# 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

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

4.     Execute the nonlinear analysis
Nonlinear Spring Connections
Properties

NLS Member End Connections
• Up to 6 uncoupled DOFs
• Member releases
M                  • Member end joint sizes
• Member eccentricities

Q
Nonlinear Spring Connections
Data Description
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 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

only. No hysteretic effects.

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

   All member modeling features
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
\$
UNITS KIPS FEET                       SPECS 1 1.0
1 FORCE Y GLO UNI FR W –25.0
Basic Nonlinear Analysis Example

\$
UNITS INCHES
LIST DISPLACEMENTS FORCES
\$ Continue nonlinear analysis
UNITS FEET
\$
CHANGES
\$
\$ Continue nonlinear analysis
\$
1 FORCE Y GLO UNI W –25.0
CHANGES
1 FORCE Y GLO UNI W –25.0
NONLINEAR ANALYSIS CONTINUE

SPECS 1 1.0
Basic Nonlinear Analysis Example
1 FORCE Y GLO UNI FR W –25.0
SPECS 1 1.0                      PRINT APPLIED MEMBER LOADS

LIST DISPLACEMENTS FORCES          NONLINEAR ANALYSIS CONTINUE
UNITS FEET
\$                                    SPECS 1 1.0
\$ Continue nonlinear analysis      UNITS INCHES
\$                                  LIST DISPLACEMENTS FORCES
CHANGES
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
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
“IncrLds”
Pushover Analysis
Basic Features

   Automated search for collapse load
factor

   All nonlinear effects supported
Pushover Analysis
Mechanics

1

f1P

Displacement
Pushover Analysis
Mechanics

2

1          (2f1)P

f1P

Displacement
Pushover Analysis
Mechanics

3

2

(3f1)P
1          (2f1)P

f1P

Displacement
Pushover Analysis
Mechanics

3

4

2

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

f1P

Displacement
Pushover Analysis
Pushover Analysis
Pushover Analysis
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

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

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
MAXIMUM NUMBER OF LOAD INCREMENTS 50
MAXIMUM NUMBER OF TRIALS 10
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

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
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
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 -----/
--------------                 -----------
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

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

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.

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
'CAP1' TO 'CAP10' FORCE Y GLO UNI FR W -752.4204
'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
MAXIMUM NUMBER OF LOAD INCREMENTS 40
MAXIMUM NUMBER OF TRIALS 11
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)

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
'CAP1' TO 'CAP10' FORCE Y GLO UNI FR W -752.4204
UNITS MM
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
MAXIMUM NUMBER OF LOAD INCREMENTS 50     \$ 50*10 = 500 mm
MAXIMUM NUMBER OF TRIALS 11
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

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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