Parameter Studies in Tcl Command Language

Silvia Mazzoni, Gregory L. Fenves

University of California, Berkeley

User Workshop 20 August 2001

Objective of Study

ðDetermine static and dynamic response of nonlinear structural systemðStatic Push-over Analysis (nonlinear)ðDynamic Time-history Analysis

(nonlinear,inelastic)

ðSeries of framesðSeries of ground motions

Analysis Procedure – the roadmap

RunFrame

Units

ParamList

GMFiles

Static

DynamicAnalysis

Parameters

NodalMesh

Materials

Elements RCcircSection

Output

Gravity

Lateral ReadSMDFile

runFRAME.tcl

FRAME

GROUND MOTION

1. wipe

2. source Units.tcl; # define units

3. source ParamList.tcl; # load up parameter values

4. source GMFiles.tcl; # load up ground-motion filenames

5. foreach Xframe $iXframe {

set Hcol [lindex $iHcol [expr $Xframe-1]]; set Lcol [lindex $iLcol [expr $Xframe-1]];

set Lbeam [lindex $iLbeam [expr $Xframe-1]]; set GrhoCol [lindex $iGrhoCol [expr $Xframe-1]]

set Weight [lindex $iWeight [expr $Xframe-1]]; set GMfact [lindex $iGMfact [expr $Xframe-1]];

set Hbeam [lindex $iHbeam [expr $Xframe-1]]; set Bbeam [lindex $iBbeam [expr $Xframe-1]];

6. source Static.tcl; # load procedure for static analysis

7. source Dynamic.tcl; # load procedure for dynamic analysis

8. puts FRAME$Xframe........FRAME$Xframe........

9. puts STATIC_ANALYSIS

10. Static $Xframe $Hcol $Lcol $Lbeam $GIbIc $GrhoCol $GPcol $GMfact ;

11. puts DYNAMIC_ANALYSIS

12. foreach GroundFile $iGroundFile {

13. puts GroundMotion$GroundFile

14. Dynamic $Xframe $Hcol $Lcol $Lbeam $GIbIc $GrhoCol $GPcol $GMfact $GroundFile;

15. }

16. }

constants

1. set in 1.;

2. set sec 1.;

3. set kip 1.;

4. set ksi [expr $kip/pow($in,2)];

5. set psi [expr $ksi/1000.];

6. set ft [expr 12.*$in];

7. set g [expr 32.2*$ft/pow($sec,2)];

8. set PI [expr 2*asin(1.0)];

9. set U 1.e10;

10. set u $U;

UNITS.tcl

basic units

engineering units

ParamList.tcl

Study Parameters Study Case

1. set iXframe “1 2 3 4 5 "

2. set iHcol "[expr 6.*$ft] [expr 5.*$ft] [expr 5*$ft] [expr 6*$ft] [expr 6*$ft] "

3. set iLcol "[expr 40.*$ft] [expr 40.25*$ft] [expr 42*$ft] [expr 42*$ft] [expr 34*$ft] "

4. set iLbeam "[expr 40.*$ft] [expr 40.25*$ft] [expr 42*$ft] [expr 42*$ft] [expr 42*$ft] "

5. set iGIbIc "1. 1. 1. 1. 1. "

6. set iGrhoCol "0.015 0.02 0.02 0.02 0.015 "

7. set iGPcol "0.05 0.0643 0.04823 0.04466 0.04466 "

8. set iGMfact "1.645 1.645 1.645 2.389 1.645 "

GMfiles.tcl

1. set iGroundFile {"CHI012" "QKP085" "E02140" "HOL360"

"ELC180" "RO3000" "CAS000“ "ARL360" }

2. # PEER/Silva Data set

3. # search: mag 6.0-7.5 # distance: 12-25km # USGS soil type C 180-360 m/sec # Free-Field Instruments

4. # filename = 'CHI012.at2'; # Imperial Valley, 1979 # 6621 Chiuauah, pga=0.27g

5. # filename = 'QKP085.at2'; # Imperial Valley, 1979 # Cucapah, pga=0.309g

6. # filename = 'E02140.at2'; # Imperial Valley, 1979 # 5515 El Centro Array #2, pga=0.315g

