRAV                           Gravitational acceleration relative to structure axis system              C

     GROU                           Groups to be reported
                                                                                                              C     2
     ELEM                           Elements to be reported
     SECT                           Sections to be reported

     DESI                           Defines design section properties
     PROF                           Section profiles for use in design
     ULCF                           Length of tubular members between stiffening rings,
                                    diaphragms etc

     CASE                           Loadcases to be reported
     COMB                           Define a combined loadcase for processing                                 C     3
     CMBV                           Define a combined loadcase for processing
     SELE                           Select/redefine a combined/basic loadcase title
     HARM                           Loadcases originating from harmonic steady state
                                    response analysis
     RENU                           Renumber a basic loadcase
     EXTR                           Loadcases allowing 33% overstress
     QUAK                           Loadcases with earthquake permitted overstress
     SAFE                           Safety factors for axial compressive, tensile and hoop
                                    compressive loading

     PRIN                           Reports to be printed
     TEXT                           Text or comment command
     TITL                           Redefine global title

     END                            Terminates Command data block                                         C

Usage

C       Compulsory command, but see notes below where applicable.

Notes

1.   See Sections 3.4 and A.12.

2.   At least one GROUP or ELEM command must be included.

3.   At least one CASE, COMB or CMBV command must be included.


                                           Table 5.4 API WSD HYDR Commands




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       SYSTEM DATA AREA 100000
       TEXT BEAMST USER MANUAL EXAMPLE STRUCTURE T0847
       JOB POST
       PROJECT MANU
       COMPONENT PILE JACA
       OPTION GOON
       END
       API ED20 HYDR
       *
       * Horizontal plan bracing level -50 m
       *
       GROU 1
       UNIT KN M
       *
       * Change tubular dimensions for one element
       *
       DESI TUB 1.0 0.05 ELEM 131
       *
       * Examine two wave cases
       *
       SELE 10 Extreme Wave 1 + Dead Loads + Topside Loads
       COMB 10 1.0 1 1.0 3 1.0 4
       SELE 11 Extreme Wave 2 + Dead Loads + Topside Loads
       COMB 11 1.0 2 1.0 3 1.0 4
       *
       * Hydrostatic information
       *
       ELEVATION    0.0 -50.0    1.025
       GRAVITY      0.0    0.0 -9.81
       *
       * Indicate that these loadcases are extreme events
       *
       EXTR 10 11
       *
       * Yield Value Constant for all elements
       *
       YIELD 3.5E05 ELEM ALL
       *
       * Out of plane unbraced lengths need redefining
       *
       UNBR FACT 2.0 1.0 ELEM 105 106
       UNBR LENG 15.0 7.5 ELEM 102 103
       *
       * Check mid-span sections
       *
       SECT 0.5 ELEM ALL
       *
       * Ask explicitly for all reports
       *
       PRIN XCHK PROP UNCK FORC STRE SUNI N MM SUM1 BOTH
       END
       STOP


                                      Figure 5.7 Example API WSD HYDR data file




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5.3.2        API Hydrostatic Unity Check Reports

A description of the column header for the two unity check reports is given in Figures 5.8 and 5.9. The final
column of each report is reserved for messages. These may be summarised as follows:

        FAIL         -            Code check failure for this member

        ***          -            Unity check value exceeds unity

        **           -            Unity check value exceeds 0.9

        FXHA         -            Net axial stress fax less than half allowable elastic hoop stress and thus
                                  eqn 3.3.4-3 not checked

                                                                                          D      
        DTRF         -            Allowed diameter thickness ratio exceeded                ≥ 300 
                                                                                           t     

        THXF         -            Wall thickness less than recommended minimum of 6mm

        YIEL         -            Yield strength greater than 414MPa (60ksi)

        MOTN         -            Geometry parameter, used in the elastic hoop buckling stress, m, greater than
                                  1.6 D/t

                                                       D      
        UDTR         -            Unconservative        > 120 
                                                        t     
Examples of the summary reports available are given in Figure 5.9.




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    Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.




                                                                                                             ..................................................................................................................................
                                                                                                             . ELEMENT    101 . NODES   1110   1120 . GROUP      1 . HYDROSTATIC COLLAPSE UNITY CHECK REPORT     UNITS (N   ,MM )      UNCK
                                                                                                             ....................................................... ---------------------------------------     -----                 ====
                                                                                                                          /        /------MEMBER STRESSES------/-------------ALLOWABLE STRESSES-------------/------UNITY CHECKS-------/
                                                                                                              LOAD SECTION/ HYDR. / AXIAL       BEND      HOOP / AXIAL /-----ELASTIC-----/----INELASTIC----/ AX HOOP -----COMB-----/ MESS.
                                                                                                              CASE NO POSN/ DEPTH /    T/C      MAX.       C   / TENSION/ AXIAL     HOOP / AXIAL      HOOP /    T    C   C1   C2    T / -----
                                                                                                                          /        /                           /        /                 /                 /                         /



                                                                                                                                        fat or fac    fb          fh      fy/SFxt    Fxe/SFxc   Fhe/SFhc   Fxc/SFxc   Fhc/SFhc   UCT   UCH UCCH1 UCCH2 UCTH

                                                                                                                                                                                                                          MAXIMA
                                                                                                                                                                                                                           CASES
                                                                                                                                                                                                                            POSN

                                                                                                            (1 line per element section position, plus 3 lines for the maximum values)



                                                                                                                                                              Figure 5.8 Detailed Hydrostatic Member Check Report




                                                                                                                                                                                                                                                              API Hydrostatic Collapse Checks
Page 5-42
                                                                                                            API RP2A(20TH.ED. JUL. 1993)          HYDROSTATIC COLLAPSE UNITY CHECK SUMMARY REPORT NO. 1         UNITS (KN ,M    )     SUM1




                                                                                                                                                                                                                                                           BEAMST User Manual
                                                                                                                                                  =====================================================         -----                 ==== ====
    Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.
                                                                                                                               /------------------------------HIGHEST UNITY CHECK----------------------------- NO. OF / NEXT HIGH /
                                                                                                             ELEM NODE1   NODE2/LOAD/----SECTION-----/---UNITY CHECKS---/-----STRESSES-----/--ELAST. ALLOW.--/ SECTIONS/UNITY   LOAD/ MESSAGES
                                                                                                              NO.              /CASE/NO.POSN DEPTH /AXIAL HOOP      COMB/   AXIAL    HOOP / AXIAL      HOOP /FAIL CHKD/CHECK    CASE/ --------
                                                                                                                               /    /                /                  /                  /                 /         /            /
                                                                                                                1     1       3/   6/ 1 0.00 1.50D+01/ 0.31C, 0.29, 0.13/4.90D+04C,5.28D+03/8.57D+05,1.80D+04/   0,   5/ 0.31C ,   8/
                                                                                                                               /    /                /                  /                  /                 /         /            /
                                                                                                                2     2       4/   8/ 3 0.90 6.00D+00/ 0.48C, 0.03, 0.05/8.29D+04C,1.41D+03/1.29D+06,4.04D+04/   0,   5/ 0.44C ,   5/
                                                                                                                               /    /                /                  /                  /                 /         /            /
                                                                                                                3     5       3/   8/ 3 0.90 4.00D+00/ 0.25T, 0.02, 0.07/3.74D+04T,9.38D+02/1.50D+05,0.00D+00/   0,   5/ 0.24T ,   5/
                                                                                                                               /    /                /                  /                  /                 /         /            /
                                                                                                                4     6       4/   5/ 3 0.90 4.00D+00/ 0.46T, 0.02, 0.22/6.90D+04T,9.38D+02/1.50D+05,0.00D+00/   0,   5/ 0.43T ,   8/
                                                                                                                               /    /                /                  /                  /                 /         /            /
                                                                                                                5     3       4/   5/ 7 1.00 5.00D+00/ 0.92C, 0.02, 0.10/1.64D+05C,1.07D+03/1.41D+06,4.83D+04/   0,   7/ 0.87C ,   8/ *
                                                                                                                               /    /                /                  /                  /                 /         /            /
                                                                                                                6     2       3/   8/ 7 1.00 5.00D+00/ 1.05T, 0.04, 1.13/1.58D+05T,1.26D+03/1.50D+05,0.00D+00/   2,   7/ 1.01TH,   5/MGTW FAIL**
                                                                                                                               /    /                /                  /                  /                 /         /            /
                                                                                                                7     4       5/   5/ 1 0.00 5.00D+00/ 1.34C, 0.01, 0.08/2.31D+05C,6.70D+02/2.25D+06,1.24D+05/   2,   7/ 1.34C ,   8/MGTW FAIL**
                                                                                                                     GLOSSARY
                                                                                                                     --------
                                                                                                                     MGTW -- GEOMETRY PARAMETER M GREATER THAN 1.6 D/T
                                                                                                                      ** -- CODE CHECK FAILURE, UNITY CHECK GREATER THAN 1.0
                                                                                                                       * -- UNITY CHECK GREATER THAN 0.9 BUT NOT EXCEEDING 1.0
                                                                                                                     FAIL -- CODE CHECK FAILURE

                                                                                                             **HYDROSTATIC COLLAPSE SUMMARY REPORT TAIL
                                                                                                                   7 .....ELEMENTS WERE SELECTED            7 .....ELEMENTS WERE CHECKED            2 .....ELEMENTS FAILED

                                                                                                            API RP2A(20TH.ED. JUL. 1993)        HYDROSTATIC COLLAPSE UNITY CHECK SUMMARY REPORT NO. 1         UNITS (KN ,M    )     SUM1 FAIL




                                                                                                                                                                                                                                                   API Hydrostatic Collapse Checks
                                                                                                                                                =====================================================         -----                 ==== ====
                                                                                                                             /------------------------------HIGHEST UNITY CHECK----------------------------- NO. OF / NEXT HIGH /
                                                                                                             ELEM NODE1 NODE2/LOAD/----SECTION-----/---UNITY CHECKS---/-----STRESSES-----/--ELAST. ALLOW.--/ SECTIONS/UNITY   LOAD/ MESSAGES
                                                                                                              NO.            /CASE/NO.POSN DEPTH /AXIAL HOOP      COMB/   AXIAL    HOOP / AXIAL      HOOP /FAIL CHKD/CHECK    CASE/ --------
                                                                                                                             /    /                /                  /                  /                 /         /            /
                                                                                                                6     2     3/   8/ 7 1.00 5.00D+00/ 1.05T, 0.04, 1.13/1.58D+05T,1.26D+03/1.50D+05,0.00D+00/   2,   7/ 1.01TH,   5/MGTW FAIL**
                                                                                                                             /    /                /                  /                  /                 /         /            /
                                                                                                                7     4     5/   5/ 1 0.00 5.00D+00/ 1.34C, 0.01, 0.08/2.31D+05C,6.70D+02/2.25D+06,1.24D+05/   2,   7/ 1.34C ,   8/MGTW FAIL**
                                                                                                                     GLOSSARY
                                                                                                                     --------
                                                                                                                     MGTW -- GEOMETRY PARAMETER M GREATER THAN 1.6 D/T
                                                                                                                      ** -- CODE CHECK FAILURE, UNITY CHECK GREATER THAN 1.0
                                                                                                                     FAIL -- CODE CHECK FAILURE

