pushover_concentrated

setareh20 · Post by **setareh20** » Sat Feb 26, 2011 11:32 pm

Dear fmk,

First of all , thank you for your attention.

There is a problem when I run the file by the name of Pushover_concentrated which is in OpenSees examples. Please guide me? (This problem goes back to the # rotSpring2DModIKModel.tcl )

Thanks

# --------------------------------------------------------------------------------------------------
# Example: 2-Story Steel Moment Frame with Concentrated Plasticity
# Centerline Model with Concentrated Plastic Hinges at Beam-Column Joint
# Created by: Laura Eads, Stanford University, 2010
# Units: kips, inches, seconds

# Element and Node ID conventions:
# 1xy = frame columns with springs at both ends
# 2xy = frame beams with springs at both ends
# 6xy = trusses linking frame and P-delta column
# 7xy = P-delta columns
# 3,xya = frame column rotational springs
# 4,xya = frame beam rotational springs
# 5,xya = P-delta column rotational springs
# where:
# x = Pier or Bay #
# y = Floor or Story #
# a = an integer describing the location relative to beam-column joint (see description where elements and nodes are defined)

###################################################################################################
# Set Up & Source Definition
###################################################################################################
wipe all; # clear memory of past model definitions
model BasicBuilder -ndm 2 -ndf 3; # Define the model builder, ndm = #dimension, ndf = #dofs
source DisplayModel2D.tcl; # procedure for displaying a 2D perspective of model
source DisplayPlane.tcl; # procedure for displaying a plane in a model
source rotSpring2DModIKModel.tcl; # procedure for defining a rotational spring (zero-length element)
source rotLeaningCol.tcl; # procedure for defining a rotational spring (zero-length element) with very small stiffness

###################################################################################################
# Define Analysis Type
###################################################################################################
# Define type of analysis: "pushover" = pushover
set analysisType "pushover";
if {$analysisType == "pushover"} {
set dataDir Concentrated-Pushover-Output; # name of output folder
file mkdir $dataDir; # create output folder
}

###################################################################################################
# Define Building Geometry, Nodes, and Constraints
###################################################################################################
# define structure-geometry parameters
set NStories 2; # number of stories
set NBays 1; # number of frame bays (excludes bay for P-delta column)
set WBay [expr 30.0*12.0]; # bay width in inches
set HStory1 [expr 15.0*12.0]; # 1st story height in inches
set HStoryTyp [expr 12.0*12.0]; # story height of other stories in inches
set HBuilding [expr $HStory1 + ($NStories-1)*$HStoryTyp]; # height of building

# calculate locations of beam/column joints:
set Pier1 0.0; # leftmost column line
set Pier2 [expr $Pier1 + $WBay];
set Pier3 [expr $Pier2 + $WBay]; # P-delta column line
set Floor1 0.0; # ground floor
set Floor2 [expr $Floor1 + $HStory1];
set Floor3 [expr $Floor2 + $HStoryTyp];

# calculate joint offset distance for beam plastic hinges
set phlat23 [expr 0.0]; # lateral dist from beam-col joint to loc of hinge on Floor 2

# calculate nodal masses -- lump floor masses at frame nodes
set g 386.2; # acceleration due to gravity
set Floor2Weight 535.0; # weight of Floor 2 in kips
set Floor3Weight 525.0; # weight of Floor 3 in kips
set WBuilding [expr $Floor2Weight + $Floor3Weight];# total building weight
set NodalMass2 [expr ($Floor2Weight/$g) / (2.0)]; # mass at each node on Floor 2
set NodalMass3 [expr ($Floor3Weight/$g) / (2.0)]; # mass at each node on Floor 3
set Negligible 1e-9; # a very smnumber to avoid problems with zero

# define nodes and assign masses to beam-column intersections of frame
# command: node nodeID xcoord ycoord -mass mass_dof1 mass_dof2 mass_dof3
# nodeID convention: "xy" where x = Pier # and y = Floor #
node 11 $Pier1 $Floor1;
node 21 $Pier2 $Floor1;
node 31 $Pier3 $Floor1;
node 12 $Pier1 $Floor2 -mass $NodalMass2 $Negligible $Negligible;
node 22 $Pier2 $Floor2 -mass $NodalMass2 $Negligible $Negligible;
node 32 $Pier3 $Floor2;
node 13 $Pier1 $Floor3 -mass $NodalMass3 $Negligible $Negligible;
node 23 $Pier2 $Floor3 -mass $NodalMass3 $Negligible $Negligible;
node 33 $Pier3 $Floor3;

# define extra nodes for plastic hinge rotational springs
# nodeID convention: "xya" where x = Pier #, y = Floor #, a = location relative to beam-column joint
# "a" convention: 2 = left; 3 = right;
# "a" convention: 6 = below; 7 = above;
# column hinges at bottom of Story 1 (base)
node 117 $Pier1 $Floor1;
node 217 $Pier2 $Floor1;
# column hinges at top of Story 1
node 126 $Pier1 $Floor2;
node 226 $Pier2 $Floor2;
node 326 $Pier3 $Floor2; # zero-stiffness spring will be used on p-delta column
# column hinges at bottom of Story 2
node 127 $Pier1 $Floor2;
node 227 $Pier2 $Floor2;
node 327 $Pier3 $Floor2; # zero-stiffness spring will be used on p-delta column
# column hinges at top of Story 2
node 136 $Pier1 $Floor3;
node 236 $Pier2 $Floor3;
node 336 $Pier3 $Floor3; # zero-stiffness spring will be used on p-delta column