7. # filename = 'HOL360.at2'; # Northridge 1994 # 24303la Hollywood Stor FF, pga=0.364

8. # search: # PGA: 0.3-0.4 # distance: 12-25km # USGS soil type C 180-360 m/sec # Free-Field Instruments

9. # filename = 'ELC180.at2'; # Imperial Valley 1940 # 117 El Centro Arry #9, pga=0.314g

10. # filename = 'Ro3000.at2'; # Northridge 1994 # 90006 Sun Valley Roncoe blvd, pga=0.307g

11. # filename = 'CAS000.at2'; # Whittier-Narrows 1987# 90078 Compton Castlegate St., pga=0.334g

12. # random search:

13. # filename = 'ARL360.at2'; # Northridge 1994 # Arletta Nordhoff Fire Station, pga=0.310g

static.tcl

1. proc Static {Xframe Hcol Lcol Lbeam GIbIc GrhoCol GPcol GMfact} {

2. set ANALYSIS "Static";

3. source analysis.tcl

4. }

1. proc Dynamic {Xframe Hcol Lcol Lbeam GIbIc GrhoCol GPcol GMfact GroundFile} {

2. set ANALYSIS "Dynamic";

3. source analysis.tcl

4. }

dynamic.tcl

analysis.tcl

1. # Create modelbuilder

2. model basic -ndm 3 -ndf 6

3. source units.tcl;

4. source parameters.tcl;

5. source nodalmesh.tcl;

6. source materials.tcl;

7. source elements.tcl;

8. source output.tcl;

9. source gravity.tcl;

10. source lateral.tcl;

11. wipeanalysis

set up parameters and variables

set up structural model

specify data output

apply loading

parameters.tcl

1. set Rcol [expr $Hcol/2]; # COLUMN radius

2. set Acol [expr $PI*pow($Rcol,2)]; # column cross-sectional area

3. set cover [expr $Hcol/15]; # column cover width

4. set IgCol [expr $PI*pow($Rcol,4)/4]; # column gross moment of inertia,uncracked

5. set IyCol $IgCol; # elastic-column properties

6. set IzCol $IgCol; # elastic-column properties

7. set IzBeam [expr $GIbIc*$IgCol]; # BEAM gross moment of inertia -- horiz Z

8. set Hbeam [expr 8*$ft]; # beam depth, not really used

9. set Bbeam [expr $IzBeam*12/pow($Hbeam,3)]; # beam width not used

10. set IyBeam [expr $Hbeam*pow($Bbeam,3)/12]; # beam gross moment of inertia--vert Y

11. set Abeam [expr $Hbeam*$Bbeam*10000]; # beam cross-sectional area

12. set GLbLc [expr $Lbeam/$Lcol]; # beam-to-column length ratio

GEOMETRY

parameters.tcl

1. set fc [expr -5.5*$ksi]; # CONCRETE Compressive Strength

2. set Ec [expr 57*$ksi*sqrt(-$fc/$psi)]; # Concrete Elastic Modulus

3. set fc1C [expr 1.26394*$fc]; # CONFINED concrete max. stress (Mander)

4. set eps1C [expr 2.*$fc1C/$Ec]; # strain at maximum stress

5. set fc2C $fc; # ultimate stress

6. set eps2C [expr 2.*$fc2C/$Ec]; # strain at ultimate stress

7. set fc1U $fc; # UNCONFINED concrete maximum stress

8. set eps1U -0.003; # strain at maximum stress

9. set fc2U [expr 0.1*$fc]; # ultimate stress

10. set eps2U -0.006; # strain at ultimate stress

11. set Fy [expr 70.*$ksi]; # STEEL yield stress

12. set epsY 0.002; # steel yield strain

13. set Fu [expr 110.*$ksi]; # ultimate stress of steel

14. set epsU 0.1; # ultimate strain of steel

15. set Es [expr $Fy/$epsY]; # Young's Modulus of steel

16. set Bs [expr ($Fu-$Fy)/($epsU-$epsY)/$Es]; # post-yield stiffness ratio of steel