                                                                                                             **HYDROSTATIC COLLAPSE SUMMARY REPORT TAIL
Page 5-43




                                                                                                                   7 .....ELEMENTS WERE SELECTED            7 .....ELEMENTS WERE CHECKED            2 .....ELEMENTS FAILED



                                                                                                                                                       Figure 5.9 Example API Hydrostatic Summary Reports
    BEAMST User Manual                                                                     API Hydrostatic Collapse Checks




5.3.3               Nomenclature


5.3.3.1               Dimensional




D               =         tube outside diameter
t               =         thickness
L               =         unbraced length of member



5.3.3.2               Acting Section Forces and Stresses


fh          =         hoop stress
fat        =          axial tensile stress
fac         =         axial compressive stress
fb          =         resultant bending stress


5.3.3.3               Allowable Stresses and Unity Checks


Fhe                   =      elastic hoop buckling stress
Fhc                   =      critical hoop buckling stress
fy                    =      yield stress
E                     =      Young’s modulus
γ                     =      Poisson’s ratio
Fb                    =      allowable bending stress
Fch                   =      allowable critical hoop buckling stress
Fxe                   =      critical axial elastic local buckling stress
Faa                   =      allowable axial elastic local buckling stress
Fxc                   =      inelastic axial local buckling stress




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UCH               =       hoop compressive unity check
UCT               =       axial tension unity check
UCTH              =       combined tension hydrostatic pressure unity check
UCCH1/2           =       combined compression hydrostatic pressure unity check




5.3.4          API Allowable Stresses and Unity Checks

Safety factors for use with local buckling and interaction formulae herein are:


     type                    axial compression           axial tension                hoop compression   bending
                             SFxc                        SFxt                         SFhc               SFb
        Ordinary             1.67-2.00                   1.67                         2.00
        Extreme              1.25-1.50                   1.25                         1.50               See 5.3.4.10

        Earthquake           1.00-1.20                   1.00                         1.20


The default values are shown underlined.

The value of SFxc is overwritten by the AISC axial compression safety factor if exceeded by the AISC value.
The AISC value is:
                                   5 3(KL/r) (KL/r )3
            (AISC E2-1)              +      -
                                   3   8 Cc    8 C3
                                                  c



where (KL/r) is the slenderness ratio and
                                             2π 2 E
                                   Cc =
                                                fy

If the slenderness ratio exceeds Cc the AISC value is taken as 23/12 (AISC E2-2).

where BEAMST default values are underlined.

In the hydrostatic collapse check the following assumptions are made:

1.     All members are unflooded.

2.     Outis assumed to be within API RP2B tolerance limits.

3.     Wave crest is assumed to be directly above the beam section position under consideration.

4.     Hydrostatic pressure is only considered for beam section positions below the static water level (=mean water
       level + tide height + storm surge height).

5.     The wave length, Lw, is adequately described by linear wave theory as follows




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            2π d
 a. If           < 0.001                                                       (shallow water)
            g T2
               w



                                   Tw
           then           Lw =
                                    gd


                          2π d                                         g T2
         Else if               ≥ 0.001                and
                                                                          w
                                                                            <d                      (deep water)
                          g T2
                             w                                          2π

                                         2
                                   gTw
         then             Lw =
                                    2π

         else             Lw is obtained iteratively from


                                     2π d 
                               2
                          gT w
                   Lw =             
                               tanh       
                                           
                          2π         Lw 

         where            d        =         static water depth
                          g        =         acceleration due to gravity
                          Tw       =         wave period


         The design head is given by


                               H w cosh[K(d- z)]
                   Hz = z +
                                2    coshKd


                                             2π
         where            K        =
                                             Lw
                          Hw       =         wave height
                          z        =         depth below static water surface


         The design head induced hoop stress is given by


                   f h = pD/ 2 t
         where            p        =         γgHz
                          γ        =         water density




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5.3.4.1         Limit Checks

     Clause/(Eqn)                                                   Commentary                                                     Message


                  3.2.2b             If             D                   ........... ........... ........... .................... DTRF
                                                       ≥300
                  3.2.2b
                                                     t
                                     If             t < 6 mm            ........... ........... ........... .................... THKF
                  C3.2                                                                                                              YIEL
                                     If             f y ≥ 60 ksi        ........... ........... ........... ....................




5.3.4.2         Elastic Hoop Buckling Stress Fhe

     Clause/(Eqn)                                                   Commentary                                                     Message


                                                                       L     D
                                          Geometric parameter M =          2
                                                                       D      t
                                          Critical hoop buckling coefficient Ch
                                                                 D
                                                      M ≥1.6
                                       If                        t
                                                                     t
                                       then           Ch = 0.44
                                                                     D
                                                             D            D
                                       If             0.825     ≤ M < 1.6         ........... ........... ........... MGTW if
                                                             t             t                                          unity check
                                                                                3                                     >1
                                                                          D
                                                                           
                                       then                       t        t 
                                                      Ch = 0.44 + 0.21        4
                                                                 D          M
                                       If                              D
                                                      3.5 ≤ M < 0.825
                                                                        t
                                       then                    0.736
                                                      Ch =
                                                            (M- 0.636)
                                       If
                                                      1.5 ≤ M < 3.5
                                       then                   0.755
                                                      Ch =
                                                           (M- 0.559)
                                       If             M < 1.5

                                       then           Ch = 0.8

                                                                         t
                                                      Fhe = 2 Ch E
                                                                         D




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5.3.4.3         Critical Hoop Buckling Stress Fhc

     Clause/(Eqn)                                                   Commentary                               Message


                                    If          Fhe > 6.2 f y
             3.2.5b.2
            (3.2.5-6)               then        Fhc = f y

                                    If          1.6 f y < Fhe≤6.2 f y

                                                           1.31 f y
                                    then        Fhc =
                                                              f 
                                                        1.15 + y 
                                                               Fhe 

                                    If          0.55 f y < Fhe≤1.6 f y

                                    then        Fhe = 0.45 f y + 0.18 Fhe

                                    If          Fhe≤0.55 f y
                                    then        Fhc = Fhe


5.3.4.4         Allowable Critical Hoop Buckling Stress Fch

     Clause/(Eqn)                                                   Commentary                               Message

             3.2.5                            Fhc
                                    Fch =
           (3.2.5-1)                         SFhc


5.3.4.5         Critical Axial Elastic Local Buckling Stress Fxe

     Clause/(Eqn)                                                   Commentary                               Message

                                   If           D
              3.2.2.b                              ≤ 60
                                                 t
             (3.2.2-3)
                                   then         Fxe = f y

                                   else if            D
                                                60 <    ≤ 300
                                                      t
                                   then               0.6 Et
                                                Fxe =
                                                        D




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5.3.4.6         Allowable Axial Elastic Local Buckling Stress Faa

     Clause/(Eqn)                                                   Commentary                               Message


                                                                 Fxe
                   3.3.4                                Faa =
                                                                SFxc




5.3.4.7         Inelastic Axial Elastic Local Buckling Stress Fxc

     Clause/(Eqn)                                                   Commentary                               Message



              (3.2.2-4)                 If          D
                                                       ≤ 60
                                                     t
                                                    Fxc = f y


                                        else                          D 
                                                                            0.25

                                                    Fxc = 1.64 - 0.23    f y ≤ Fxe
                                                          
                                                                       t     



5.3.4.8         Hoop Compressive Unity Check UCH

     Clause/(Eqn)                                                   Commentary                               Message


                                                                       SFhc
      (3.3.4-2)                                        UCH = f h
                                                                        Fhc




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5.3.4.9         Axial Tension Unity Check UCT

     Clause/(Eqn)                                                   Commentary                                             Message


           (A in eqn                                                  SFxt
           3.3.3-1)                                   UCT = f at
                                                                       fy



5.3.4.10 Combined Compression and Hydrostatic Pressure Unity Check UCCH1/2

     Clause/(Eqn)                                                   Commentary                                             Message


           (3.3.4-1)                                                                     SFxc f b SFb
                                                       UCCH1 = (f ac + 0.5 f h )              +
                                                                                          Fxc    fy
            3.3.5                                      where      SFb = fy/Fb
                                                       or             = fy/1.33Fb              for extreme
                                                                      = fy/1.7Fb               for earthquake

           (3.3.4-3)            If           f ac > 0.5 Fha

                                            where                Fhe
                                                        Fha =
                                                                 SFh
                                                                                     2
                                                      f ac-0.5 Fha +  f h 
                                then
                                             UCCH 2 =                
                                                                          
                                                                           
                                                      Faa -0.5 Fha  Fha 
                                else         no UCCH 2 is printed ............. ............. ............. ............     FXHA

                               Note:

                                     If the beam section position centre line is above static water level, no
                                     hydrostatic collapse check is performed and the message NOCK
                                     results.



5.3.4.11 Combined Tension and Hydrostatic Pressure Unity Check UCTH

     Clause/(Eqn)                                                   Commentary                                             Message



           (3.3.3-1)                                   UCTH = UCT + UCH + 2υ UCT UCH
                                                                2     2




                                                        where υ = 0.3




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     BEAMST User Manual                                                                     API Punching Shear Joint Checks




5.4 API Punching Shear Joint Check (API WSD PUNC)


5.4.1       Overview

The API WSD PUNC command in BEAMST requests that punching shear calculations be performed to API
recommendations for tubular joints Ref. 2. The joints may consist of TUBE elements and/or other beam types
that have been assigned tubular sections in the structural analysis.

Joints for punching shear post-processing are selected using the JOINt command in BEAMST which specifies
the node numbers at joint positions. All joints are assumed ‘simple’. Elements may be excluded from the joint
punching shear check using the SECOndary command.

