Gt s Pushover Analysis

GTSTRUDLPushover Analysis

How Do You Do It?What Do You Get?

GTSTRUDL Users GroupJune 18-21, 2003

Clearwater Beach, FL

Topics Basic Nonlinear Analysis Procedure Member Material Nonlinearity

Nonlinear Member End ConnectionsPlastic Hinge

Basic Incremental Nonlinear Analysis Example

Basic Pushover Analysis Procedure Pushover Analysis Features and Mechanics Pushover Analysis Examples

Steel Frame with Nonlinear Member End ConnectionsSteel Frame with Plastic HingesRC Frame with Plastic Hinges by Force ControlRC Frame with Plastic Hinges by Displacement Control

Basic Nonlinear Analysis Procedure1. 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 analysisFORM 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 ConnectionsProperties

M

NLS Member End Connections

• Up to 6 uncoupled DOFs

• Elastic loading/unloading behavior

• Any member loads

• Member releases

• Member end joint sizes

• Member eccentricities

Nonlinear Spring ConnectionsData Description

UNITS KIPS INCHES RADIANS

NONLINEAR SPRING PROPERTIES

CURVE ‘Mz’ MOMENT VS ROTATION SYMMETRIC

0.0 0.0 -

2100.0 0.3E-3 -

2100.0 0.3E-2 -

1000.0 0.301E-2 -

1000.0 0.01

NONLINEAR EFFECTS

NLS CONNECTION MEMBERS 1 TO 7 START MOMENT Z 'Mz' -

END MOMENT Z 'Mz'

Mz

2100

1000

.0003 .003 .01

Plastic Hinge EffectsBasic Geometry

LH

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

characteristics, etc.

Plastic Hinge EffectsBasic Geometry

Supported Cross Section Shapes

• Steel sections from tables

Wide flange, channel, tee, tube, pipe

• Reinforced concrete sections

Plastic Hinge EffectsProperties

LH

UX

Y

Z

yf

Hinge/slider


Steel Stress-Strain Model

(Balan, Filippou, Popov, 1998)

Residual Stress Model for

Wide Flange Sections


Confined Concrete Stress-Strain Model

(Mander, Priestley, Park, 1988)

Plastic Hinge Effects Properties -- Material Property Defaults

Default Concrete Properties

FCP = 4000 psi

EC0 = 0.002

E = 60200FCP psi

Fr = 7.5FCP psi

Plastic Hinge EffectsProperties – Material Stress-Strain

Examples

Steel Stress-Strain Curve, fy = 68 ksi

0

10

20

30

40

50

60

70

80

90

100

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

Strain

Str

ess

(ksi

)

Eh = 163.6 ksi (default)

Eh = 245.4 ksi

Fy = 68 ksi

E = 29000 ksish = 0.0075

fsu = 95 ksi

u = 0.09

Eh = 163.6 ksi, 245.4 ksi

Confined and Unconfined Concrete Stress-Strain Curve60-inch Circular Cross Section, fcp = 5.28 ksi

0

1

2

3

4

5

6

7

8

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018

Strain

Str

ess

(ksi

)

Confined: Hoops = #8 @ 6 inches

Unconfined

Plastic Hinge EffectsProperties – Material Stress-Strain

Examples

fc’ = 5.28 ksi

c0 = 0.002

sp = 0.005

fys = 68 ksi

Moment-Rotation: GTStrudl vs SEQMCCircular Cross Section, Diam = 60 inches, 14 #14, Spiral #6@3", Cover = 1.25"

0

1000

2000

3000

4000

5000

6000

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

Plastic Hinge Rotation (rad)

Mo

me

nt

(k-f

t)

GTStrudl, P = 1000 K

SEQMC, P = 1000 K

Plastic Hinge EffectsProperties – RC Plastic Hinge Behavior

Material Properties

Concrete Steel

fc’ = 6 ksi Fy = 44 ksi

c0 = 0.002 E = 29000 ksi

sp = 0.005 sh = 0.02

fys = 60 ksi fsu = 66 ksi

u = 0.076

Eh = 392.0 ksi

Plastic Hinge EffectsSummary of Characteristics

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

Neutral axis shift automatically takeninto account by equilibrium

corrections.

