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New Nonlinear Analysis Features

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					   GTSTRUDL
Pushover Analysis
 How Do You Do It?
 What Do You Get?




  GTSTRUDL Users Group
     June 18-21, 2003
   Clearwater Beach, FL
                     Topics
   Basic Nonlinear Analysis Procedure
   Member Material Nonlinearity
     Nonlinear Member End Connections
     Plastic Hinge
   Basic Incremental Nonlinear Analysis Example
   Basic Pushover Analysis Procedure
   Pushover Analysis Features and Mechanics
   Pushover Analysis Examples
     Steel Frame with Nonlinear Member End Connections
     Steel Frame with Plastic Hinges
     RC Frame with Plastic Hinges by Force Control
     RC Frame with Plastic Hinges by Displacement Control
     Basic Nonlinear Analysis Procedure
1.     Define nonlinearity
         NL geometry, T/C only, NL springs, Cable elements, NL
         member end connections, Plastic hinges, Hysteretic
         friction damper element, NLS4PH spring element

2.     Define independent load(s) to be activated
       for the nonlinear analysis
            FORM LOAD…

3.     Specify the nonlinear analysis control
       parameters
         Iteration and convergence control

4.     Execute the nonlinear analysis
Nonlinear Effects Menu
Nonlinear Effects Menu
Nonlinear Spring Element Menus
Nonlinear Spring Element Menus
Nonlinear Spring Element Menus
    Nonlinear Spring Connections
             Properties

                   NLS Member End Connections
                   • Up to 6 uncoupled DOFs
                   • Elastic loading/unloading behavior
                   • Any member loads
                   • Member releases
M                  • Member end joint sizes
                   • Member eccentricities




                    Q
         Nonlinear Spring Connections
                       Data Description
UNITS KIPS INCHES RADIANS
NONLINEAR SPRING PROPERTIES
CURVE ‘Mz’ MOMENT VS ROTATION SYMMETRIC
   0.0    0.0    -
                                 Mz
2100.0    0.3E-3 -
                                 2100
2100.0    0.3E-2 -
1000.0    0.301E-2 -             1000

1000.0    0.01


                                        .0003            .003   .01
                                                                      Q
NONLINEAR EFFECTS
  NLS CONNECTION MEMBERS 1 TO 7 START MOMENT Z 'Mz' -
                                 END     MOMENT Z 'Mz'
Plastic Hinge Effects
     Basic Geometry



         X-Section details:   shape, dimensions,location
                              of reinforcing steel,
         material             characteristics, etc.




LH
            Plastic Hinge Effects
                Basic Geometry

Supported Cross Section Shapes
• Steel sections from tables
      Wide flange, channel, tee, tube, pipe
• Reinforced concrete sections
Plastic Hinge Effects
     Properties
                     QY

                          Hinge/slider


      yf


                                         UX



                LH

           QZ
         Plastic Hinge Effects
                    Properties




                                 Residual Stress Model for
                                 Wide Flange Sections



Steel Stress-Strain Model
(Balan, Filippou, Popov, 1998)
  Plastic Hinge Effects
           Properties




Confined Concrete Stress-Strain Model
      (Mander, Priestley, Park, 1988)
              Plastic Hinge Effects
Properties -- Material Property Defaults

 Steel specs Data Item                         Default Value
          E                                      29000 ksi
         FY                                       60 ksi
         ESH                        (32 - .45FY)(FY/29000) (FY in ksi)
         EH                         EH = 0.5*(FSU - FY)/(ESU - ESH)
         ESU                                       0.05
         FSU                                      1.5FY

                         Default Concrete Properties
                              FCP = 4000 psi
                              EC0 = 0.002
                              E    = 60200FCP psi
                              Fr = 7.5FCP psi
                                       Plastic Hinge Effects
                Properties – Material Stress-Strain Examples

                                                       Steel Stress-Strain Curve, fy = 68 ksi


               100


               90


               80

                                                                         Eh = 163.6 ksi (default)
               70
                                                                         Eh = 245.4 ksi

               60
Stress (ksi)




               50                                                   Fy = 68 ksi
                                                                    E = 29000 ksi
               40
                                                                    esh = 0.0075
               30                                                   fsu = 95 ksi
                                                                    eu = 0.09
               20
                                                                    Eh = 163.6 ksi, 245.4
               10
                                                                    ksi