Joints are automatically classed as K, T or Y depending on the joint geometry as follows.

1.   The chord member is the member with the greatest outside diameter.

2.   If two or more potential chord members have equal diameters; BEAMST will consider the two with the
     largest wall thicknesses and for each loadcase selected will check the one most heavily stressed against all
     brace members.

3.   In the case of two or more potential chord members with equal diameters and wall thicknesses, the first two
     encountered as shown in the Cross Check Report will be considered.

4.   If the CHORd command is used to specify a chord member, this alone will be considered. If two chords are
     specified, the most heavily stressed chord will be checked against all brace members for each loadcase
     selected.

5.   All members not selected as chord members are treated as brace members (unless defined as secondary),
     with each brace-chord pair being checked.


BEAMST selects ‘simple’ joint (brace-chord pair) ‘types’ as follows:

1.   Brace members ‘perpendicular’ to the chord members (smaller included angle less than or equal to 80
     degrees) as T joints.

2.   Single non-‘perpendicular’ braces are classified as Y joints. Two non-perpendicular braces on the same
     side of the chord are classified as K joints.

3.   Cross or Double(DT) joints must be user specified.

4.   In the case of user defined K and X joints, no search is performed for a second brace member in the same
     brace-chord plane as the first brace.




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5.   Brace members specified on joint TYPE commands are automatically selected as braces in the above brace-
     chord member selection process.

6.   No conflict between CHORd command specified members and brace members specified on joint TYPE
     commands is allowed.


BEAMST will only check selected joints in which two or more incident members are tubular and of circular
section. All other selected joints are automatically bypassed.

The user may override these classifications using the TYPE and CHOR commands.                              Interpolated joint
classifications may be defined using the TYPE command. For K joints a gap dimension appropriate to the joint
may be specified in the TYPE command. A default gap dimension may be specified using the GAPD command.

The detailed joint punching shear unity check report provides information on joint geometric parameters, type,
acting chord and brace stresses, punching shear, Qf and Qq factors, punching shear allowable(s), and unity
checks. This may be requested using the PRINt UNCK command. The maximum unity check is flagged for
ease of reference. When an interpolatory joint type classification is being employed two sets of punching shear
allowables are reported, one for each joint classification type and these pertain to joints classified as 100% of the
respective joint types.

Summary report 3 comprises the highest unity check for each selected loadcase for each joint.

Summary report 4 comprises the three worst unity checks for each selected joint, together with the distribution of
unity check values. This distribution provides information on the number of unity checks exceeding an upper
limit (default 1.0), less than a lower limit (default 0.5), and the number in the mid range.

BEAMST commands applicable to the API punching stress command are given in Table 5.5 and are described in
detail in Section 3.4. An example data file is given in Figure 5.10.

For the purpose of simulating joint locally thickened tubulars or joint cans a STUB command is available for re-
definition of member outer diameters and wall thicknesses at the joint.

To calculate allowable punching shear stress to API procedures member yield strengths must be specified and a
YIELd command must be included for this purpose.

The one third increase in basic allowable punching shear stress permitted by the API recommendation for design
extreme environmental conditions can be requested on a loadcase basis using the EXTReme command in
BEAMST. For earthquake (seismic) loadcases a larger increase in basic allowable punching shear is permitted
and the QUAK command will select it for the loadcases specified.




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       Command                                                Description                               Usage      Note
     API WSD PUNC                 API joint check header command                                         C

     UNIT                         Units of length and force                                              C         1
     YIEL                         Yield stress

     JOIN                         Joint numbers to be reported
     TYPE                         Joint type and brace element definition
     CHOR                         Chord elements at a joint
     SECO                         Secondary members to be ignored in checks

     DESI                         Defines design section properties
     GAPD                         Define default gap dimension
     PROF                         Section profiles for use in design
                                  Tubular member end stub dimensions
     STUB

     CASE                         Basic loadcases
     COMB                         Define a combined loadcase for processing                                  C         2
     CMBV                         Define a combined loadcase for processing
     SELE                         Select/redefine a combined/basic loadcase title
     SPEC                         Loadcases originating from response spectrum analysis
     RENU                         Renumber a basic loadcase
     QUAK                         Loadcases with earthquake permitted overstress
     EXTR                         Loadcase allowing extreme loading overstress

     PRIN                         Reports to be printed
     TEXT                         Text or comment command
     TITLE                        Redefine global title

     END                          Terminates command data block                                          C


Usage
C.         Compulsory command, but see notes below where applicable.

Notes

1.    See Sections 3.4 and A.12.

2.    At least one CASE, COMB or CMBV command must be included.



                                           Table 5.5 API WSD PUNC Commands




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       SYSTEM DATA AREA 100000
       TEXT BEAMST USER MANUAL EXAMPLE STRUCTURE T0847
       JOB POST
       PROJECT MANU
       COMPONENT PILE JACA
       OPTION GOON
       END
       API ED20 PUNC
       *
       * Investigate all joints in the model except where
       * only one element is connected
       *
       JOINT ALL
       NOT JOINTS 1315 1355 5110 5150
       *
       * Ignore dummy elements
       *
       SECONDARY ELEMENTS 801 802
       UNIT KN M
       *
       * Change tubular dimensions for one element
       *
       DESI TUB 1.0 0.05 ELEM 131
       *
       * Examine two wave cases
       *
       SELE 10 Extreme Wave 1 + Dead Loads + Topside Loads
       COMB 10 1.0 1 1.0 3 1.0 4
       SELE 11 Extreme Wave 2 + Dead Loads + Topside Loads
       COMB 11 1.0 2 1.0 3 1.0 4
       *
       * Indicate that these loadcases are extreme events
       *
       EXTR 10 11
       *
       * Yield Value Constant for all elements
       *
       YIELD 3.5E05 ELEM ALL
       *
       * Specify the chord elements for one of the joints
       *
       CHORD 1130 122 123
       *
       * Set some joints as being Y
       *
       TYPE.OF.JOINT 1130 Y 102
       TYPE.OF.JOINT 1130 Y 103
       *
       * Ask explicitly for all reports
       *
       PRIN XCHK UNCK SUNI N MM SUM3 BOTH SUM4 BOTH
       END
       STOP


                                      Figure 5.10 Example API WSD PUNC data file




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5.4.2        API Punching Shear Check Reports

A description of the column headers for the detailed report is given in Figure 5.11. The final column is reserved
for messages. These may be summarised as follows:

        ***          -            Unity check value exceeds unity

        **           -            Unity check value exceeds 0.9

        NO
        UNI          -            Brace angle θ is less than 20 degrees so no unity checks are calculated
        CHK

        BTA
        GT           -            β ratio is greater than unity so no unity checks are calculated
        ONE

        +            -            Largest unity check

        N            -            If the first combined unity check exceeds unity (UCBN) then the second unity
                                  check cannot be calculated (UCCO)


Examples of the summary reports available are given in Figures 5.12 and 5.13.




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    Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.




                                                                                                             API RP2A(20TH.ED. JUL. 1993)                     JOINT PUNCHING SHEAR UNITY CHECK REPORT                        UNITS (N  ,MM )        UNCK
                                                                                                                                                              ---------------------------------------                        -----                  ====
                                                                                                              JOINT    CHORD LC. NO/ CHOR DIAM   BETA /   F -CHORD FA-BRACE/ QF-AX QF-IP QF-OP/ VP-AXIAL              VP-IP    VP-OP / AX-UC     BEND.UC/P/F
                                                                                                                       BRACE JT1-PC/ CHOR THIC   TAU /    FY-CHORD FB-IP    / QQAX1 QQIP1 QQOP1/ ALL.1.AX            ALL.1.IP ALL.1.OP/ IP-UC    A+BN.UC/===
                                                                                                                             JT2-PC/    GAP      THETA/   ALL.AISC FB-OP    / QQAX2 QQIP2 QQOP2/ ALL.2.AX            ALL.2.IP ALL.2.OP/ OP-UC    JOIN.UC/

                                                                                                                                             D     β       2         2     2 faxb        Qfax   Qfip   Qfop   vpax   vpip     vpop    UCax      UCBN
                                                                                                                                                          f axc + f ipc + f opc
                                                                                                                                             T     τ           fyc            fipb       Qqax   Qqip   Qqop   vpax   vpip     vpop    UCip      UCCO
                                                                                                                                             g     θ           0.4αfyc            fopb   Qqax   Qqip   Qqop   vpax   vpip     vpop    UCop      UCjt


                                                                                                                                                                                                100% type2           100% type2

                                                                                                                                                                                                100% type1           100% type1




                                                                                                            (3 lines per chord brace pair)




                                                                                                                                                                                                                                                                   API Punching Shear Joint Checks
                                                                                                                                                               Figure 5.11 Detailed Joint Punching Shear Report
Page 5-56
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                                                                                                            API RP2A(20TH.ED. JUL. 1993)                JOINT PUNCHING SHEAR UNITY CHECK SUMMARY REPORT NO. 3                        SUM3
    Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.