# beam hinges at Floor 2
node 122 [expr $Pier1 + $phlat23] $Floor2;
node 223 [expr $Pier2 - $phlat23] $Floor2;
# beam hinges at Floor 3
node 132 [expr $Pier1 + $phlat23] $Floor3;
node 233 [expr $Pier2 - $phlat23] $Floor3;

# constrain beam-column joints in a floor to have the same lateral displacement using the "equalDOF" command
# command: equalDOF $MasterNodeID $SlaveNodeID $dof1 $dof2...
set dof1 1; # constrain movement in dof 1 (x-direction)
equalDOF 12 22 $dof1; # Floor 2: Pier 1 to Pier 2
equalDOF 12 32 $dof1; # Floor 2: Pier 1 to Pier 3
equalDOF 13 23 $dof1; # Floor 3: Pier 1 to Pier 2
equalDOF 13 33 $dof1; # Floor 3: Pier 1 to Pier 3

# assign boundary condidtions
# command: fix nodeID dxFixity dyFixity rzFixity
# fixity values: 1 = constrained; 0 = unconstrained
# fix the base of the building; pin P-delta column at base
fix 11 1 1 1;
fix 21 1 1 1;
fix 31 1 1 0; # P-delta column is pinned

###################################################################################################
# Define Section Properties and Elements
###################################################################################################
# define material properties
set Es 29000.0; # steel Young's modulus

# define column section W24x131 for Story 1 & 2
set Acol_12 38.5; # cross-sectional area
set Icol_12 4020.0; # moment of inertia
set Mycol_12 20350.0; # yield moment

# define beam section W27x102 for Floor 2 & 3
set Abeam_23 30.0; # cross-sectional area (full section properties)
set Ibeam_23 3620.0; # moment of inertia (full section properties)
set Mybeam_23 10938.0; # yield moment at plastic hinge location (i.e., My of RBS section, if used)
# note: In this example the hinges form right at the beam-column joint, so using an RBS doesn't make sense;
# however, it is done here simply for illustrative purposes.

# determine stiffness modifications to equate the stiffness of the spring-elastic element-spring subassembly to the stiffness of the actual frame member
# Reference: Ibarra, L. F., and Krawinkler, H. (2005). "Global collapse of frame structures under seismic excitations," Technical Report 152,
# The John A. Blume Earthquake Engineering Research Center, Department of Civil Engineering, Stanford University, Stanford, CA.
# calculate modified section properties to account for spring stiffness being in series with the elastic element stiffness
set n 10.0; # stiffness multiplier for rotational spring

# calculate modified moment of inertia for elastic elements
set Icol_12mod [expr $Icol_12*($n+1.0)/$n]; # modified moment of inertia for columns in Story 1 & 2
set Ibeam_23mod [expr $Ibeam_23*($n+1.0)/$n]; # modified moment of inertia for beams in Floor 2 & 3
# calculate modified rotational stiffness for plastic hinge springs
set Ks_col_1 [expr $n*6.0*$Es*$Icol_12mod/$HStory1]; # rotational stiffness of Story 1 column springs
set Ks_col_2 [expr $n*6.0*$Es*$Icol_12mod/$HStoryTyp]; # rotational stiffness of Story 2 column springs
set Ks_beam_23 [expr $n*6.0*$Es*$Ibeam_23mod/$WBay]; # rotational stiffness of Floor 2 & 3 beam springs

# set up geometric transformations of element
set PDeltaTransf 1;
geomTransf PDelta $PDeltaTransf; # PDelta transformation

# define elastic column elements using "element" command
# command: element elasticBeamColumn $eleID $iNode $jNode $A $E $I $transfID
# eleID convention: "1xy" where 1 = col, x = Pier #, y = Story #
# Columns Story 1
element elasticBeamColumn 111 117 126 $Acol_12 $Es $Icol_12mod $PDeltaTransf; # Pier 1
element elasticBeamColumn 121 217 226 $Acol_12 $Es $Icol_12mod $PDeltaTransf; # Pier 2
# Columns Story 2
element elasticBeamColumn 112 127 136 $Acol_12 $Es $Icol_12mod $PDeltaTransf; # Pier 1
element elasticBeamColumn 122 227 236 $Acol_12 $Es $Icol_12mod $PDeltaTransf; # Pier 2

# define elastic beam elements
# eleID convention: "2xy" where 2 = beam, x = Bay #, y = Floor #
# Beams Story 1
element elasticBeamColumn 212 122 223 $Abeam_23 $Es $Ibeam_23mod $PDeltaTransf;
# Beams Story 2
element elasticBeamColumn 222 132 233 $Abeam_23 $Es $Ibeam_23mod $PDeltaTransf;