                0
                     0   0.01   0.02     0.03   0.04        0.05       0.06       0.07       0.08   0.09   0.1
                                                           Strain
                                         Plastic Hinge Effects
                       Properties – Material Stress-Strain Examples
                                            Confined and Unconfined Concrete Stress-Strain Curve
                                                 60-inch Circular Cross Section, fcp = 5.28 ksi
               8



               7



               6

                                              Confined: Hoops = #8 @ 6 inches
               5
                                              Unconfined
Stress (ksi)




               4

                                                    fc’ = 5.28 ksi
               3                                   ec0 = 0.002
                                                   esp = 0.005
               2
                                                   fys = 68 ksi

               1



               0
                   0     0.002   0.004     0.006        0.008            0.01   0.012      0.014   0.016   0.018
                                                                Strain
                                        Plastic Hinge Effects
                           Properties – RC Plastic Hinge Behavior
                                                      Moment-Rotation: GTStrudl vs SEQMC
                                    Circular Cross Section, Diam = 60 inches, 14 #14, Spiral #6@3", Cover = 1.25"
                6000




                5000




                                                                          GTStrudl, P = 1000 K
                4000
                                                                          SEQMC, P = 1000 K
Moment (k-ft)




                                                                     Material Properties
                3000
                                                      Concrete                                       Steel
                                                      fc’ = 6 ksi                                   Fy = 44 ksi
                2000
                                                      ec0 = 0.002                                   E = 29000 ksi
                                                      esp = 0.005                                   esh = 0.02
                                                      fys = 60 ksi                                  fsu = 66 ksi
                                                                                                    eu = 0.076
                1000
                                                                                                    Eh = 392.0 ksi



                   0
                       0     0.01        0.02          0.03              0.04                0.05      0.06          0.07   0.08
                                                              Plastic Hinge Rotation (rad)
          Plastic Hinge Effects
       Summary of Characteristics


   Compact behavior; e.g. no local buckling,
    etc.

   Neutral axis shift automatically taken
    into account by equilibrium corrections.

   Failure is based on combined normal
    stress only (axial plus bending).
        Plastic Hinge Effects
      Summary of Characteristics

   Elastic loading/unloading behavior
    only. No hysteretic effects.

   May be mixed with any other member
    nonlinearity including NLS connections
    (DOFs may not overlap).

   All member modeling features
    supported:   member loads, member
    releases, member eccentricities, etc.
               Plastic Hinge Effects
Data Description Example – WF Section

                        NTF   UNITS INCHES KIPS
                              NONLINEAR EFFECTS
                                GEOMETRY MEMBERS 1 TO 4
                                PLASTIC HINGE START END –
                 ND
 NTW                              FIBER GEOMETRY NTF 1 NTW 1 –
                                        NBF 8 ND 8 LH 10.0 -
                                  STEEL FY 50.0 FSU 50.01 ESU 1.0 -
                                        ALPHA 0.5 –
                                MEMBERS 1 TO 4
       NBF



Fiber Grid for W21X68
                             Plastic Hinge Effects
Data Description Example – Rectangular RC Section

      Top Bars           y

                                COVER
                                             UNITS INCHES KIPS
                                             NONLINEAR EFFECTS
                                               PLASTIC HINGE START -
                                               FIBER GEOMETRY NB 10 NH 20 LH 20.0 -
                                        H,
                                               STEEL FY 60.0 FYS 36.0 -
                                        NH
  z                                            R-C RECTANGLE B 24.0 H 40.0 FCP 5.0 -
                                               BARS ASTM START -
                                                 BOTTOM 5 10 TOP 5 10 SIDE 3 10 -
                                                 TIES 3 2 3 2.0 -
                                                 COVER 4.061 -
                 Bottom Bars
                                               MEMBERS 1 TO 4
                    B,
                    NB
Nonlinear Analysis Procedure