                                                                                                                                                        =====================================================                        ==== ====
                                                                                                            ( AX=AXIAL UC., IP=IN PLANE BENDING UC., OP=OUT OF PLANE BENDING UC., BN=COMBINED BENDING UC., CO=AXIAL+BENDING COMB UC.
                                                                                                                                                                                                        1 = CHORD 1 , 2 = CHORD 2 )
                                                                                                             JOINT CHORD CHORD BRACE /      JOINT WORST LOAD / NO. OF L.C./---------------UNITY CHECKS FOR REQUESTED LOAD CASES---------------
                                                                                                                        1      2        /STRENGTH UN CK CASE / FAIL CHKD /CASES      8       9
                                                                                                            -----------------------------------------------------------------------------------------------------------------------------------
                                                                                                                 2      6      0      2 /    1.32 0.45CO    9 /    0     2 /    0.33CO1 0.45CO1
                                                                                                            -----------------------------------------------------------------------------------------------------------------------------------
                                                                                                                 3      1      3      5 /    1.40 0.66CO    8 /    0     2 /    0.66CO2 0.19CO2
                                                                                                                 3      1      3      6 /    0.72 0.88CO    8 /    0     2 /    0.88CO2 0.46OP2
                                                                                                            -----------------------------------------------------------------------------------------------------------------------------------
                                                                                                                 4      2      4      5 /    1.17 1.32BN    8 /    2     2 /    1.32BN1 1.32BN1
                                                                                                                 4      2      4      7 /    0.76 1.20CO    8 /    1     2 /    1.20CO1 0.92OP1
                                                                                                            -----------------------------------------------------------------------------------------------------------------------------------
                                                                                                                 5      7      0      3 /    0.97 0.22CO    8 /    0     2 /    0.22CO1 0.20OP1

                                                                                                             **PUNCHING SHEAR SUMMARY REPORT TAIL
                                                                                                                   6 .....JOINTS WERE SELECTED              6 .....JOINTS WERE CHECKED               1 .....JOINTS FAILED
                                                                                                                                                            6 .....BRACE-CHORD PAIRS CHECKED         2 .....BRACE-CHORD PAIRS FAILED

                                                                                                            API RP2A(20TH.ED. JUL. 1993)                JOINT PUNCHING SHEAR UNITY CHECK SUMMARY REPORT NO. 3                        SUM3 FAIL




                                                                                                                                                                                                                                                      API Punching Shear Joint Checks
                                                                                                                                                        =====================================================                        ==== ====
                                                                                                            ( AX=AXIAL UC., IP=IN PLANE BENDING UC., OP=OUT OF PLANE BENDING UC., BN=COMBINED BENDING UC., CO=AXIAL+BENDING COMB UC.
                                                                                                                                                                                                        1 = CHORD 1 , 2 = CHORD 2 )
                                                                                                             JOINT CHORD CHORD BRACE /      JOINT WORST LOAD / NO. OF L.C./---------------UNITY CHECKS FOR REQUESTED LOAD CASES---------------
                                                                                                                        1      2        /STRENGTH UN CK CASE / FAIL CHKD /CASES      8       9
                                                                                                            -----------------------------------------------------------------------------------------------------------------------------------
                                                                                                                 4      2      4      5 /    1.17 1.32BN    8 /    2     2 /    1.32BN1 1.32BN1
                                                                                                                 4      2      4      7 /    0.76 1.20CO    8 /    1     2 /    1.20CO1 0.92OP1

                                                                                                             **PUNCHING SHEAR SUMMARY REPORT TAIL
                                                                                                                   6 .....JOINTS WERE SELECTED              6 .....JOINTS WERE CHECKED               1 .....JOINTS FAILED
                                                                                                                                                            6 .....BRACE-CHORD PAIRS CHECKED         2 .....BRACE-CHORD PAIRS FAILED
Page 5-57




                                                                                                                                                  Figure 5.12 Example Joint Punching Check Summary Report 3
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                                                                                                            API RP2A(20TH.ED. JUL. 1993)                JOINT PUNCHING SHEAR UNITY CHECK SUMMARY REPORT NO. 4                        SUM4
                                                                                                                                                        =====================================================                        ==== ====
                                                                                                                                                  THREE WORST UNITY CHECKS    ( AX=AXIAL LOAD UC, IP=IN-PLANE BEND UC, OP=OUT-PLANE BEND UC,
                                                                                                                                                  ------------------------                      BN=COMB BEND UC, CO=COMB BEND+AXIAL UC. )
                                                                                                                   /------------FIRST-----------/-----------SECOND-----------/------------THIRD-----------/NO. OF CHORD-BRACE PAIR UNITY CHECKS
                                                                                                             JOINT / CHORD BRACE UNITY     LOAD / CHORD BRACE UNITY     LOAD / CHORD BRACE UNITY     LOAD /                GE      GE      LT
                                                                                                                   /               CHECK   CASE /               CHECK   CASE /               CHECK   CASE / FAIL CHKD     1.00    0.50    0.50
                                                                                                            -----------------------------------------------------------------------------------------------------------------------------------
                                                                                                                 2 /     6      2 0.45CO      9 /     6      2 0.33CO      8 /     0      0 0.00        0 /    0     2       0       0       2
                                                                                                                 3 /     3      6 0.88CO      8 /     3      5 0.66CO      8 /     3      6 0.46OP      9 /    0     4       0       2       2
                                                                                                                 4 /     2      5 1.32BN      8 /     2      5 1.32BN      9 /     2      7 1.20CO      8 /    3     4       3       1       0
                                                                                                                 5 /     7      3 0.22CO      8 /     7      3 0.20OP      9 /     0      0 0.00        0 /    0     2       0       0       2

                                                                                                              **PUNCHING SHEAR SUMMARY REPORT TAIL
                                                                                                                    1 .....JOINTS WERE SELECTED              6 .....JOINTS WERE CHECKED              1 .....JOINTS FAILED
                                                                                                                                                             6 .....BRACE-CHORD PAIRS CHECKED        2 .....BRACE-CHORD PAIRS FAILED

                                                                                                            API RP2A(20TH.ED. JUL. 1993)                JOINT PUNCHING SHEAR UNITY CHECK SUMMARY REPORT NO. 4                        SUM4 FAIL
                                                                                                                                                        =====================================================                        ==== ====
                                                                                                                                                  THREE WORST UNITY CHECKS    ( AX=AXIAL LOAD UC, IP=IN-PLANE BEND UC, OP=OUT-PLANE BEND UC,




                                                                                                                                                                                                                                                      API Punching Shear Joint Checks
                                                                                                                                                  ------------------------                      BN=COMB BEND UC, CO=COMB BEND+AXIAL UC. )
                                                                                                                   /------------FIRST-----------/-----------SECOND-----------/------------THIRD-----------/NO. OF CHORD-BRACE PAIR UNITY CHECKS
                                                                                                             JOINT / CHORD BRACE UNITY     LOAD / CHORD BRACE UNITY     LOAD / CHORD BRACE UNITY     LOAD /                GE      GE      LT
                                                                                                                   /               CHECK   CASE /               CHECK   CASE /               CHECK   CASE / FAIL CHKD     1.00    0.50    0.50
                                                                                                            -----------------------------------------------------------------------------------------------------------------------------------
                                                                                                                 4 /     2      5 1.32BN      8 /     2      5 1.32BN      9 /     2      7 1.20CO      8 /    3     4       3       1       0

                                                                                                             **PUNCHING SHEAR SUMMARY REPORT TAIL
                                                                                                                   1 .....JOINTS WERE SELECTED              6 .....JOINTS WERE CHECKED               1 .....JOINTS FAILED
                                                                                                                                                            6 .....BRACE-CHORD PAIRS CHECKED         2 .....BRACE-CHORD PAIRS FAILED
Page 5-58




                                                                                                                                                  Figure 5.13 Example Joint Punching Check Summary Report 4
     BEAMST User Manual                                                                     API Punching Shear Joint Checks




5.4.3       Nomenclature


5.4.3.1            Dimensional




            D        =     chord diameter
            d        =     brace diameter
            R        =     chord radius
            T        =     chord thickness
            t        =     brace thickness
            γ        =     ratio between the chord radius and thickness R/T
            τ        =     ratio between the thickness of the brace and chord t/T
            θ        =     angle between brace and chord
            β        =     ratio between the diameter of the brace and chord d/D
            g        =     K joint gap



5.4.3.2            Acting Forces and Stresses


            vp       =     acting punching shear (1 each for axial, in-plane and out-of-plane bending)
            faxc     =     chord axial stress component
            fipc     =     chord in-plane bending stress
            fopc     =     chord out-of-plane bending stress
            fa       =     brace axial stress component
            fip      =     brace in-plane bending stress
            fop      =     brace out-of-plane bending stress
            fb       =     resultant brace bending stress




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5.4.3.3           Allowable Stresses and Unity Checks


            fyb      =     brace yield stress
            fyc      =     chord yield stress
            Vp       =     allowable punching shear (1 each for axial, in-plane and out-of-plane bending
                           components)
            UCax =         axial punching shear unity check
            UCip =         in-plane bending punching shear unity check
            UCop =         out-of-plane bending punching shear unity check
            UCBN =         combined bending punching shear unity check
            UCCO =         combined axial and bending punching shear unity check
            UCjt     =     joint strength unity check




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5.4.4       API Allowable Stresses and Unity Checks


5.4.4.1         Acting Punching Shear Vp

   Clause/(eqn)                                                Commentary                                    Message

      (4.3.1-1)                 Vp       =      τ f sin θ

                                where

                                f        =      nominal axial, in-plane bending, or out-of-plane
                                                bending stress in the brace. The acting shear is
                                                calculated separately for each of these stress
                                                components.




5.4.4.2         Chord Design Factor Qf

   Clause/(eqn)                                                Commentary                                    Message

                                 Qf       =     1.0 - λγ A2

                                 where

                                 λ        =     0.030 brace axial stress
                                          =     0.045 brace inbending
                                          =     0.021 brace outbending

                                                         2       2           2
                                 A        =         f axc + f ipc + f opc
                                                             µ f yc
                                 µ        =     0.6 ORDINARY loadcase
                                          =     0.8 EXTREME loadcase
                                          =     1.0 EARTHQUAKE loadcase

                                 Qf is set to 1.0 if all extreme fibre stresses in the chord are tensile.




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5.4.4.3         Geometry and Load Factor Qq

   Clause/(eqn)                                                Commentary                                         Message

    Table 4.3.1-1             If                β > 0.6

                              then                             0.3
                                                Qβ =
                                                         β (1 - 0.833β )
                              else              Qβ > 1.0


                              For K joints


                              If                γ > 20


                              then                         4g
                                                Q g = 1.8 -   ≥ 1.0
                                                           D
                              else                         0.1g
                                                Qg = 1.8 -      ≥ 1.0
                                                            T
                              Qq is obtained from

                                                                         Load
                              Joint
                              Type        Axial               Axial          In-plane            Out-of-plane
                                          Tension             Comp           Bending               Bending

                                                  0.2 
                                            1.1 +
                                                      Q
                                                    β  g
                                K
                                                      

                                                        0.2
                              T&Y               1.1 +                                                   0.67 
                                                        β                            0.67      1.37 +        Q
                                                                            3.72 +
                                                                                        β                β  β
                                                                                                             
                                               0.2            0.2 
                                       1.1 +            1.1 +     Q
                                               β               β  g
                                X                                 



                             If the loadcase is classified as EARTHQUAKE and the stresses in the
                             chord result from a combination of static and spectral loadcases, the
                             spectral stress component is multiplied by a factor of 2. If, however,
                             the resulting maximum stress (fa + fb) exceeds the yield stress, the
                             stress components fa, fip, fop are factored such that fa + fb = fy and thus
                             represent the capacity of the join chord away from the joint. The
                             factored stresses are printed in the output report. (Clause 2.3.6e para
                             1).