# define p-delta columns and rigid links
set TrussMatID 600; # define a material ID
set Arigid 1000.0; # define area of truss section (make much larger than A of frame elements)
set Irigid 100000.0; # moment of inertia for p-delta columns (make much larger than I of frame elements)
uniaxialMaterial Elastic $TrussMatID $Es; # define truss material
# rigid links
# command: element truss $eleID $iNode $jNode $A $materialID
# eleID convention: 6xy, 6 = truss link, x = Bay #, y = Floor #
element truss 622 22 32 $Arigid $TrussMatID; # Floor 2
element truss 623 23 33 $Arigid $TrussMatID; # Floor 3

# p-delta columns
# eleID convention: 7xy, 7 = p-delta columns, x = Pier #, y = Story #
element elasticBeamColumn 731 31 326 $Arigid $Es $Irigid $PDeltaTransf; # Story 1
element elasticBeamColumn 732 327 336 $Arigid $Es $Irigid $PDeltaTransf; # Story 2

# display the model with the node numbers
DisplayModel2D NodeNumbers

###################################################################################################
# Define Rotational Springs for Plastic Hinges
###################################################################################################
# define rotational spring properties and create spring elements using "rotSpring2DModIKModel" procedure
# rotSpring2DModIKModel creates a uniaxial material spring with a bilinear response based on Modified Ibarra Krawinkler Deterioration Model
# references provided in rotSpring2DModIKModel.tcl
# input values for Story 1 column springs
set McMy 1.05; # ratio of capping moment to yield moment, Mc / My
set LS 1000.0; # basic strength deterioration (a very large # = no cyclic deterioration)
set LK 1000.0; # unloading stiffness deterioration (a very large # = no cyclic deterioration)
set LA 1000.0; # accelerated reloading stiffness deterioration (a very large # = no cyclic deterioration)
set LD 1000.0; # post-capping strength deterioration (a very large # = no deterioration)
set cS 1.0; # exponent for basic strength deterioration (c = 1.0 for no deterioration)
set cK 1.0; # exponent for unloading stiffness deterioration (c = 1.0 for no deterioration)
set cA 1.0; # exponent for accelerated reloading stiffness deterioration (c = 1.0 for no deterioration)
set cD 1.0; # exponent for post-capping strength deterioration (c = 1.0 for no deterioration)
set th_pP 0.025; # plastic rot capacity for pos loading
set th_pN 0.025; # plastic rot capacity for neg loading
set th_pcP 0.3; # post-capping rot capacity for pos loading
set th_pcN 0.3; # post-capping rot capacity for neg loading
set ResP 0.4; # residual strength ratio for pos loading
set ResN 0.4; # residual strength ratio for neg loading
set th_uP 0.4; # ultimate rot capacity for pos loading
set th_uN 0.4; # ultimate rot capacity for neg loading
set DP 1.0; # rate of cyclic deterioration for pos loading
set DN 1.0; # rate of cyclic deterioration for neg loading
set a_mem [expr ($n+1.0)*($Mycol_12*($McMy-1.0)) / ($Ks_col_1*$th_pP)]; # strain hardening ratio of spring
set b [expr ($a_mem)/(1.0+$n*(1.0-$a_mem))]; # modified strain hardening ratio of spring (Ibarra & Krawinkler 2005, note: Eqn B.5 is incorrect)

# define column springs
# Spring ID: "3xya", where 3 = col spring, x = Pier #, y = Story #, a = location in story
# "a" convention: 1 = bottom of story, 2 = top of story
# command: rotSpring2DModIKModel id ndR ndC K asPos asNeg MyPos MyNeg LS LK LA LD cS cK cA cD th_p+ th_p- th_pc+ th_pc- Res+ Res- th_u+ th_u- D+ D-
# col springs @ bottom of Story 1 (at base)
rotSpring2DModIKModel 3111 11 117 $Ks_col_1 $b $b $Mycol_12 [expr -$Mycol_12] $LS $LK $LA $LD $cS $cK $cA $cD $th_pP $th_pN $th_pcP $th_pcN $ResP $ResN $th_uP $th_uN $DP $DN;
rotSpring2DModIKModel 3211 21 217 $Ks_col_1 $b $b $Mycol_12 [expr -$Mycol_12] $LS $LK $LA $LD $cS $cK $cA $cD $th_pP $th_pN $th_pcP $th_pcN $ResP $ResN $th_uP $th_uN $DP $DN;
#col springs @ top of Story 1 (below Floor 2)
rotSpring2DModIKModel 3112 12 126 $Ks_col_1 $b $b $Mycol_12 [expr -$Mycol_12] $LS $LK $LA $LD $cS $cK $cA $cD $th_pP $th_pN $th_pcP $th_pcN $ResP $ResN $th_uP $th_uN $DP $DN;
rotSpring2DModIKModel 3212 22 226 $Ks_col_1 $b $b $Mycol_12 [expr -$Mycol_12] $LS $LK $LA $LD $cS $cK $cA $cD $th_pP $th_pN $th_pcP $th_pcN $ResP $ResN $th_uP $th_uN $DP $DN;