                   MAXIMUM NUMBER OF CYCLES 50
                   CONVERGENCE TOLERANCE -
                     DISPLACEMENT 0.001

                   NONLINEAR ANALYSIS
      Basic Nonlinear Analysis Example
                 100 k/ft
                                                     STRUDL 'NL1' 'BASIC NONLINEAR FRAME
                                                        ANALYSIS'
           1       1                 2
                                                     UNITS INCHES KIPS
                                                     JOINT COORDS
                   10.000 FT         5                  1 0.0 180.0 S
                                                        2 120.0 180.0
                                     3
                                                        3 120.0 135.0
                                                        4 120.0 90.0
                                     4
                                                        5 120.0 45.0
       Ax = 10000 in2
                                     4   15.000 FT      6 120.0 0.0 S
       Ig = 100 in4
       Ic = 200 in4                                  JOINT RELEASES
                                     3
       E   = 10000 ksi                                  1 6 MOMENT Z
                                     5
                                                     TYPE PLANE FRAME
                                     2               MEMBER INC
                                                       1 1 2; 2 6 5
Y
                                 6                     3 5 4; 4 4 3;
Z X
                      SUPPORT FX FY FZ MX MY           532
Basic Nonlinear Analysis Example

CONSTANTS
  E 10000.0                         NONLINEAR EFFECTS
                                      GEOMETRY MEMBERS 2 TO 5
MEMBER PROPERTIES
  1      AX 10000.0 IZ 100.0        MAXIMUM NUMBER OF CYCLES 50
  2 TO 5 AX 10000.0 IZ 200.0        CONVERGENCE TOLERANCE -
                                      DISPLACEMENT 0.001
$
$ Perform nonlinear analysis in 4
                                    NONLINEAR ANALYSIS
$ load increments.
$
                                    CREATE LOAD COMBINATION ‘Inc1’ -
UNITS KIPS FEET                       SPECS 1 1.0
LOAD 1
MEMBER LOADS
  1 FORCE Y GLO UNI FR W –25.0
   Basic Nonlinear Analysis Example

$
                                   UNITS INCHES
$ Load increment 2
                                   LIST DISPLACEMENTS FORCES
$ Continue nonlinear analysis
                                   UNITS FEET
$
CHANGES
                                   $
LOAD 1
                                   $ Load increment 3
ADDITIONS
                                   $ Continue nonlinear analysis
MEMBER LOADS
                                   $
  1 FORCE Y GLO UNI W –25.0
                                   CHANGES
                                   LOAD 1
PRINT APPLIED MEMBER LOADS
                                   ADDITIONS
                                   MEMBER LOADS
LOAD LIST 1
                                     1 FORCE Y GLO UNI W –25.0
NONLINEAR ANALYSIS CONTINUE

                                   PRINT APPLIED MEMBER LOADS
CREATE LOAD COMBINATION ‘Inc2’ -
  SPECS 1 1.0
   Basic Nonlinear Analysis Example
LOAD LIST 1
NONLINEAR ANALYSIS CONTINUE        MEMBER LOADS
                                     1 FORCE Y GLO UNI FR W –25.0
CREATE LOAD COMBINATION ‘Inc3’ -
  SPECS 1 1.0                      PRINT APPLIED MEMBER LOADS

UNITS INCHES                       LOAD LIST 1
LIST DISPLACEMENTS FORCES          NONLINEAR ANALYSIS CONTINUE
UNITS FEET
                                   CREATE LOAD COMBINATION ‘Inc4’ -
$                                    SPECS 1 1.0
$ Loading increment 4
$ Continue nonlinear analysis      UNITS INCHES
$                                  LIST DISPLACEMENTS FORCES
CHANGES
LOAD 1                             FINISH
ADDITIONS
     Basic Pushover Analysis Procedure

1.     Define nonlinearity
         NL geometry, T/C only, NL springs, Cable elements, NL
         member end connections, Plastic hinges, Hysteretic
         friction damper element, NLS4PH spring element


2.     Define independent loads to be used as the
       incremental and optional constant loads for
       the pushover analysis
     Basic Pushover Analysis Procedure



3.    Specify the pushover analysis control
      parameters
        Incremental load, optional constant load, Iteration and
        convergence control for equilibrium iterations and
        collapse detection


4.    Execute the pushover analysis
             Pushover Analysis
                 Basic Features
   Nonlinear static analysis
   Automatic creation of load increments
   Automatic storage of load increment
    results
     Creation of intermediate load step conditions
     Intermediate load step conditions contain both
     results and applied loadings.
     Intermediate load steps stored in load group
     “IncrLds”
             Pushover Analysis
               Basic Features


   Automated search for collapse load
    factor


   All nonlinear effects supported
         Pushover Analysis
               Mechanics