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5.4.4.4         Allowable Punching Shear Vp

   Clause/(eqn)                                                Commentary                                    Message

    (4.3.1-2)
    (AISC F4-1)                  Vp       =                   f yc 
                                                 α Qf Qq            ≤ 0.4α f yc
                                 where                        0.6γ 

                                 α        =     1.0 ORDINARY loadcase
                                          =     1.33 EXTREME loadcase
                                          =     1.7 EARTHQUAKE loadcase
                                 Qf       =     design factor for the presence of axial load in the chord
                                 Qq       =     factor dependent on geometry and type of loading

                                 As with the acting punching shear, the allowable shear is
                                 calculated separately for each component of brace loading.




5.4.4.5         Punching Shear Unity Checks

 Clause/(eqn)                                                  Commentary                                   Message

                                Unity checks are calculated for each component of brace loading, ie



                                                            vp 
                                              UCax =        
                                                           V 
                                                            p ax
                                                            
                                              UCip =        vp 
                                                           V 
                                                            p ip

                                              UCop =        vp 
                                                            
                                                           V 
                                                            p op




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5.4.4.6          Combined Axial and Bending Stress Unity Checks

   Clause/(eqn)                                                    Commentary                                                 Message

        (4.3.1-3a)                                         2              2
                                 UCBN =           vp   vp 
                                                   + 
                                                 V  V 
                                                  p ip  p op

                                 If         UCBN > 1.0 ......... ........................ .................................         N



                                                                                              2               2
        (4.3.1-3b)                                 vp   2       
                                                    + arcsin  vp  +  vp 
                                 UCCO =
                                                  V 
                                                   p ax π     V p ip  V p  op
                                 If an interpolatory joint type classification is specified two sets of
                                 geometry and loading factors Qq are calculated (Qq1 and Qq2). Two
                                 corresponding sets of API punching shear allowables are then
                                 calculated where each assumes the joint to be 100% of the
                                 respective types. If the joint is specified as C% joint type 1, the
                                 axial unity check is calculated as:


                                 UCax =           C       vp    100 - C                vp 
                                                                                           
                                                          V  + 100                    V 
                                                 100      p1 ax                        p 2 ax
                                 with UCip and UCop being calculated in a similar manner. The
                                 combined unity checks are calculated as before using the
                                 interpolated unity check values corresponding to each component
                                 of stress.




5.4.4.7          Joint Strength Unity Check

   Clause/(eqn)                                                    Commentary                                                 Message

       (4.1-1)                                      UCjt       =
                                                                          f yb (γτ sin θ )
                                                                        f yc(11 + 1.5 / β )




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5.4.5       Spectral Expansion for Joint Checks (API PUNC)

In response spectrum analysis using modal superposition (Ref. 12) structure displacements and forces calculated
represent estimated maxima. Such estimated maxima are, in general, unsigned (positive).

For the purpose of checking joints to API, a series of worst static-spectral possible loadcases must be generated
from the member unsigned spectral and signed static end forces.

The signs applied to the spectral end forces when generating a series of worst cases depends upon the unity
check being considered and details of the signs adopted/deduced are given in this section.

In BEAMST it is assumed that unity checks can be performed by considering the combination of static and
dynamic conditions to be purely a static condition.

There are eight possible unique combinations of signs, or ‘spectral expansions’, which can be applied to
unsigned spectral axial and local bending stresses:

        2 - axial (tension and compression)
        x
        2 - local Y bending (hog and sag)
        x
        2 - local Z bending (hog and sag)


and each is denoted by a single alphabetic letter code in BEAMST in the range R-Y as shown in Table 5.6. The
spectral expansion codes indicating the signs chosen by BEAMST for both the chord and brace member spectral
stresses are appended to the loadcase number in the unity check report, the code for the chord member being
appended first.

In general the influence of both the chord and brace members’ acting stress is such that by maximising the total
acting chord and brace stresses the resulting unity check values are also maximised. In such cases BEAMST
adopts the chord and brace member spectral axial and local bending stresses of the same sign as the static axial
and local bending static stresses respectively. There is one condition in which the above does not hold and this
may be summarised as follows:

If when the above procedure is followed and all extreme fibres in the chord are in tension, Qf is set to unity. In
such cases BEAMST searches for a spectral expansion which causes the largest compressive extreme fibre stress
and adopts it if found. This allows a smaller value of Qf to be calculated thus minimizing the allowables.

An example of a spectral expansion report for joint checks is given in Figure 5.14.




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                   Spectral                            Axial                     Local                  Local
                   Expansion                           Stress                    YY bend                Z-Z bend


                        R                                 +                          +                     +

                        S                                 +                          +                     -

                        T                                 +                          -                     -

                        U                                 +                          -                     -

                        V                                 _                          +                     +

                        W                                 -                          +                     -

                        X                                 _                          _                     +

                        Y                                 _                          _                     _

                        Z                                 0.0                        0.0                   0.0




Table 5.6 Automatic Signed Spectral Expansion codes for joint checks and the respective signs applied to
                                        Chord/Brace unsigned Spectral Constituents


Note


Spectral expansion Z represents the trivial case of static components only in a static-spectral loadcase.




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                                                                                                            API RP2A(20TH.ED. JUL. 1993)                 JOINT PUNCHING SHEAR UNITY CHECK REPORT                UNITS (N   ,MM )      UNCK
                                                                                                                                                         ---------------------------------------                -----                 ====
                                                                                                             JOINT CHORD LC. NO/ CHOR DIAM BETA / F -CHORD FA-BRACE/ QF-AX QF-IP QF-OP/ VP-AXIAL        VP-IP     VP-OP / AX-UC BEND.UC/P/F
                                                                                                                    BRACE JT1-PC/ CHOR THIC TAU / FY-CHORD FB-IP        / QQAX1 QQIP1 QQOP1/ ALL.1.AX ALL.1.IP ALL.1.OP/ IP-UC A+BN.UC/===
                                                                                                                          JT2-PC/    GAP     THETA/ ALL.AISC FB-OP      / QQAX2 QQIP2 QQOP2/ ALL.2.AX ALL.2.IP ALL.2.OP/ OP-UC JOIN.UC/
                                                                                                            ---------------------------------------------------------------------------------------------------------------------------------
                                                                                                              1110    101   10 /1.000D+00 1.000/ 6.983D+01 2.691D+01/ 0.969 0.953 0.978/ 2.691D+01 2.336D+01 1.288D+02/ 0.458      0.608 /
                                                                                                                      107 T 100/3.000D-02 1.000/ 3.500D+02 2.336D+01/ 1.300 4.390 3.665/ 5.878D+01 1.867D+02 1.673D+02/ 0.125      1.027+/***
                                                                                                                                /5.080D-02 90.000/ 1.867D+02 1.288D+02/                   /                             / 0.770    1.333 /***
                                                                                                            ---------------------------------------------------------------------------------------------------------------------------------
                                                                                                                      101   11SS/1.000D+00 1.000/ 1.526D+02 1.977D+01/ 0.905 0.858 0.934/ 1.977D+01 1.195D+01 1.350D+02/ 0.282     0.443 /
                                                                                                                      107 T 100/3.000D-02 1.000/ 3.500D+02 1.195D+01/ 1.300 4.390 3.665/ 7.000D+01 2.240D+02 2.035D+02/ 0.053      0.746+/
                                                                                                                                /5.080D-02 90.000/ 2.380D+02 1.350D+02/                   /                             / 0.663    1.333 /***
                                                                                                            ---------------------------------------------------------------------------------------------------------------------------------
                                                                                                              1110    101   10 /1.000D+00 1.000/ 6.983D+01 4.159D+01/ 0.969 0.953 0.978/ 4.130D+01 8.588D-01 4.754D+01/ 0.703      0.081 /
                                                                                                                      908 T 100/3.000D-02 1.000/ 3.500D+02 8.647D-01/ 1.300 4.390 3.665/ 5.878D+01 1.867D+02 1.673D+02/ 0.005      0.886+/
                                                                                                                                /5.080D-02 83.279/ 1.867D+02 4.786D+01/                   /                             / 0.284    1.324 /***




                                                                                                                                                                                                                                                    API Punching Shear Joint Checks
                                                                                                            ---------------------------------------------------------------------------------------------------------------------------------
                                                                                                                      101   11SS/1.000D+00 1.000/ 1.526D+02 1.868D+00/ 0.905 0.858 0.934/ 1.855D+00 1.385D+01 3.677D+01/ 0.027     0.036 /
                                                                                                                      908 T 100/3.000D-02 1.000/ 3.500D+02 1.395D+01/ 1.300 4.390 3.665/ 7.000D+01 2.240D+02 2.035D+02/ 0.062      0.149 /
                                                                                                                                /5.080D-02 83.279/ 2.380D+02 3.703D+01/                   /                             / 0.181+ 1.324 /***
                                                                                                            ---------------------------------------------------------------------------------------------------------------------------------
                                                                                                              1110    101   10 /1.000D+00 0.800/ 6.983D+01 9.339D+00/ 0.969 0.953 0.978/ 4.004D+00 5.624D+00 2.586D+01/ 0.040      0.053 /
                                                                                                                      141 K 100/3.000D-02 0.833/ 3.500D+02 1.312D+01/ 2.201 4.558 2.481/ 9.954D+01 1.867D+02 1.133D+02/ 0.030      0.188 /
                                                                                                                                /5.080D-02 30.964/ 1.867D+02 6.032D+01/                   /                             / 0.228+ 0.555 /
                                                                                                            ---------------------------------------------------------------------------------------------------------------------------------
                                                                                                                      101   11SS/1.000D+00 0.800/ 1.526D+02 4.376D+00/ 0.905 0.858 0.934/ 1.876D+00 4.504D+00 3.009D+01/ 0.016     0.048 /
                                                                                                                      141 K 100/3.000D-02 0.833/ 3.500D+02 1.051D+01/ 2.201 4.558 2.481/ 1.185D+02 2.325D+02 1.378D+02/ 0.019      0.157 /
                                                                                                                                /5.080D-02 30.964/ 2.380D+02 7.018D+01/                   /                             / 0.218+ 0.555 /
Page 5-67




                                                                                                                                                            Figure 5.14 Spectral Expansion Report
     BEAMST User Manual                                                                        API Nominal Load Joint Checks




5.5 API Nominal Load Check (API WSD NOMI)


5.5.1       Overview

The API WSD NOMI command requests that a nominal load joint check be performed as an alternative to the
API punching shear check and both are designed to give equivalent results. The nominal load check differs from
the punching shear check in that allowables are expressed in terms of brace loads rather than stresses and the
factor Qu replaces Qq. The two checks may be performed by interchanging PUNC and NOMI in the API header
command.