# recompute strain hardening since Story 2 is not the same height as Story 1
set a_mem [expr ($n+1.0)*($Mycol_12*($McMy-1.0)) / ($Ks_col_2*$th_pP)]; # strain hardening ratio of spring
set b [expr ($a_mem)/(1.0+$n*(1.0-$a_mem))]; # modified strain hardening ratio of spring (Ibarra & Krawinkler 2005, note: there is mistake in Eqn B.5)
# col springs @ bottom of Story 2 (above Floor 2)
rotSpring2DModIKModel 3121 12 127 $Ks_col_2 $b $b $Mycol_12 [expr -$Mycol_12] $LS $LK $LA $LD $cS $cK $cA $cD $th_pP $th_pN $th_pcP $th_pcN $ResP $ResN $th_uP $th_uN $DP $DN;
rotSpring2DModIKModel 3221 22 227 $Ks_col_2 $b $b $Mycol_12 [expr -$Mycol_12] $LS $LK $LA $LD $cS $cK $cA $cD $th_pP $th_pN $th_pcP $th_pcN $ResP $ResN $th_uP $th_uN $DP $DN;
#col springs @ top of Story 2 (below Floor 3)
rotSpring2DModIKModel 3122 13 136 $Ks_col_2 $b $b $Mycol_12 [expr -$Mycol_12] $LS $LK $LA $LD $cS $cK $cA $cD $th_pP $th_pN $th_pcP $th_pcN $ResP $ResN $th_uP $th_uN $DP $DN;
rotSpring2DModIKModel 3222 23 236 $Ks_col_2 $b $b $Mycol_12 [expr -$Mycol_12] $LS $LK $LA $LD $cS $cK $cA $cD $th_pP $th_pN $th_pcP $th_pcN $ResP $ResN $th_uP $th_uN $DP $DN;

# create region for frame column springs
# command: region $regionID -ele $ele_1_ID $ele_2_ID...
region 1 -ele 3111 3211 3112 3212 3121 3221 3122 3222;

# define beam springs
# Spring ID: "4xya", where 4 = beam spring, x = Bay #, y = Floor #, a = location in bay
# "a" convention: 1 = left end, 2 = right end
# redefine the rotations since they are not the same
set th_pP 0.02;
set th_pN 0.02;
set th_pcP 0.16;
set th_pcN 0.16;
set a_mem [expr ($n+1.0)*($Mybeam_23*($McMy-1.0)) / ($Ks_beam_23*$th_pP)]; # strain hardening ratio of spring
set b [expr ($a_mem)/(1.0+$n*(1.0-$a_mem))]; # modified strain hardening ratio of spring (Ibarra & Krawinkler 2005, note: there is mistake in Eqn B.5)
#beam springs at Floor 2
rotSpring2DModIKModel 4121 12 122 $Ks_beam_23 $b $b $Mybeam_23 [expr -$Mybeam_23] $LS $LK $LA $LD $cS $cK $cA $cD $th_pP $th_pN $th_pcP $th_pcN $ResP $ResN $th_uP $th_uN $DP $DN;
rotSpring2DModIKModel 4122 22 223 $Ks_beam_23 $b $b $Mybeam_23 [expr -$Mybeam_23] $LS $LK $LA $LD $cS $cK $cA $cD $th_pP $th_pN $th_pcP $th_pcN $ResP $ResN $th_uP $th_uN $DP $DN;
#beam springs at Floor 3
rotSpring2DModIKModel 4131 13 132 $Ks_beam_23 $b $b $Mybeam_23 [expr -$Mybeam_23] $LS $LK $LA $LD $cS $cK $cA $cD $th_pP $th_pN $th_pcP $th_pcN $ResP $ResN $th_uP $th_uN $DP $DN;
rotSpring2DModIKModel 4132 23 233 $Ks_beam_23 $b $b $Mybeam_23 [expr -$Mybeam_23] $LS $LK $LA $LD $cS $cK $cA $cD $th_pP $th_pN $th_pcP $th_pcN $ResP $ResN $th_uP $th_uN $DP $DN;

# create region for beam springs
region 2 -ele 4121 4122 4131 4132;

# define p-delta column spring: zero-stiffness elastic spring
#Spring ID: "5xya" where 5 = leaning column spring, x = Pier #, y = Story #, a = location in story
# "a" convention: 1 = bottom of story, 2 = top of story
# rotLeaningCol ElemID ndR ndC
rotLeaningCol 5312 32 326; # top of Story 1
rotLeaningCol 5321 32 327; # bottom of Story 2
rotLeaningCol 5322 33 336; # top of Story 2