Load P




    1

         f1P


                             Displacement
         Pushover Analysis
               Mechanics

Load P




    2




    1          (2f1)P

         f1P


                             Displacement
         Pushover Analysis
               Mechanics

Load P



    3




    2



                        (3f1)P
    1          (2f1)P

         f1P


                                 Displacement
         Pushover Analysis
               Mechanics

Load P



    3

    4

    2



                        (3f1)P   (2f1 + rf1)P
    1          (2f1)P

         f1P


                                         Displacement
   Pushover Analysis
Menu and Command Syntax
   Pushover Analysis
Menu and Command Syntax
   Pushover Analysis
Menu and Command Syntax
                               Pushover Analysis
    Steel Frame Example with NLS Connections



                  W8X58           W8X58               W8X58              W8X58
           x               x              x                     x                x




16.00 FT


               W8X58                          W8X58                              W8X58


           x                              x                                      x

Y                      20.00 FT                               40.00 FT

Z   X
                      Pushover Analysis
 Steel Frame Example with NLS Connections


IND LOAD PA1__001


               4.00           x               x
          o
          x           x
                      o               o
                                      x


                                      -3.00


                      -8.00




          x                   x               x
                   Pushover Analysis
 Steel Frame Example with NLS Connections

                    Define NLS Connections

UNITS INCHES KIPS RADIANS
NONLINEAR SPRING PROPERTIES                  Mz

CURVE 'Mz' MOMENT VS ROTATION SYMMETRY
   0.0   0.0 -
2149.2   0.326477E-3 -   $ Mp       2149.2

2149.2   1.0
NONLINEAR EFFECTS
  NLS CONNECTION MEMBERS 1 TO 7 –
  START MOMENT Z 'Mz' -
                                             .326E-3   1.0   Q
  END    MOMENT Z 'Mz'                       (Mp/EI)
              Pushover Analysis
Steel Frame Example with NLS Connections

Define Pushover Analysis Control, Execute Analysis

      PUSHOVER ANALYSIS DATA
         INCREMENTAL LOAD 1
         MAXIMUM NUMBER OF LOAD INCREMENTS 50
         MAXIMUM NUMBER OF TRIALS 10
         LOADING RATE 1.000000
         CONVERGENCE RATE 0.800000
         CONVERGENCE TOLERANCE COLLAPSE 0.000100
         CONVERGENCE TOLERANCE DISPLACEMENT 0.000500
         MAXIMUM NUMBER OF CYCLES 50
      END
      PERFORM PUSHOVER ANALYSIS
          Pushover Analysis
Steel Frame Example with NLS Connections
          Pushover Analysis
Steel Frame Example with NLS Connections
          Pushover Analysis
Steel Frame Example with NLS Connections
                                 Pushover Analysis
Steel Frame Example with NLS Connections
                                            Load Factor vs Displacement X, Joint 4


              10


               9


               8


               7


               6
Load Factor




               5                                                                 NLS Connection


               4


               3


               2


               1


               0
                   0   0.5   1      1.5           2             2.5          3           3.5      4   4.5
                                          Displacement X, Joint 4 (inches)
          Pushover Analysis
Steel Frame Example with NLS Connections
            Pushover Analysis
Steel Frame Example with Plastic Hinges

               Define Plastic Hinges
   UNITS INCHES KIPS RADIANS
   NONLINEAR EFFECTS
     PLASTIC HINGE START END -
     FIBER GEOMETRY NTF 2 NTW 1 NBF 1 ND 10 LH 4.0 -
     STEEL FY 36.0 FSU 36.1 ESU 1.0
     MEMBERS 1 TO 7

                                   s

                               36 ksi




                                                             e
                                                       1.0
                     Pushover Analysis
Steel Frame Example with Plastic Hinges
 **** INFO_STPACP -- The current collapse load factor = 8.89632
                      Load components and results are stored in the following intermediate
 loads:
                         PA1__001 PA1__002 PA1__003 PA1__004
                         PA1__005 PA1__006 PA1__007 PA1__008
                         PA1__009 PA1__010 PA1__011 PA1__012
                         PA1__013 PA1__014 PA1__015 PA1__016
                         PA1__017 PA1__018 PA1__019 PA1__020
                         PA1__021 PA1__022 PA1__023 PA1__024
                         PA1__025 PA1__026 PA1__027 PA1__028
                         PA1__029 PA1__030 PA1__031

  **** INFO_STPACP -- The incremental loads above are stored in load group IncrLds .



     /----- Push-over Analysis Load Factor History -----/
          Load Increment                 Load Factor
          --------------                 -----------
             PA1__001                     1.00000
             PA1__002                     2.00000
             PA1__003                     3.00000
                           .
                           .
                           .