The joints may consist of TUBE elements and/or other beam types that have been assigned tubular sections in
the structural analysis.

Joints for punching shear post-processing are selected using the JOINt command in BEAMST which specifies
the node numbers at joint positions. All joints are assumed ‘simple’. Elements may be excluded from the joint
punching shear check using the SECOndary command.

Joints are automatically classed as K, T or Y depending on the joint geometry as follows.

1.   The chord member is the member with the greatest outside diameter.

2.   If two or more potential chord members have equal diameters; BEAMST will consider the two with the
     largest wall thicknesses and for each loadcase selected will check the one most heavily stressed against all
     brace members.

3.   In the case of two or more potential chord members with equal diameters and wall thicknesses, the first two
     encountered as shown in the Cross Check Report will be considered.

4.   If the CHORd command is used to specify a chord member, this alone will be considered. If two chords are
     specified, the most heavily stressed chord will be checked against all brace members for each loadcase
     selected.

5.   All members not selected as chord members are treated as brace members (unless defined as secondary),
     with each brace-chord pair being checked.


BEAMST selects ‘simple’ joint (brace-chord pair) ‘types’ as follows:

1.   Brace members ‘perpendicular’ to the chord members (smaller included angle less than or equal to 80
     degrees) as T joints.

2.   Single non-‘perpendicular’ braces are classified as Y joints. Two non-perpendicular braces on the same
     side of the chord are classified as K joints.




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3.   Cross or Double(DT) joints must be user specified.

4.   In the case of user defined K and X joints, no search is performed for a second brace member in the same
     brace-chord plane as the first brace.

5.   Brace members specified on joint TYPE commands are automatically selected as braces in the above brace-
     chord member selection process.

6.   No conflict between CHORd command specified members and brace members specified on joint TYPE
     commands is allowed.


BEAMST will only check selected joints in which two or more incident members are tubular and of circular
section. All other selected joints are automatically bypassed.

The user may override these classifications using the TYPE and CHOR commands.                              Interpolated joint
classifications may be defined using the TYPE command. For K joints a gap dimension appropriate to the joint
may be specified in the TYPE command. A default gap dimension may be specified using the GAPD command.

The detailed joint punching shear unity check report provides information on joint geometric parameters, type,
acting chord and brace stresses, punching shear, Qf and Qq factors, punching shear allowable(s), and unity
checks. This may be requested using the PRINt UNCK command. The maximum unity check is flagged for
ease of reference. When an interpolatory joint type classification is being employed two sets of punching shear
allowables are reported, one for each joint classification type and these pertain to joints classified as 100% of the
respective joint types.

Summary report 3 comprises the highest unity check for each selected loadcase for each joint.

Summary report 4 comprises the three worst unity checks for each selected joint, together with the distribution of
unity check values. This distribution provides information on the number of unity checks exceeding an upper
limit (default 1.0), less than a lower limit (default 0.5), and the number in the mid range.

BEAMST commands applicable to the API punching stress command are given in Table 5.7 and are described in
detail in Section 3.4. An example data file is given in Figure 5.15.




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       BEAMST User Manual                                                                      API Nominal Load Joint Checks



       Command                                                Description                                Usage     Note
     API WSD PUNC                 API joint check header command                                           C

     UNIT                         Units of length and force                                                C         1
     YIEL                         Yield stress

     JOIN                         Joint numbers to be reported
     TYPE                         Joint type and brace element definition
     CHOR                         Chord elements at a joint
     SECO                         Secondary members to be ignored in checks

     DESI                         Defines design section properties
     GAPD                         Define default gap dimension
     PROF                         Section profiles for use in design
     STUB                         Tubular member end stub dimensions

     CASE                         Basic loadcases
     COMB                         Define a combined loadcase for processing                                C          2
     CMBV                         Define a combined loadcase for processing
     SELE                         Select/redefine a combined/basic loadcase title
     SPEC                         Loadcases originating from response spectrum analysis
     RENU                         Renumber a basic loadcase
     QUAK                         Loadcases with earthquake permitted overstress
     EXTR                         Loadcase allowing extreme loading overstress

     PRIN                         Reports to be printed
     TEXT                         Text or comment command
     TITLE                        Redefine global title

     END                          Terminates command data block                                            C


Usage
C.         Compulsory command, but see notes below where applicable.

Notes

1.    See Sections 3.4 and A.12.

2.    At least one CASE, COMB or CMBV command must be included


                                           Table 5.7 API WSD NOMI Commands




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       SYSTEM DATA AREA 100000
       TEXT BEAMST USER MANUAL EXAMPLE STRUCTURE T0847
       JOB POST
       PROJECT MANU
       COMPONENT PILE JACA
       OPTION GOON
       END
       API ED20 NOMI
       *
       * Investigate all joints in the model except where
       * only one element is connected
       *
       JOINT ALL
       NOT JOINTS 1315 1355 5110 5150
       *
       * Ignore dummy elements
       *
       SECONDARY ELEMENTS 801 802
       UNIT KN M
       *
       * Change tubular dimensions for one element
       *
       DESI TUB 1.0 0.05 ELEM 131
       *
       * Examine two wave cases
       *
       SELE 10 Extreme Wave 1 + Dead Loads + Topside Loads
       COMB 10 1.0 1 1.0 3 1.0 4
       SELE 11 Extreme Wave 2 + Dead Loads + Topside Loads
       COMB 11 1.0 2 1.0 3 1.0 4
       *
       * Indicate that these loadcases are extreme events
       *
       EXTR 10 11
       *
       * Yield Value Constant for all elements
       *
       YIELD 3.5E05 ELEM ALL
       *
       * Specify the chord elements for one of the joints
       *
       CHORD 1130 122 123
       *
       * Set some joints as being Y
       *
       TYPE.OF.JOINT 1130 Y 102
       TYPE.OF.JOINT 1130 Y 103
       *
       * Ask explicitly for all reports
       *
       PRIN XCHK UNCK SUNI N MM SUM3 BOTH SUM4 BOTH
       END
       STOP
                       Figure 5.15 Example API WSD NOMI data file




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     BEAMST User Manual                                                                        API Nominal Load Joint Checks


5.5.2        API Nominal Load Check Reports

The detailed nominal load unity check report provides information on joint geometric parameters, type, acting
chord and brace loading, Qf, and Qu factors, nominal load allowables and unity checks. This may be requested
using the PRINt UNCK command. The maximum unitity check is flagged for ease of reference. When an
interpolatory joint type classification is being employed, two sets of nominal load allowables are reported, one
for each joint classification type, and these pertain to joints classified as 100% of the respective joint types.

A description of the column headers for the detailed report is given in Figure 5.15. The final column is reserved
for messages. These may be summarised as follows.

        ***          -            Unity check value exceeds unity

        **           -            Unity check value exceeds 0.9

        NO
        UNI          -            Brace angle θ is less than 20 degress so no unity checks are calculated
        CHK

        BTA
        GT           -            β ratio is greater than unity so no unity checks are calculated
        ONE

        +            -            Largest unity check

        N            -            If the first combined unity check exceeds unity (UCBN) then the secondary unity
                                  check cannot be calculated (UCCO).


Examples of the summary reports available are given in Figures 5.17 and 5.18.




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    Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.




                                                                                                                                                                                                                                                                BEAMST User Manual
                                                                                                            API RP2A(20TH.ED. JUL. 1993)                       JOINT NOMINAL LOAD UNITY CHECK REPORT                         UNITS (N  ,MM )        UNCK
                                                                                                                                                               ---------------------------------------                       -----                  ====
                                                                                                             JOINT   CHORD LC. NO/CHOR DIAM      BETA /   F -CHORD FA-BRACE/ QF-AX QF-IP QF-OP/ P -AXIAL               M -IP     M -OP / AX-UC    BEND.UC/P/F
                                                                                                                     BRACE JT1-PC/CHOR THIC      TAU /    FY-CHORD FB-IP    / QUAX1 QUIP1 QUOP1/ ALL.1.AX             ALL.1.IP ALL.1.OP/ IP-UC    A+BN.UC/===
                                                                                                                           JT2-PC/   GAP         THETA/   ALL.AISC FB-OP    / QUAX2 QUIP2 QUOP2/ ALL.2.AX             ALL.2.IP ALL.2.OP/ OP-UC    JOIN.UC/
                                                                                                                                             D     β       2          2     2 faxb     Qfax   Qfip   Qfop     P       Mip      Mop     UCax      UCBN
                                                                                                                                                          f axc + f ipc + f opc
                                                                                                                                             T     τ           fyc            fipb     Quax   Quip   Quop      Pa     Maip     Maop   UCip    UCCO
                                                                                                                                             g     θ           0.4αfyc        fopb     Quax   Quip   Quop      Pa     Maip     Maop   UCop    UCjt


                                                                                                                                                                                              100% type2               100% type2

                                                                                                                                                                                              100% type1               100% type1



                                                                                                            (3 lines per chord brace pair)




                                                                                                                                                                                                                                                                    API Nominal Load Joint Checks
                                                                                                                                                                     Figure 5.16 Detailed Joint Nominal Load Report
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                                                                                                                                                                                                                                                  BEAMST User Manual
                                                                                                            API RP2A(20TH.ED. JUL. 1993)                JOINT NOMINAL LOAD   UNITY CHECK SUMMARY REPORT NO. 3                        SUM3
                                                                                                                                                        =====================================================                        ==== ====
                                                                                                            ( AX=AXIAL UC., IP=IN PLANE BENDING UC., OP=OUT OF PLANE BENDING UC., BN=COMBINED BENDING UC., CO=AXIAL+BENDING COMB UC.
                                                                                                                                                                                                        1 = CHORD 1 , 2 = CHORD 2 )
                                                                                                             JOINT CHORD CHORD BRACE /      JOINT WORST LOAD / NO. OF L.C./---------------UNITY CHECKS FOR REQUESTED LOAD CASES---------------
                                                                                                                        1      2        /STRENGTH UN CK CASE / FAIL CHKD /CASES      8       9
                                                                                                            -----------------------------------------------------------------------------------------------------------------------------------
                                                                                                                 2      6      0      2 /    1.32 0.46CO    9 /    0     2 /    0.34CO1 0.46CO1
                                                                                                            -----------------------------------------------------------------------------------------------------------------------------------
                                                                                                                 3      1      3      5 /    1.40 0.68CO    8 /    0     2 /    0.68CO2 0.20OP2
                                                                                                                 3      1      3      6 /    0.72 0.90CO    8 /    0     2 /    0.90CO2 0.48OP2
                                                                                                            -----------------------------------------------------------------------------------------------------------------------------------
                                                                                                                 4      2      4      5 /    1.17 1.36BN    8 /    2     2 /    1.36BN1 1.36BN1
                                                                                                                 4      2      4      7 /    0.76 1.16CO    8 /    1     2 /    1.16CO1 0.90OP1
                                                                                                            -----------------------------------------------------------------------------------------------------------------------------------
                                                                                                                 5      7      0      3 /    0.97 0.23CO    8 /    0     2 /    0.23CO1 0.21OP1