# create region for P-Delta column springs
region 3 -ele 5312 5321 5322;

############################################################################
# Eigenvalue Analysis
############################################################################
set pi [expr 2.0*asin(1.0)]; # Definition of pi
set nEigenI 1; # mode i = 1
set nEigenJ 2; # mode j = 2
set lambdaN [eigen [expr $nEigenJ]]; # eigenvalue analysis for nEigenJ modes
set lambdaI [lindex $lambdaN [expr 0]]; # eigenvalue mode i = 1
set lambdaJ [lindex $lambdaN [expr $nEigenJ-1]]; # eigenvalue mode j = 2
set w1 [expr pow($lambdaI,0.5)]; # w1 (1st mode circular frequency)
set w2 [expr pow($lambdaJ,0.5)]; # w2 (2nd mode circular frequency)
set T1 [expr 2.0*$pi/$w1]; # 1st mode period of the structure
set T2 [expr 2.0*$pi/$w2]; # 2nd mode period of the structure
puts "T1 = $T1 s"; # display the first mode period in the command window
puts "T2 = $T2 s"; # display the second mode period in the command window

############################################################################
# Gravity Loads & Gravity Analysis
############################################################################
# apply gravity loads
#command: pattern PatternType $PatternID TimeSeriesType
pattern Plain 101 Constant {

# point loads on leaning column nodes
# command: load node Fx Fy Mz
set P_PD2 [expr -398.02]; # Floor 2
set P_PD3 [expr -391.31]; # Floor 3
load 32 0.0 $P_PD2 0.0; # Floor 2
load 33 0.0 $P_PD3 0.0; # Floor 3

# point loads on frame column nodes
set P_F2 [expr 0.5*(-1.0*$Floor2Weight-$P_PD2)]; # load on each frame node in Floor 2
set P_F3 [expr 0.5*(-1.0*$Floor3Weight-$P_PD3)]; # load on each frame node in Floor 3
# Floor 2 loads
load 12 0.0 $P_F2 0.0;
load 22 0.0 $P_F2 0.0;
# Floor 3 loads
load 13 0.0 $P_F3 0.0;
load 23 0.0 $P_F3 0.0;
}

# Gravity-analysis: load-controlled static analysis
set Tol 1.0e-6; # convergence tolerance for test
constraints Plain; # how it handles boundary conditions
numberer RCM; # renumber dof's to minimize band-width (optimization)
system BandGeneral; # how to store and solve the system of equations in the analysis (large model: try UmfPack)
test NormDispIncr $Tol 6; # determine if convergence has been achieved at the end of an iteration step
algorithm Newton; # use Newton's solution algorithm: updates tangent stiffness at every iteration
set NstepGravity 10; # apply gravity in 10 steps
set DGravity [expr 1.0/$NstepGravity]; # load increment
integrator LoadControl $DGravity; # determine the next time step for an analysis
analysis Static; # define type of analysis static or transient
analyze $NstepGravity; # apply gravity

# maintain constant gravity loads and reset time to zero
loadConst -time 0.0
puts "Model Built"

############################################################################
# Recorders
############################################################################
# record drift histories
# drift recorder command: recorder Drift -file $filename -iNode $NodeI_ID -jNode $NodeJ_ID -dof $dof -perpDirn $Record.drift.perpendicular.to.this.direction
recorder Drift -file $dataDir/Drift-Story1.out -iNode 11 -jNode 12 -dof 1 -perpDirn 2;
recorder Drift -file $dataDir/Drift-Story2.out -iNode 12 -jNode 13 -dof 1 -perpDirn 2;
recorder Drift -file $dataDir/Drift-Roof.out -iNode 11 -jNode 13 -dof 1 -perpDirn 2;

# record base shear reactions
recorder Node -file $dataDir/Vbase.out -node 117 217 31 -dof 1 reaction;

# record story 1 column forces in global coordinates
recorder Element -file $dataDir/Fcol111.out -ele 111 force;
recorder Element -file $dataDir/Fcol121.out -ele 121 force;
recorder Element -file $dataDir/Fcol731.out -ele 731 force;

# record response history of all frame column springs (one file for moment, one for rotation)
recorder Element -file $dataDir/MRFcol-Mom-Hist.out -region 1 force;
recorder Element -file $dataDir/MRFcol-Rot-Hist.out -region 1 deformation;

# record response history of all frame beam springs (one file for moment, one for rotation)
recorder Element -file $dataDir/MRFbeam-Mom-Hist.out -region 2 force;
recorder Element -file $dataDir/MRFbeam-Rot-Hist.out -region 2 deformation;

#######################################################################################
# #
# Analysis Section #
# #
#######################################################################################

############################################################################
# Pushover Analysis #
############################################################################
if {$analysisType == "pushover"} {
puts "Running Pushover..."
# assign lateral loads and create load pattern: use ASCE 7-10 distribution
set lat2 16.255; # force on each frame node in Floor 2
set lat3 31.636; # force on each frame node in Floor 3
pattern Plain 200 Linear {
load 12 $lat2 0.0 0.0;
load 22 $lat2 0.0 0.0;
load 13 $lat3 0.0 0.0;
load 23 $lat3 0.0 0.0;
}

# display deformed shape:
set ViewScale 5;
DisplayModel2D DeformedShape $ViewScale ; # display deformed shape, the scaling factor needs to be adjusted for each model

# displacement parameters
set IDctrlNode 13; # node where disp is read for disp control
set IDctrlDOF 1; # degree of freedom read for disp control (1 = x displacement)
set Dmax [expr 0.1*$HBuilding]; # maximum displacement of pushover: 10% roof drift
set Dincr [expr 0.01]; # displacement increment