             PA1__029                      8.88739
             PA1__030                      8.89477
             PA1__031                      8.89632

  **** INFO_STPACP -- Time to complete pushover analysis =    20.39 seconds.
                                    Pushover Analysis
                       Steel Frame Example with Plastic Hinges
                                                 Load Factor vs Displacement X, Joint 4


              10


              9


              8


              7


              6
                                                                                    NLS Connection
Load Factor




              5                                                                     Fiber Plastic Hinge

              4


              3


              2


              1


              0
                   0      0.5   1     1.5           2             2.5           3             3.5         4   4.5
                                            Displacem ent X, Joint 4 (inches)
                   Pushover Analysis
Steel Frame Example with Plastic Hinges

     {    107} > LIST PLASTIC HINGE STATUS MEMBER 5



         Plastic Hinge Status
         ====================

                                     % Plastic Hinge Formation
          Member      Load        Member Start        Member End
          ------      ----        ------------        ----------

          5           PA1__006          0                58
          5           PA1__007         82                95
          5           PA1__008         91                95
          5           PA1__009         95                95
          5           PA1__010         95                97
          5           PA1__011         95                97
          5           PA1__012         95                97
          5           PA1__013         97                97
                      Pushover Analysis
        Steel Frame Example with Plastic Hinges

                               97 x                               93
         x 93                                                             x
    93
                                                   x                          93


                97 x 97




Y                         95                                     97
    x                          x                                      x

Z   X

                   Summary of Plastic Hinge Status at Collapse
                               Plastic Hinge Effects
             Steel Frame Example with Plastic Hinges
{    120} > LIST PLASTIC HINGE DISPLACEMENTS MEMBER 5 6

********************************
* RESULTS FROM LATEST ANALYSIS *
********************************

ACTIVE UNITS (UNLESS INDICATED OTHERWISE):
    LENGTH          WEIGHT          ANGLE               TEMPERATURE       TIME
     INCH            KIP             RAD                   DEGF          SEC

Plastic Hinge Displacements
===========================
                                                         Plastic Hinge Displacements Start/End
 Member        Load                           TX            TY        …     RX            RY            RZ
 ------        ----                     ---------------------------   …        ---------------------------------

 5           PA1__001         Start      -.305162E-04                                             0.993818E-02
                              End        -.305162E-04                                             -.119583E-01
 6           PA1__001         Start      -.156177E-04                                             -.596274E-02
                              End        -.156177E-04                                             0.630324E-02
 5           PA1__002         Start      -.610324E-04                                             0.198764E-01
                              End        -.610324E-04                                             -.239166E-01
 6           PA1__002         Start      -.312355E-04                                             -.119255E-01
                         Pushover Analysis
      Steel Frame Example with Plastic Hinges

{    124} > UNITS INCHES KIPS
{    125} > LOAD LIST 'PA1__031'
{    126} > LIST PLASTIC HINGE STRESSES RMIN 4.0 MEMBER 5

********************************
* RESULTS FROM LATEST ANALYSIS *
********************************




ACTIVE UNITS (UNLESS INDICATED OTHERWISE):
    LENGTH          WEIGHT          ANGLE            TEMPERATURE         TIME
     INCH            KIP             DEG                DEGF            SEC



Plastic Hinge Stresses/Strains, Load = PA1__031
===============================================
 Member Start/End Fiber         Stress        Strain        Matrl      Y          Z      Ax
 ------ --------- -----         ------        ------        -----    -----      -----   -----
 5         Start       1           36.000   0.0453201       Steel   -4.173      0.000   3.358
                      14          -36.000 -0.0768598        Steel    4.173      0.000   3.358

 5            End        1          -36.000   -0.0976905    Steel   -4.173      0.000   3.358
                        14           36.000    0.0576494    Steel    4.173      0.000   3.358
                     Pushover Analysis
    Steel Frame Example with Plastic Hinges
                                         6
                                        x
                           5
                          x