                                                                                                             **NOMINAL LOAD    SUMMARY REPORT TAIL
                                                                                                                   6 .....JOINTS WERE SELECTED                6 .....JOINTS WERE CHECKED               1 .....JOINTS FAILED
                                                                                                                                                              6 .....BRACE-CHORD PAIRS CHECKED         2 .....BRACE-CHORD PAIRS FAILED

                                                                                                            API RP2A(20TH.ED. JUL. 1993)                JOINT NOMINAL LOAD   UNITY CHECK SUMMARY REPORT NO. 3                        SUM3 FAIL
                                                                                                                                                                                                                                     ==== ====




                                                                                                                                                                                                                                                      API Nominal Load Joint Checks
                                                                                                                                                        =====================================================
                                                                                                            ( AX=AXIAL UC., IP=IN PLANE BENDING UC., OP=OUT OF PLANE BENDING UC., BN=COMBINED BENDING UC., CO=AXIAL+BENDING COMB UC.
                                                                                                                                                                                                        1 = CHORD 1 , 2 = CHORD 2 )
                                                                                                             JOINT CHORD CHORD BRACE /      JOINT WORST LOAD / NO. OF L.C./---------------UNITY CHECKS FOR REQUESTED LOAD CASES---------------
                                                                                                                        1      2        /STRENGTH UN CK CASE / FAIL CHKD /CASES      8       9
                                                                                                            -----------------------------------------------------------------------------------------------------------------------------------
                                                                                                                 4      2      4      5 /    1.17 1.36BN    8 /    2     2 /    1.36BN1 1.36BN1
                                                                                                                 4      2      4      7 /    0.76 1.16CO    8 /    1     2 /    1.16CO1 0.90OP1

                                                                                                             **NOMINAL LOAD    SUMMARY REPORT TAIL
                                                                                                                   6 .....JOINTS WERE SELECTED                6 .....JOINTS WERE CHECKED               1 .....JOINTS FAILED
Page 5-75




                                                                                                                                                              6 .....BRACE-CHORD PAIRS CHECKED         2 .....BRACE-CHORD PAIRS FAILED



                                                                                                                                                     Figure 5.17 Example Joint Nominal Load Summary Report 3
    Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.




                                                                                                                                                                                                                                                  BEAMST User Manual
                                                                                                            API RP2A(20TH.ED. JUL. 1993)                JOINT NOMINAL LOAD   UNITY CHECK SUMMARY REPORT NO. 4                        SUM4
                                                                                                                                                        =====================================================                        ==== ====
                                                                                                                                                  THREE WORST UNITY CHECKS    ( AX=AXIAL LOAD UC, IP=IN-PLANE BEND UC, OP=OUT-PLANE BEND UC,
                                                                                                                                                  ------------------------                      BN=COMB BEND UC, CO=COMB BEND+AXIAL UC. )
                                                                                                                   /------------FIRST-----------/-----------SECOND-----------/------------THIRD-----------/NO. OF CHORD-BRACE PAIR UNITY CHECKS
                                                                                                             JOINT / CHORD BRACE UNITY     LOAD / CHORD BRACE UNITY     LOAD / CHORD BRACE UNITY     LOAD /                GE      GE      LT
                                                                                                                   /               CHECK   CASE /               CHECK   CASE /               CHECK   CASE / FAIL CHKD     1.00    0.50    0.50
                                                                                                            -----------------------------------------------------------------------------------------------------------------------------------
                                                                                                                 2 /     6      2 0.46CO      9 /     6      2 0.34CO      8 /     0      0 0.00        0 /    0     2       0       0       2
                                                                                                                 3 /     3      6 0.90CO      8 /     3      5 0.68CO      8 /     3      6 0.48OP      9 /    0     4       0       2       2
                                                                                                                 4 /     2      5 1.36BN      8 /     2      5 1.36BN      9 /     2      7 1.16CO      8 /    3     4       3       1       0
                                                                                                                 5 /     7      3 0.23CO      8 /     7      3 0.21OP      9 /     0      0 0.00        0 /    0     2       0       0       2

                                                                                                              **NOMINAL LOAD    SUMMARY REPORT TAIL
                                                                                                                    1 .....JOINTS WERE SELECTED                6 .....JOINTS WERE CHECKED               1 .....JOINTS FAILED
                                                                                                                                                               6 .....BRACE-CHORD PAIRS CHECKED         2 .....BRACE-CHORD PAIRS FAILED

                                                                                                            API RP2A(20TH.ED. JUL. 1993)                JOINT NOMINAL LOAD   UNITY CHECK SUMMARY REPORT NO. 4                        SUM4 FAIL
                                                                                                                                                        =====================================================                        ==== ====
                                                                                                                                                  THREE WORST UNITY CHECKS    ( AX=AXIAL LOAD UC, IP=IN-PLANE BEND UC, OP=OUT-PLANE BEND UC,
                                                                                                                                                  ------------------------                      BN=COMB BEND UC, CO=COMB BEND+AXIAL UC. )
                                                                                                                   /------------FIRST-----------/-----------SECOND-----------/------------THIRD-----------/NO. OF CHORD-BRACE PAIR UNITY CHECKS




                                                                                                                                                                                                                                                      API Nominal Load Joint Checks
                                                                                                             JOINT / CHORD BRACE UNITY     LOAD / CHORD BRACE UNITY     LOAD / CHORD BRACE UNITY     LOAD /                GE      GE      LT
                                                                                                                   /               CHECK   CASE /               CHECK   CASE /               CHECK   CASE / FAIL CHKD     1.00    0.50    0.50
                                                                                                            -----------------------------------------------------------------------------------------------------------------------------------
                                                                                                                 4 /     2      5 1.36BN      8 /     2      5 1.36BN      9 /     2      7 1.16CO      8 /    3     4       3       1       0

                                                                                                             **NOMINAL LOAD    SUMMARY REPORT TAIL
                                                                                                                   1 .....JOINTS WERE SELECTED                 6 .....JOINTS WERE CHECKED               1 .....JOINTS FAILED
                                                                                                                                                               6 .....BRACE-CHORD PAIRS CHECKED         2 .....BRACE-CHORD PAIRS FAILED



                                                                                                                                                      Figure 5.18 Example Joint Nominal Load Summary Report 4
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5.5.3       Nomenclature


5.5.3.1            Dimensional




            D        =     chord diameter
            d        =     brace diameter
            R        =     chord radius
            T        =     chord thickness
            t        =     brace thickness
            γ        =     ratio between the chord radius and thickness R/T
            τ        =     ratio between the thickness of the brace and chord t/T
            θ        =     angle between brace and chord
            β        =     ratio between the diameter of the brace and chord d/D
            g        =     K joint gap


5.5.3.2            Acting Forces and Stresses


            P        =     brace axial force
            Mip      =     brace in-plane bending moment
            Mop      =     brace out-of-plane bending moment
            faxc     =     chord axial stress component
            fipc     =     chord in-plane bending stress
            fopc     =     chord out-of-plane bending stress
            fa       =     brace axial stress component
            fip      =     brace in-plane bending stress




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            fop      =     brace out-of-plane bending stress
            fb       =     resultant brace bending stress


5.5.3.3           Allowable Stresses and Unity Checks



            fyc      =     chord yield stress
            Pa       =     allowable axial force
            Maip     =     allowable in-plane bending moment
            Maop     =     allowable out-of-plane bending moment
            UCax =         axial force unity check
            UCip =         in-plane bending unity check
            UCop =         out-of-plane bending unity check
            UCBN =         combined bending unity check
            UCCO =         combined axial and bending unity check
            UCjt     =     joint strength unity check




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5.5.4       API Allowable Nominal Loads and Unity Checks


5.5.4.1         Chord Design Factor Qf

   Clause/(eqn)                                                Commentary                                     Message

                              Q f = 1.0 - λγ A2
                              where
                                λ = 0.030 brace axial stress
                                  = 0.045 brace in-plane bending
                                  = 0.021 brace out-of-plane bending
                                         f axc + f ipc + f opc
                                A=
                                                µ f yc
                                µ = 0.6        ORDINARY loadcase
                                  = 0.8        EXTREME loadcase
                                  = 1.0        EARTHQUAKE loadcase

                             Qf is set to 1.0 if all extreme fibre stresses in the chord are tensile.




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5.5.4.2         Ultimate Strength Factor Qu

   Clause/(eqn)                                                Commentary                                         Message

    Table 4.3.1-2             If                   β > 0.6
                                                                  0.3
                              then                Qβ =
                                                           β (1 - 0.833β )
                              else                Q β > 1.0

                              For K Joints

                              If                   γ > 20
                                                                   4g
                              then                 Q g = 1.8 -        ≥ 1.0
                                                                   D
                              else                                 0.1g
                                                  Q g = 1.8 -
                                                                    T
                              Qu is obtained from
                                                                          Load
                              Joint
                              Type        Axial               Axial          In-plane            Out-of-plane
                                          Tension             Comp           Bending               Bending


                                   K            (3.4 + 19 β ) Qg


                              T&Y                  3.4 + 19 β                3.4 + 19 β         (3.4 + 13β ) Qβ


                                   X     3.4 + 19 β (3.4 + 13β ) Qβ


                             If the loadcase is classified as EARTHQUAKE and the stresses in the
                             chord result from a combination of static and spectral loadcases, the
                             spectral stress component is multiplied by a factor of 2. If, however,
                             the resulting maximum stress (fa + fb) exceeds the yield stress, the
                             stress components fa, fip, fop are factored such that fa + fb = fy and thus
                             represent the capacity of the join chord away from the joint. The
                             factored stesses are printed in the output report. (Clause 2.3.6e para
                             1).