Failure is based on combined normal stress only (axial plus bending).

Plastic Hinge EffectsSummary 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 EffectsData Description Example – WF Section

Fiber Grid for W21X68

UNITS INCHES KIPS

NONLINEAR EFFECTS

GEOMETRY MEMBERS 1 TO 4

PLASTIC HINGE START END –

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 4NBF

NDNTW

NTF

Plastic Hinge EffectsData Description Example – Rectangular RC

Section

UNITS INCHES KIPS

NONLINEAR EFFECTS

PLASTIC HINGE START -

FIBER GEOMETRY NB 10 NH 20 LH 20.0 -

STEEL FY 60.0 FYS 36.0 -

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 -

MEMBERS 1 TO 4

H,

NH

B,

NB

COVER

Si d

e B

ars

Bottom Bars

y

z

Top Bars

Nonlinear Analysis Procedure

MAXIMUM NUMBER OF CYCLES 50

CONVERGENCE TOLERANCE -

DISPLACEMENT 0.001

NONLINEAR ANALYSIS

Basic Nonlinear Analysis Example

STRUDL 'NL1' 'BASIC NONLINEAR FRAME ANALYSIS'

UNITS INCHES KIPSJOINT COORDS

1 0.0 180.0 S2 120.0 180.03 120.0 135.04 120.0 90.05 120.0 45.06 120.0 0.0 S

JOINT RELEASES

1 6 MOMENT Z TYPE PLANE FRAMEMEMBER INC 1 1 2; 2 6 5 3 5 4; 4 4 3; 5 3 2

Ax = 10000 in2

Ig = 100 in4

Ic = 200 in4

E = 10000 ksi

X

Y

Z

1

2

3

4

5

1 2

3

4

5

6

SUPPORT FX FY FZ MX MY

15.000 FT

10.000 FT

100 k/ft


CONSTANTS E 10000.0

MEMBER PROPERTIES 1 AX 10000.0 IZ 100.0 2 TO 5 AX 10000.0 IZ 200.0

$$ Perform nonlinear analysis in 4$ load increments.$

UNITS KIPS FEETLOAD 1MEMBER LOADS 1 FORCE Y GLO UNI FR W –25.0

NONLINEAR EFFECTS

GEOMETRY MEMBERS 2 TO 5


CONVERGENCE TOLERANCE -

DISPLACEMENT 0.001

NONLINEAR ANALYSIS

CREATE LOAD COMBINATION ‘Inc1’ -

SPECS 1 1.0


$$ Load increment 2$ Continue nonlinear analysis$CHANGESLOAD 1ADDITIONSMEMBER LOADS 1 FORCE Y GLO UNI W –25.0

PRINT APPLIED MEMBER LOADS

LOAD LIST 1NONLINEAR ANALYSIS CONTINUE

CREATE LOAD COMBINATION ‘Inc2’ - SPECS 1 1.0

UNITS INCHESLIST DISPLACEMENTS FORCESUNITS FEET

$$ Load increment 3$ Continue nonlinear analysis$CHANGESLOAD 1ADDITIONSMEMBER LOADS 1 FORCE Y GLO UNI W –25.0





UNITS INCHESLIST DISPLACEMENTS FORCESUNITS FEET

$$ Loading increment 4$ Continue nonlinear analysis$CHANGESLOAD 1ADDITIONS

MEMBER LOADS 1 FORCE Y GLO UNI FR W –25.0




UNITS INCHESLIST DISPLACEMENTS FORCES

FINISH

Basic Pushover Analysis Procedure

1. Define nonlinearityNL 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 andcollapse detection

4. Execute the pushover analysis

Pushover AnalysisBasic 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 AnalysisBasic Features