# (+Tension, -Compression)

MATERIAL PROPERTIES

parameters.tcl

1. set NbCol 20; # number of column longitudinal-reinf. bars

2. set AsCol [expr $GrhoCol*$Acol]; # total steel area in column section

3. set AbCol [expr $AsCol/$NbCol]; # bar area of column longitudinal reinforcement

4. set riCol 0.0; # inner radius of column section

5. set roCol $Rcol; # outer radius of column section

6. set np 5; # Number of integration points

7. set IDcore 1; # ID tag for core concrete

8. set IDcover 2; # ID tag for cover concrete

9. set IDsteel 3; # ID tag for steel

10. set nfCoreR 8; # number of radial fibers in core

11. set nfCoreT 16; # number of tangential fibers in core

12. set nfCoverR 2; # number of radial fibers in cover

13. set nfCoverT 16; # number of tangential fibers in cover

14. set IDcolFlex 2; # ID tag for column section in flexure

15. set IDcolTors 10; # ID tag for column section in torsion

16. set IDcolSec 1; # ID tag for column section

17. set IDcolTrans 1; # ID tag for column transformation, defining element normal

18. set IDbeamTrans 2; # ID tag for beam transformation, defining element normal

COLUMN & BEAM SECTION

1. set Pdl [expr -$GPcol*$Acol*$fc]; # gravity axial load per column (-ve value = )

2. set Weight [expr $Pdl*2]; # super-structure weight

3. set Wbeam [expr $Weight/$Lbeam]; # gravity DL distributed along beam length

4. set Mdl [expr $Wbeam*pow($Lbeam,2)/12]; # nodal moment due to distributed DL

5. set Mass [expr $Weight/$g]; # mass of superstructure

6. set Mnode [expr $Mass/2]; # nodal mass for each column joint

parameters.tcl DEAD LOAD

parameters.tcl

1. set xDamp 0.02; # modal damping ratio

2. set const [expr 12*$Ec*$IgCol/pow($Lcol,3)]; # condensed-K constant

3. set numer [expr $IgCol*$Lbeam+6*$IzBeam*$Lcol]; # condensed-K numerator

4. set denom [expr 3.*$IzBeam*$Lcol+2.*$IgCol*$Lbeam]; # condensed-K denominator

5. set Kgross [expr $const*$numer/$denom]; # condensed K of portal frame

6. set Gcrack 0.5; # cracked-stiffness factor

7. set Kcracked [expr $Kgross*$Gcrack]; # cracked stiffness

8. set omega [expr sqrt($Kcracked/$Mass)]; # natural frequency (rad/sec)

9. set Tperiod [expr 2*$PI/$omega]; # period (sec.)

10. set alphaM 0; # M-prop. RAYLEIGH damping

11. set betaK 0; # K-prop. RAYLEIGH damping – CURRENT K

12. set betaKcomm [expr 2*$xDamp/$omega]; # K-prop. RAYLEIGH damping – COMMITTED K

13. set betaKinit 0; # K-prop. RAYLEIGH damping – INITIAL K

DAMPING

D = alphaM*M + betaK*Kcurrent + betaKcomm*Kcommitted + betaKinit*Kinit

parameters.tcl

1. set DxPush [expr 0.1*$in]; # Displacement increment for pushover analysis

2. set DmaxPush [expr 20*$in]; # maximum displamcement for pushover analysis

3. set DtAnalysis [expr 0.005*$sec]; # time-step Dt for lateral analysis

4. set DtGround [expr 0.02*$sec]; # time-step Dt for input grond motion

5. set TmaxGround [expr 50 *$sec]; # maximum duration of ground-motion analysis

6. set gamma 0.5; # gamma value for newmark integration

7. set beta 0.25; # beta value for newmark integration

ANALYSIS

NodalMesh.tcl1. set IDctrlNode 3;

2. # Define nodes; # frame is in X-Y plane (X-horizontal, Y-vertical)