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5.5.4.3          Allowable Nominal Loads

   Clause/(eqn)                                                Commentary                                     Message

    (4.3.1-4a)
    (AISC F4-1)                                   f yc T 2  0.4α f yc A
                                  P a = α Qu Q f            ≤
                                                  1.7 sin θ   τ sin θ
                                                            
   (4.3.1-4b)
                                                                        2
                                                 f yc T 2               0.4α f yc A 2I
                                  Ma = α Qu Q f             x (0.8d ) ≤
                                                 1.7 sin θ                τ sin θ d
                                                           
                                 where

                                  α = 1.0 ORDINARY loadcase
                                    = 1.33 EXTREME loadcase
                                    = 1.7 EARTHQUAKE loadcase




5.5.4.4          Nominal Load Unity Checks

   Clause/(eqn)                                                Commentary                                     Message

                               Unity checks are calculated for each component of
                               brace loading, ie.

                                                              P
                                                      UC ax =  
                                                               P a  ax
                                                              M 
                                                      UC ip =      
                                                               M a ip
                                                              M 
                                                      UC op =      
                                                               M a  op




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5.5.4.5         Combined Axial and Bending Unity Checks

   Clause/(eqn)                                                  Commentary                                                   Message

                                                     2               2
       (4.3.1-5a)                     M  M 
                              UC BN =       +      
                                       M a ip  M a  op
                              If    UC BN > 1.0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   N

       (4.3.1-5b)                                                                    2               2
                                      P       2  M  M 
                              UC CO =   + arcsin 
                                        π               +      
                                       P a ax     M a ip  M a  op




5.5.4.6         Interpolated Joints

   Clause/(eqn)                                                  Commentary                                                   Message

                           If an interpolatory joint type classification is specified, two sets of
                           geometry and loading factors Qu are calculated (Qu1 and Qu2). Two
                           corresponding sets of nominal load allowables are then computed
                           where each assumes the joint to be 100% of the respective types. If
                           the joint is specified as C% joint type 1, the axial unit check is
                           calculated as:
                                                              C  P        100 - C  P 
                                               UC ax >                  +            
                                                                       
                                                             100  P a1 ax  100  P a2 ax
                                                                                       
                           with VCip and UCop being calculated in a similar manner. The
                           combined unity checks are calculated as before using the interpolated
                           unity check values corresponding to each component of stress.




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5.5.4.7         Joint Strength Unity Check

   Clause/(eqn)                                                     Commentary                                Message

                                                 f    yb
                                                           (γτ sin θ )
                                 UC jt =
         (4.1-1)                             f   yc
                                                      (11 + 1.5/β )
                               If




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5.5.5       Spectral Expansion for Joint Checks (API NOMI)

In response spectrum analysis using modal superposition (Ref. 12) structure displacements and forces calculated
represent estimated maxima. Such estimated maxima are, in general, unsigned (positive).

For the purpose of checking joints to API, a series of worst static-spectral possible loadcases must be generated
from the member unsigned spectral and signed static end forces.

The signs applied to the spectral end forces when generating a series of worst cases depends upon the unity
check being considered and details of the signs adopted/deduced are given in this section.

In BEAMST it is assumed that unity checks can be performed by considering the combination of static and
dynamic conditions to be purely a static condition.

There are eight possible unique combinations of signs, or ‘spectral expansions’, which can be applied to
unsigned spectral axial and local bending stresses:

        2 - axial (tension and compression)
        x
        2 - local Y bending (hog and sag)
        x
        2 - local Z bending (hog and sag)


and each is denoted by a single alphabetic letter code in BEAMST in the range R-Y as shown in Table 5.8. The
spectral expansion codes indicating the signs chosen by BEAMST for both the chord and brace member spectral
stresses are appended to the loadcase number in the unity check report, the code for the chord member being
appended first.

In general the influence of both the chord and brace members’ acting stress is such that by maximising the total
acting chord and brace stresses the resulting unity check values are also maximised. In such cases BEAMST
adopts the chord and brace member spectral axial and local bending stresses of the same sign as the satic axial
and local bending static stresses respectively. There is one condition in which the above does not hold and this
may be summarised as follows:

If a cross joint is specified two values of the axial components of Qq/Qu may be calculated depending on
whether the axial stress in the brace is compressive or tensile. If a large spectral axial stress is to be combined
with a small tensile static stress it is not obvious which spectral expansion leads to the worst unity check value.
A small compressive axial stress may produce a smaller allowable than a higher tensile stress. BEAMST
considers both possibilities and adopts a spectral expansion which leads to the worst unity check.

An example of a spectral expansion report for joint checks is given in Figure 5.19.




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                   Spectral                            Axial                     Local                  Local
                   Expansion                           Stress                    YY bend                Z-Z bend


                        R                                 +                          +                     +

                        S                                 +                          +                     -

                        T                                 +                          -                     -

                        U                                 +                          -                     -

                        V                                 _                          +                     +

                        W                                 -                          +                     -

                        X                                 _                          _                     +

                        Y                                 _                          _                     _

                        Z                                 0.0                        0.0                   0.0




Table 5.8 Automatic Signed Spectral Expansion codes for joint checks and the respective signs applied to
                                        Chord/Brace unsigned Spectral Constituents


Note


Spectral expansion Z represents the trivial case of static components only in a static-spectral loadcase.




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    Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.




                                                                                                            API RP2A(20TH.ED. JUL. 1993)                 JOINT NOMINAL LOAD UNITY CHECK REPORT                  UNITS (N   ,MM )      UNCK
                                                                                                                                                         ---------------------------------------                -----                 ====
                                                                                                             JOINT CHORD LC. NO/CHOR DIAM BETA / F -CHORD FA-BRACE/ QF-AX QF-IP QF-OP/ P -AXIAL           M -IP     M -OP / AX-UC BEND.UC/P/F
                                                                                                                    BRACE JT1-PC/CHOR THIC TAU / FY-CHORD FB-IP       / QUAX1 QUIP1 QUOP1/ ALL.1.AX ALL.1.IP ALL.1.OP/ IP-UC A+BN.UC/===
                                                                                                                          JT2-PC/   GAP     THETA/ ALL.AISC FB-OP     / QUAX2 QUIP2 QUOP2/ ALL.2.AX ALL.2.IP ALL.2.OP/ OP-UC JOIN.UC/
                                                                                                            -----------------------------------------------------------------------------------------------------------------------------------
                                                                                                              1110    101   10 /1.000D+00 1.000/ 6.983D+01 2.691D+01/ 0.969 0.953 0.978/ 2.460D+03 5.028D+02 2.773D+03/ 0.459        0.605 /
                                                                                                                      107 T 100/3.000D-02 1.000/ 3.500D+02 2.336D+01/ 22.400 22.400 18.683/ 5.362D+03 4.018D+03 3.612D+03/ 0.125     1.026+/***
                                                                                                                                /5.080D-02 90.000/ 1.867D+02 1.288D+02/                     /                              / 0.768   1.333 /***
                                                                                                            -----------------------------------------------------------------------------------------------------------------------------------
                                                                                                                      101   11SS/1.000D+00 1.000/ 1.526D+02 1.977D+01/ 0.905 0.858 0.934/ 1.807D+03 2.571D+02 2.906D+03/ 0.283       0.440 /
                                                                                                                      107 T 100/3.000D-02 1.000/ 3.500D+02 1.195D+01/ 22.400 22.400 18.683/ 6.386D+03 4.840D+03 4.395D+03/ 0.053     0.745+/
                                                                                                                                /5.080D-02 90.000/ 2.380D+02 1.350D+02/                     /                              / 0.661   1.333 /***
                                                                                                            -----------------------------------------------------------------------------------------------------------------------------------
                                                                                                              1110    101   10 /1.000D+00 1.000/ 6.983D+01 4.159D+01/ 0.969 0.953 0.978/ 3.802D+03 1.861D+01 1.030D+03/ 0.704        0.080 /
                                                                                                                      908 T 100/3.000D-02 1.000/ 3.500D+02 8.647D-01/ 22.400 22.400 18.683/ 5.399D+03 4.046D+03 3.637D+03/ 0.005     0.887+/
                                                                                                                                /5.080D-02 83.279/ 1.867D+02 4.786D+01/                     /                              / 0.283   1.324 /***
                                                                                                            -----------------------------------------------------------------------------------------------------------------------------------
                                                                                                                      101   11SS/1.000D+00 1.000/ 1.526D+02 1.868D+00/ 0.905 0.858 0.934/ 1.708D+02 3.003D+02 7.970D+02/ 0.027       0.036 /




                                                                                                                                                                                                                                                      API Nominal Load Joint Checks
                                                                                                                      908 T 100/3.000D-02 1.000/ 3.500D+02 1.395D+01/ 22.400 22.400 18.683/ 6.430D+03 4.874D+03 4.425D+03/ 0.062     0.148 /
                                                                                                                                /5.080D-02 83.279/ 2.380D+02 3.703D+01/                     /                              / 0.180+ 1.324 /***
                                                                                                            -----------------------------------------------------------------------------------------------------------------------------------
                                                                                                              1110    101   10 /1.000D+00 0.800/ 6.983D+01 9.339D+00/ 0.969 0.953 0.978/ 5.685D+02 1.500D+02 6.899D+02/ 0.040        0.052 /
                                                                                                                      141 K 100/3.000D-02 0.833/ 3.500D+02 1.312D+01/ 30.330 18.600 10.117/ 1.411D+04 4.979D+03 3.041D+03/ 0.030     0.187 /
                                                                                                                                /5.080D-02 30.964/ 1.867D+02 6.032D+01/                     /                              / 0.227+ 0.555 /
                                                                                                            -----------------------------------------------------------------------------------------------------------------------------------
                                                                                                                      101   11SS/1.000D+00 0.800/ 1.526D+02 4.376D+00/ 0.905 0.858 0.934/ 2.664D+02 1.201D+02 8.027D+02/ 0.016       0.047 /
                                                                                                                      141 K 100/3.000D-02 0.833/ 3.500D+02 1.051D+01/ 30.330 18.600 10.117/ 1.681D+04 6.250D+03 3.701D+03/ 0.019     0.156