# analysis commands
constraints Plain; # how it handles boundary conditions
numberer RCM; # renumber dof's to minimize band-width (optimization)
system BandGeneral; # how to store and solve the system of equations in the analysis (large model: try UmfPack)
test NormUnbalance 1.0e-6 400; # tolerance, max iterations
algorithm Newton; # use Newton's solution algorithm: updates tangent stiffness at every iteration
integrator DisplacementControl $IDctrlNode $IDctrlDOF $Dincr; # use displacement-controlled analysis
analysis Static; # define type of analysis: static for pushover
set Nsteps [expr int($Dmax/$Dincr)];# number of pushover analysis steps
set ok [analyze $Nsteps]; # this will return zero if no convergence problems were encountered
puts "Pushover complete"; # display this message in the command window
}

wipe all;

############################################################################################
# rotSpring2DModIKModel.tcl
#
# This routine creates a uniaxial material spring with deterioration
#
# Spring follows: Bilinear Response based on Modified Ibarra Krawinkler Deterioration Model
#
# Written by: Dimitrios G. Lignos, Ph.D.
#
# Variables
# $eleID = Element Identification (integer)
# $nodeR = Retained/master node
# $nodeC = Constrained/slave node
# $K = Initial stiffness after the modification for n (see Ibarra and Krawinkler, 2005)
# $asPos = Strain hardening ratio after n modification (see Ibarra and Krawinkler, 2005)
# $asNeg = Strain hardening ratio after n modification (see Ibarra and Krawinkler, 2005)
# $MyPos = Positive yield moment (with sign)
# $MyNeg = Negative yield moment (with sign)
# $LS = Basic strength deterioration parameter (see Lignos and Krawinkler, 2009)
# $LK = Unloading stiffness deterioration parameter (see Lignos and Krawinkler, 2009)
# $LA = Accelerated reloading stiffness deterioration parameter (see Lignos and Krawinkler, 2009)
# $LD = Post-capping strength deterioration parameter (see Lignos and Krawinkler, 2009)
# $cS = Exponent for basic strength deterioration
# $cK = Exponent for unloading stiffness deterioration
# $cA = Exponent for accelerated reloading stiffness deterioration
# $cD = Exponent for post-capping strength deterioration
# $th_pP = Plastic rotation capacity for positive loading direction
# $th_pN = Plastic rotation capacity for negative loading direction
# $th_pcP = Post-capping rotation capacity for positive loading direction
# $th_pcN = Post-capping rotation capacity for negative loading direction
# $ResP = Residual strength ratio for positive loading direction
# $ResN = Residual strength ratio for negative loading direction
# $th_uP = Ultimate rotation capacity for positive loading direction
# $th_uN = Ultimate rotation capacity for negative loading direction
# $DP = Rate of cyclic deterioration for positive loading direction
# $DN = Rate of cyclic deterioration for negative loading direction
#
# References:
# Ibarra, L. F., and Krawinkler, H. (2005). “Global collapse of frame structures under seismic excitations,” Technical Report 152, The John A. Blume Earthquake Engineering Research Center, Department of Civil Engineering, Stanford University, Stanford, CA.
# Ibarra, L. F., Medina, R. A., and Krawinkler, H. (2005). “Hysteretic models that incorporate strength and stiffness deterioration,” International Journal for Earthquake Engineering and Structural Dynamics, Vol. 34, No.12, pp. 1489-1511.
# Lignos, D. G., and Krawinkler, H. (2010). “Deterioration Modeling of Steel Beams and Columns in Support to Collapse Prediction of Steel Moment Frames”, ASCE, Journal of Structural Engineering (under review).
# Lignos, D. G., and Krawinkler, H. (2009). “Sidesway Collapse of Deteriorating Structural Systems under Seismic Excitations,” Technical Report 172, The John A. Blume Earthquake Engineering Research Center, Department of Civil Engineering, Stanford University, Stanford, CA.
#
############################################################################################
#
proc rotSpring2DModIKModel {eleID nodeR nodeC K asPos asNeg MyPos MyNeg LS LK LA LD cS cK cA cD th_pP th_pN th_pcP th_pcN ResP ResN th_uP th_uN DP DN} {
#
# Create the zero length element
uniaxialMaterial Bilin $eleID $K $asPos $asNeg $MyPos $MyNeg $LS $LK $LA $LD $cS $cK $cA $cD $th_pP $th_pN $th_pcP $th_pcN $ResP $ResN $th_uP $th_uN $DP $DN;

element zeroLength $eleID $nodeR $nodeC -mat $eleID -dir 6

# Constrain the translational DOF with a multi-point constraint
# retained constrained DOF_1 DOF_2 ... DOF_n
equalDOF $nodeR $nodeC 1 2
}