Automated search for collapse

load factor

All nonlinear effects supported

Pushover AnalysisMechanics

f1P

Displacement

Load P

1


f1P

(2f1)P

Displacement

Load P

1

2


f1P

(2f1)P(3f1)P

Displacement

Load P

1

3

2


f1P

(2f1)P(3f1)P

Displacement

Load P

(2f1 + rf1)P

1

3

4

2

Pushover AnalysisMenu and Command Syntax



Pushover AnalysisSteel Frame Example with NLS

Connections

X

Y

Z

x x x

x x xx x

xxxx

xxxx

16.00 FT

xxxx xxxx

20.00 FT

xxxx xxxx

40.00 FT

W8X58 W8X58 W8X58

W8X58 W8X58 W8X58 W8X58


Connections

x x x

x x xx x

IND LOAD PA1__001

4.00o

-8.00

o

-3.00

o


Connections

UNITS INCHES KIPS RADIANS

NONLINEAR SPRING PROPERTIES

CURVE 'Mz' MOMENT VS ROTATION SYMMETRY

0.0 0.0 -

2149.2 0.326477E-3 - $ Mp

2149.2 1.0

NONLINEAR EFFECTS

NLS CONNECTION MEMBERS 1 TO 7 –

START MOMENT Z 'Mz' -

END MOMENT Z 'Mz'

Mz

2149.2

.326E-3 1.0

(Mp/EI)

Define NLS Connections


Connections

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


END

PERFORM PUSHOVER ANALYSIS

Define Pushover Analysis Control, Execute Analysis


Connections


Connections


Connections


Connections


Connections

Pushover AnalysisSteel Frame Example with 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

36 ksi

1.0

Define 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.

Load Factor vs Displacement X, Joint 4

0

1

2

3

4

5

6

7

8

9

10

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

Displacement X, Joint 4 (inches)

Lo

ad F

acto

r NLS Connection

Fiber Plastic Hinge



{ 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


Summary of Plastic Hinge Status at Collapse

X

Y

Z

x x x

x x x

x

x93

95

97

93

93

97

97

97 93

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


{ 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

{ 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


X

Y

Z

xx5

xx6


{ 105} > LIST PUSHOVER DUCTILITY RATIO TX TARGET JOINT 6 ******************************** * RESULTS FROM LATEST ANALYSIS * ******************************** Pushover Analysis Ductility Ratio ================================= Target joint = 6 DOF = TX Ductility Ratio = 3.213516

X

Y

Z

xx5

xx6

R U

UDuctility

6ult

6y (1st any PH)

{ 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


{ 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 AnalysisStrategies

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 AnalysisStrategies

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 AnalysisRC Frame Example with Plastic Hinges, Force

Control

X

Y

Z

xxxx

xxxx

13.250 M

xxxx xxxx

14.650 M

SUPPORT FX FY FZ MX MY

xxxx xxxx

10.650 M

B = 2.35 M, H = 2.00 M

Diam = 1.75 M

Total Mass:Self weight + 76.778

Kg/Mapplied to cap= 1.413x106 Kg

Member Ecc = 1 M


Control

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'

Define Nonlinearity: NL Geometry + Plastic Hinges


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


Control

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


END


Specify Pushover Analysis Control and Execute


Control

Lateral Displacement vs Lateral Load Factor, Force Control AnalysisJoint C5

0

2

4

6

8

10

12

14

16

0 50 100 150 200 250 300 350

Displacement (mm)

Lo

ad F

acto

r

Force Contol

Instability:C = 305.55 mm

Vbs = 15.22*200 Kn =

3044 Kn (.23g)


Control

Pushover AnalysisRC 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

UNITS KN METERSDEAD LOAD 'DL' DIR -Y ALL JOINTSMEMBER LOADS 'CAP1' TO 'CAP10' FORCE Y GLO UNI FR W -752.4204UNITS MMLOADING 'PUSH'

JOINT DISPLACEMENT 'C5' 'C10' DISPLACEMENT X 10.0


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 100END



Control

Lateral Displacement vs Lateral Load FactorJoint C5

0

2

4

6

8

10

12

14

16

0 100 200 300 400 500 600

Displacement (mm)

Lo

ad F

acto

r

Force Contol

Displacement Control

C = 500 mm

Vbs = 2991 Kn

Instability:C = 305.55 mm

Vbs = 15.22*200 Kn =

3044 Kn (.23g)

Documents

Gt s Pushover Analysis