Y

Z   X
    {   103} > LIST PLASTIC HINGE DUCTILITY RATIO RZ MEMBERS 5 6

    ********************************
    * RESULTS FROM LATEST ANALYSIS *
    ********************************


    Plastic Hinge Ductility Ratios
    ===============================

                          Ductility Ratios -- Displacement = RZ
     Member                   Start             End
     ------                  -------          -------

    5                          32.565          56.941
    6                           0.683           1.634
                 Pushover Analysis
    Steel Frame Example with Plastic Hinges
                             6
                            x
                       5
                      x



Y

Z    X

{    105} > LIST PUSHOVER DUCTILITY RATIO TX TARGET JOINT 6

********************************
* RESULTS FROM LATEST ANALYSIS *
                                                              U6ult
********************************       RDuctility   
                                                        U6y   (1st any PH)

Pushover Analysis Ductility Ratio
=================================
  Target joint = 6        DOF = TX
    Ductility Ratio = 3.213516
                     Pushover Analysis
    Steel Frame Example with Plastic Hinges


{   116} > LIST PLASTIC HINGE DUCTILITY RATIO RZ YIELD STRAIN STEEL 0.00124 -
{   117} >_MEMBERS 5 6

********************************
* RESULTS FROM LATEST ANALYSIS *
********************************


Plastic Hinge Ductility Ratios
===============================

                           Ductility Ratios -- Displacement = RZ
 Member                   Start    Yld Ld           End     Yld Ld
 ------                  ------- --------         ------- --------

5                         32.57    PA1__007        56.94   PA1__006
6                          0.65    PA1__007         1.63   PA1__006
                             Pushover Analysis
         Steel Frame Example with Plastic Hinges


{     118} > LIST PUSHOVER DUCTILITY RATIO TX YIELD STRAIN STEEL 0.00124 TARGET JOINT 6

    ********************************
    * RESULTS FROM LATEST ANALYSIS *
    ********************************


    Pushover Analysis Ductility Ratio
    =================================
      Target joint = 6        DOF = TX   (Yield Loading PA1__006, Member 5      , Material STEEL   )
        Ductility Ratio = 3.213516
                     Pushover Analysis
Steel Frame Example with Plastic Hinges

{   113} > LIST PUSHOVER LIMIT LOADS STRAIN 0.00124 STEEL MEMBERS EXISTING

********************************
* RESULTS FROM LATEST ANALYSIS *
********************************


Pushover Analysis Limit Point Loads: Strain =         0.0012400, Material = Steel
=================================================================================

 Member         Limit Ld Start      Limit Ld End
 ------         --------------      ------------

1                    ---               PA1__027
2                  PA1__024              ---
3                  PA1__019            PA1__023
4                  PA1__027            PA1__007
5                  PA1__007            PA1__006
6                    ---                 ---
7                    ---               PA1__024
             Pushover Analysis
                    Strategies

   Do a conventional nonlinear analysis first.
    Use FORM LOAD to create a version of your
    incremental load scaled to size of first increment.

   Use a larger collapse load convergence
    tolerance (~0.01) for the first pushover
    analysis attempt.

   Keep the loading rate on the smaller side.
    It’s better to have two to four load
    increments that are basically linear.
            Pushover Analysis
                  Strategies

   Larger convergence rate values -- 0.6 to
    0.8 -- seem to perform better, i.e. result
    in a more economical number of load
    increments.

   ~50 appears to be the most economical
    maximum number of nonlinear analysis
    cycles, particularly with NLS elements, NLS
    connections, and plastic hinges.
                      Pushover Analysis
RC Frame Example with Plastic Hinges, Force Control
                                                                    14.650 M

                                      x                                                        x      x
                                                              B = 2.35 M,   H = 2.00 M




               Member Ecc = 1 M




                                              Diam = 1.75 M


                                                                                                    13.250 M

Total Mass:
         Self weight + 76.778 Kg/M
         applied to cap
         = 1.413x106 Kg

                           Y

                           Z      X       x                                                    x
                                                                     10.650 M

                                                                                     SUPPORT FX FY FZ MX MY
                Pushover Analysis
RC Frame Example with Plastic Hinges, Force Control