###########################################################################################################
# rotLeaningCol.tcl
# Procedure that creates a zero-stiffness elastic rotational spring for the leaning column
# and constrains the translations DOFs of the spring.
#
# Written by: Laura Eads
# Date: 07/16/2010
#
# Formal arguments
# eleID - unique element ID for this zero length rotational spring
# nodeR - node ID which will be retained by the multi-point constraint
# nodeC - node ID which will be constrained by the multi-point constraint
#
##########################################################################################################

proc rotLeaningCol {eleID nodeR nodeC} {

#Spring Stiffness
set K 1e-9; # k/in

# Create the material and zero length element (spring)
uniaxialMaterial Elastic $eleID $K
element zeroLength $eleID $nodeR $nodeC -mat $eleID -dir 6

# Constrain the translational DOF with a multi-point constraint
# retained constrained DOF_1 DOF_2
equalDOF $nodeR $nodeC 1 2
}

############################################################################################
# rotSect2DModIKModel.tcl
#
# This routine creates a section with elastic axial and bilinear flexural response
#
# Behavior follows: Bilinear Response based on Modified Ibarra Krawinkler Deterioration Model
#
# Written by: Dimitrios G. Lignos, Ph.D.
#
# Variables
# $eleID = Element Identification (integer)
# $E = Young's modulus
# $A = Cross-sectional area
# $K = Initial stiffness after the modification for n (see Ibarra and Krawinkler, 2005)
# $asPos = Strain hardening ratio after n modification (see Ibarra and Krawinkler, 2005)
# $asNeg = Strain hardening ratio after n modification (see Ibarra and Krawinkler, 2005)
# $MyPos = Positive yield moment (with sign)
# $MyNeg = Negative yield moment (with sign)
# $LS = Basic strength deterioration parameter (see Lignos and Krawinkler, 2009)
# $LK = Unloading stiffness deterioration parameter (see Lignos and Krawinkler, 2009)
# $LA = Accelerated reloading stiffness deterioration parameter (see Lignos and Krawinkler, 2009)
# $LD = Post-capping strength deterioration parameter (see Lignos and Krawinkler, 2009)
# $cS = Exponent for basic strength deterioration
# $cK = Exponent for unloading stiffness deterioration
# $cA = Exponent for accelerated reloading stiffness deterioration
# $cD = Exponent for post-capping strength deterioration
# $th_pP = Plastic rotation capacity for positive loading direction
# $th_pN = Plastic rotation capacity for negative loading direction
# $th_pcP = Post-capping rotation capacity for positive loading direction
# $th_pcN = Post-capping rotation capacity for negative loading direction
# $ResP = Residual strength ratio for positive loading direction
# $ResN = Residual strength ratio for negative loading direction
# $th_uP = Ultimate rotation capacity for positive loading direction
# $th_uN = Ultimate rotation capacity for negative loading direction
# $DP = Rate of cyclic deterioration for positive loading direction
# $DN = Rate of cyclic deterioration for negative loading direction
#
# References:
# Ibarra, L. F., and Krawinkler, H. (2005). “Global collapse of frame structures under seismic excitations,” Technical Report 152, The John A. Blume Earthquake Engineering Research Center, Department of Civil Engineering, Stanford University, Stanford, CA.
# Ibarra, L. F., Medina, R. A., and Krawinkler, H. (2005). “Hysteretic models that incorporate strength and stiffness deterioration,” International Journal for Earthquake Engineering and Structural Dynamics, Vol. 34, No.12, pp. 1489-1511.
# Lignos, D. G., and Krawinkler, H. (2010). “Deterioration Modeling of Steel Beams and Columns in Support to Collapse Prediction of Steel Moment Frames”, ASCE, Journal of Structural Engineering (under review).
# Lignos, D. G., and Krawinkler, H. (2009). “Sidesway Collapse of Deteriorating Structural Systems under Seismic Excitations,” Technical Report 172, The John A. Blume Earthquake Engineering Research Center, Department of Civil Engineering, Stanford University, Stanford, CA.
#
############################################################################################

proc rotSect2DModIKModel {eleID E A K asPos asNeg MyPos MyNeg LS LK LA LD cS cK cA cD th_pP th_pN th_pcP th_pcN ResP ResN th_uP th_uN DP DN} {

# Create the material and section
uniaxialMaterial Bilin $eleID $K $asPos $asNeg $MyPos $MyNeg $LS $LK $LA $LD $cS $cK $cA $cD $th_pP $th_pN $th_pcP $th_pcN $ResP $ResN $th_uP $th_uN $DP $DN;
uniaxialMaterial Elastic [expr 10*$eleID + 1] [expr $E*$A]; # this is not used as a material, this is an axial-force-strain response
section Aggregator $eleID [expr 10*$eleID + 1] P $eleID Mz; # combine axial and flexural behavior into one section (no P-M interaction here)