3. node 1 0.0 0.0 0.0

4. node 2 $Lbeam 0.0 0.0

5. node 3 0.0 $Lcol 0.0 -mass $Mnode 0.0 0.0 0.0 0.0 0.0

6. node 4 $Lbeam $Lcol 0.0 -mass $Mnode 0.0 0.0 0.0 0.0 0.0

7. # Boundary conditions; # node DX DY DZ RX RY RZ ! 1: fixed, 0: released

8. fix 1 1 1 1 1 1 1;

9. fix 2 1 1 1 1 1 1

10. fix 3 0 0 1 1 1 0

11. fix 4 0 0 1 1 1 0

12. # 3---------------------------4

13. # | |

14. # | |

15. # --1-- --2--

materials.tcl concrete

1. set ConcreteMaterialType “inelastic”

2. if {$ConcreteMaterialType == “elastic”} {

3. uniaxialMaterial Elastic $IDcore $Ec

4. uniaxialMaterial Elastic $Idcover $Ec

5. }

6. if {$ConcreteMaterialType == “inelastic”} {

7. # uniaxial Kent-Scott-Park concrete model w/ linear unload/reload, no T strength (-ve comp.)

8. uniaxialMaterial Concrete01 $Idcore $fc1C $eps1C $fc2C $eps2C; # Core

9. uniaxialMaterial Concrete01 $Idcover $fc1U $eps1U $fc2U $eps2U; # Cover

10. }

materials.tcl1. set SteelMaterialType “bilinear”

2. if {$SteelMaterialType == “elastic”} {

3. uniaxialMaterial Elastic $IDsteel $Es

4. }

5. if {$SteelMaterialType == “bilinear”} {

6. # Reinforcing steel, uniaxial bilinear steel model with isotropic hardening.

7. # Fy: yield strength, E0: initial elastic tangent modulus b: hardening ratio

8. # a1,a2,a3,a4 are optinonal parameters controlling isotropic hardening (default given)

9. # tag Fy E0 b <a1 a2 a3 a4>

10. uniaxialMaterial Steel01 $IDsteel $Fy $Es $Bs

11. }

12. if {$SteelMaterialType == “hysteretic”} {

13. # Reinforcing steel, uniaxial hysteretic steel model with isotropic hardening.

14. uniaxialMaterial Hysteretic $IDsteel $Fy $epsY $Fu $epsU -$Fy -$epsY -$Fu -$epsU

$pinchX $pinchY $damage1 $damage2 $betaMU

}

steel

elements.tcl

1. set ColumnType “inelastic”;

2. source RCcircSection.tcl; # proc to define circular fiber section– flexure

3. RCcircSection $IDcolFlex $riCol $roCol $cover $IDcore $IDcover $IDsteel $NbCol $AbCol $nfCoreR $nfCoreT $nfCoverR $nfCoverT

4. uniaxialMaterial Elastic $ IDcolTors $GJ; # Define torsion

5. section Aggregator $IDcolSec $IDcolTors T -section $IDcolFlex; # attach torsion & flex

6. geomTransf Linear $IDcolTrans 0 0 1; # no 2nd-order effects, define element normal

7.

8. if {$ColumnType == “elastic”} {

9. element elasticBeamColumn 1 1 3 $Acol $Ec $G $J $IyCol $IzCol $IDcolTrans

10. element elasticBeamColumn 2 2 4 $Acol $Ec $G $J $IyCol $IzCol $IDcolTrans }

11. if {$ColumnType == “inelastic”} {

12. # element element type ID, node I, node J, no. int pts, section ID, transf. ID

13. element nonlinearBeamColumn 1 1 3 $np $IDcolSec $IDcolTrans

14. element nonlinearBeamColumn 2 2 4 $np $IDcolSec $IDcolTrans }

15. geomTransf Linear $IDbeamTrans 0 0 1; # BEAM transformation, define element normal

16. element elasticBeamColumn 3 3 4 $Abeam $Ec $G $J $ IyBeam $IzBeam $IDbeamTrans