 Define Nonlinearity: NL Geometry + Plastic Hinges


 UNITS KIPS INCHES
 NONLINEAR EFFECTS
   PLASTIC HINGE -
        END FIBER GEOM NR 60 NTH 32 LH 56.53 -
        STEEL FY 68.0 FSU 95.0 ESH 0.0075 ESU .06 EH 289.5 -
        R-C CIRC B 68.9 FCP 5.28 EC0 .002 FYS 68.0 -
        BARS ASTM END CIRC 35 14 HOOP 8 6.00 COV 2.0 -
   MEMBER 'COL4' 'COL8'
   GEOMETRY MEMBERS 'COL1' TO 'COL8'
                 Pushover Analysis
RC Frame Example with Plastic Hinges, Force Control


   Define Incremental Force and Constant Loads
 UNITS KN METERS
 DEAD LOAD 'DL' DIR -Y ALL JOINTS
 MEMBER LOADS
   'CAP1' TO 'CAP10' FORCE Y GLO UNI FR W -752.4204
 LOADING 'PUSH'
 JOINT LOADS
   'C5' 'C10' FORCE X 100.0
               Pushover Analysis
RC Frame Example with Plastic Hinges, Force Control


    Specify Pushover Analysis Control and Execute

          PUSHOVER ANALYSIS DATA
            CONSTANT LOAD 'DL'
            INCREMENTAL LOAD 'PUSH'
            MAXIMUM NUMBER OF LOAD INCREMENTS 40
            MAXIMUM NUMBER OF TRIALS 11
            LOADING RATE 1.0
            CONVERGENCE RATE 0.6
            CONVERGENCE TOLERANCE COLLAPSE 0.0005
            CONVERGENCE TOLERANCE EQUIL 0.0001
            MAXIMUM NUMBER OF CYCLES 100
          END

          PERFORM PUSHOVER ANALYSIS
                             Pushover Analysis
         RC Frame Example with Plastic Hinges, Force Control

                            Lateral Displacement vs Lateral Load Factor, Force Control Analysis
                                                         Joint C5
              16



              14



              12
                                                                                Instability:
                                                                                DC = 305.55 mm
              10                                                                Vbs = 15.22*200 Kn =
                                                                                       3044 Kn (.23g)
Load Factor




              8



              6                                                  Force Contol


              4



              2



              0
                   0   50      100               150               200              250            300   350
                                                   Displacement (mm)
              Pushover Analysis
RC Frame Example with Plastic Hinges, Force Control
                   Pushover Analysis
RC Frame Example with Plastic Hinges, Displacement Control


Define Incremental Displacement and Constant Loads

STATUS SUPPORT -
  ‘C1’ ‘C6’ 'C5' 'C10'
JOINT RELEASES
  'C1' 'C6' MOMENT Z
 'C5' 'C10' FORCE Y MOMENT X Y Z                     D       D

UNITS KN METERS
DEAD LOAD 'DL' DIR -Y ALL JOINTS
MEMBER LOADS
  'CAP1' TO 'CAP10' FORCE Y GLO UNI FR W -752.4204
UNITS MM
LOADING 'PUSH'
JOINT DISPLACEMENT
  'C5' 'C10' DISPLACEMENT X 10.0
                 Pushover Analysis
RC Frame Example with Plastic Hinges, Displacement Control


   Specify Pushover Analysis Control and Execute

 PUSHOVER ANALYSIS DATA
   CONSTANT LOAD 'DL'
   INCREMENTAL LOAD 'PUSH'
   MAXIMUM NUMBER OF LOAD INCREMENTS 50     $ 50*10 = 500 mm
   MAXIMUM NUMBER OF TRIALS 11
   LOADING RATE 1.0
   CONVERGENCE RATE 0.6
   CONVERGENCE TOLERANCE COLLAPSE 0.00100
   CONVERGENCE TOLERANCE EQUIL 0.0001
   MAXIMUM NUMBER OF CYCLES 100
 END

 PERFORM PUSHOVER ANALYSIS
                                   Pushover Analysis
                   RC Frame Example with Plastic Hinges, Displacement Control

                                         Lateral Displacement vs Lateral Load Factor
                                                          Joint C5
              16



              14



              12
                                                                                         DC = 500 mm
                                     Instability:                                        Vbs = 2991 Kn
              10
                                     DC = 305.55 mm
Load Factor




                                     Vbs = 15.22*200 Kn =
              8                             3044 Kn (.23g)


              6                                                     Force Contol

                                                                    Displacement Control
              4



              2



              0
                   0         100       200                   300                   400                   500   600
                                                    Displacem ent (m m )

				
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