CO

LU

MN

BE

AM

output.tcl

1. if {$ANALYSIS == "Static"} {

2. # Record nodal displacements

3. recorder Node DStatFrame$Xframe.out disp -time -node $IDctrlNode -dof 1

4. # Record element forces

5. for {set iel 1} {$iel <= 2} {incr iel 1} {

6. recorder Element $iel -file El[expr $iel]FStatFrame$Xframe.out force

7. }

8. }

9. if {$ANALYSIS == "Dynamic"} {

10. # Record nodal displacements

11. recorder Node DDynaFrame[expr $Xframe]_$GroundFile.out disp -time -node

$IDctrlNode -dof 1

1. # Record element forces

2. for {set iel 1} {$iel <= 2} {incr iel 1} {

3. recorder Element $iel -time -file El[expr $iel]FDynaFrame[expr $Xframe]_$GroundFile.out force

4. }

5. }

gravity.tcl

1. # set up solution procedure

2. system SparseGeneral; # solution procedure, Super-LU, how it solves system of equations

3. constraints Plain; # how it handles boundary conditions, Plain: removes restrained DOFs

4. # set up convergence criteria

5. test NormUnbalance 1.e-5 20 0; # tolerance, max no. of iter., and print code, 1: every iter.

6. algorithm Newton; # use Newton's solution algorithm: updates tangent K at every iter.

7. numberer RCM; # renumber dof's to minimize band-width (optimization)

8. # set up load stepping # variable load-step

9. integrator LoadControl 0 1 0 0; # : Do init. incr., desired # of iter. to conv., Dmax, Dmin

10. analysis Static; # set up type of analysis, static for gravity

11. pattern Plain 1 Constant {

12. load $IDctrlNode 0.0 -$Pdl 0.0 0.0 0.0 -$Mdl; # Fx Fy Fz Mx My Mz

13. load [expr $IDctrlNode+1] 0.0 -$Pdl 0.0 0.0 0.0 +$Mdl }

14. analyze 1; # APPLY GRAVITY DL

lateral.tcl static

1. set PUSHOVER "DispControl"; # run displacement-controlled static pushover analysis

2. if {$ANALYSIS == "Static"} {

3. # Set lateral load pattern

4. pattern Plain 2 Linear {

5. load $IDctrlNode 100.0 0.0 0.0 0.0 0.0 0.0

6. load [expr $IDctrlNode+1] 100.0 0.0 0.0 0.0 0.0 0.0 }

7. if {$PUSHOVER == "LoadControl"} {

8. integrator LoadControl 0.2 4 0.1 2.0

9. set Nsteps 20

10. analysis Static

11. } elseif {$PUSHOVER == "DispControl"} {

12. integrator DisplacementControl $IDctrlNode 1 $DxPush 1 $DxPush $DxPush

13. set Nsteps [expr int($DmaxPush/$DxPush)]

14. analysis Static

15. } else { puts stderr "Invalid PUSHOVER option“ }

16. }

lateral.tcl dynamic

1. elseif {$ANALYSIS == "Dynamic"} {

2. wipeAnalysis

3. system SparseGeneral

4. constraints Plain

5. test NormUnbalance 1.0e-2 20 0

6. algorithm Newton

7. numberer RCM

8. integrator Newmark $gamma $beta $alphaM $betaK $betaKcomm $betaKinit; #damping

9. analysis Transient

10. set Nsteps [expr int($TmaxGround/$DtAnalysis)];

11. source ReadSMDFile.tcl; # read in procedure definition to convert data file types

12. set outFile $GroundFile.g3; # set variable holding new filename (PEER files have .at2 extension)

13. ReadSMDFile $GroundFile.at2 $outFile dt; # call procedure to convert the ground-motion file

14. set GMfatt [expr $g*$GMfact]; # data in input file is factor of g

15. set Gaccel "Series -dt $dt -filePath $outFile -factor $GMfatt"; # time series information

16. pattern UniformExcitation 2 1 -accel $Gaccel; # create uniform excit., 2:tag, 1:direxn

17. } else { puts stderr “Invalid ANALYSIS option” }

18. analyze $Nsteps $DtAnalysis Applies to both static & dynamic analyses