}

proc DisplayModel2D { {ShapeType nill} {dAmp 5} {xLoc 10} {yLoc 10} {xPixels 512} {yPixels 384} {nEigen 1} } {
######################################################################################
## DisplayModel2D $ShapeType $dAmp $xLoc $yLoc $xPixels $yPixels $nEigen
######################################################################################
## display Node Numbers, Deformed or Mode Shape in 2D problem
## Silvia Mazzoni & Frank McKenna, 2006
##
## ShapeType : type of shape to display. # options: ModeShape , NodeNumbers , DeformedShape
## dAmp : relative amplification factor for deformations
## xLoc,yLoc : horizontal & vertical location in pixels of graphical window (0,0=upper left-most corner)
## xPixels,yPixels : width & height of graphical window in pixels
## nEigen : if nEigen not=0, show mode shape for nEigen eigenvalue
##
#######################################################################################
global TunitTXT; # load time-unit text
global ScreenResolutionX ScreenResolutionY; # read global values for screen resolution

if { [info exists TunitTXT] != 1} {set TunitTXT ""}; # set blank if it has not been defined previously.

if { [info exists ScreenResolutionX] != 1} {set ScreenResolutionX 1024}; # set default if it has not been defined previously.
if { [info exists ScreenResolutionY] != 1} {set ScreenResolutionY 768}; # set default if it has not been defined previously.

if {$xPixels == 0} {
set xPixels [expr int($ScreenResolutionX/2)];
set yPixels [expr int($ScreenResolutionY/2)]
set xLoc 10
set yLoc 10
}
if {$ShapeType == "nill"} {
puts ""; puts ""; puts "------------------"
puts "View the Model? (N)odes, (D)eformedShape, anyMode(1),(2),(#). Press enter for NO."
gets stdin answer
if {[llength $answer]>0 } {
if {$answer != "N" & $answer != "n"} {
puts "Modify View Scaling Factor=$dAmp? Type factor, or press enter for NO."
gets stdin answerdAmp
if {[llength $answerdAmp]>0 } {
set dAmp $answerdAmp
}
}
if {[string index $answer 0] == "N" || [string index $answer 0] == "n"} {
set ShapeType NodeNumbers
} elseif {[string index $answer 0] == "D" ||[string index $answer 0] == "d" } {
set ShapeType DeformedShape
} else {
set ShapeType ModeShape
set nEigen $answer
}
} else {
return
}
}

if {$ShapeType == "ModeShape" } {
set lambdaN [eigen $nEigen]; # perform eigenvalue analysis for ModeShape
set lambda [lindex $lambdaN [expr $nEigen-1]];
set omega [expr pow($lambda,0.5)]
set PI [expr 2*asin(1.0)]; # define constant
set Tperiod [expr 2*$PI/$omega]; # period (sec.)
set fmt1 "Mode Shape, Mode=%.1i Period=%.3f %s "
set windowTitle [format $fmt1 $nEigen $Tperiod $TunitTXT]
} elseif {$ShapeType == "NodeNumbers" } {
set windowTitle "Node Numbers"
} elseif {$ShapeType == "DeformedShape" } {
set windowTitle "Deformed Shape"
}

set viewPlane XY
recorder display $windowTitle $xLoc $yLoc $xPixels $yPixels -wipe ; # display recorder
DisplayPlane $ShapeType $dAmp $viewPlane $nEigen 0
after 2000; #pause for 2 seconds to display
}

proc DisplayPlane {ShapeType dAmp viewPlane {nEigen 0} {quadrant 0}} {
######################################################################################
## DisplayPlane $ShapeType $dAmp $viewPlane $nEigen $quadrant
######################################################################################
## setup display parameters for specified viewPlane and display
## Silvia Mazzoni & Frank McKenna, 2006
##
## ShapeType : type of shape to display. # options: ModeShape , NodeNumbers , DeformedShape
## dAmp : relative amplification factor for deformations
## viewPlane : set local xy axes in global coordinates (XY,YX,XZ,ZX,YZ,ZY)
## nEigen : if nEigen not=0, show mode shape for nEigen eigenvalue
## quadrant: quadrant where to show this figure (0=full figure)
##
######################################################################################

set Xmin [lindex [nodeBounds] 0]; # view bounds in global coords - will add padding on the sides
set Ymin [lindex [nodeBounds] 1];
set Zmin [lindex [nodeBounds] 2];
set Xmax [lindex [nodeBounds] 3];
set Ymax [lindex [nodeBounds] 4];
set Zmax [lindex [nodeBounds] 5];

set Xo 0; # center of local viewing system
set Yo 0;
set Zo 0;

set uLocal [string index $viewPlane 0]; # viewPlane local-x axis in global coordinates
set vLocal [string index $viewPlane 1]; # viewPlane local-y axis in global coordinates

if {$viewPlane =="3D" } {
set uMin $Zmin+$Xmin
set uMax $Zmax+$Xmax
set vMin $Ymin
set vMax $Ymax
set wMin -10000
set wMax 10000
vup 0 1 0; # dirn defining up direction of view plane
} else {
set keyAxisMin "X $Xmin Y $Ymin Z $Zmin"
set keyAxisMax "X $Xmax Y $Ymax Z $Zmax"
set axisU [string index $viewPlane 0];
set axisV [string index $viewPlane 1];
set uMin [string map $keyAxisMin $axisU]
set uMax [string map $keyAxisMax $axisU]
set vMin [string map $keyAxisMin $axisV]
set vMax [string map $keyAxisMax $axisV]
if {$viewPlane =="YZ" || $viewPlane =="ZY" } {
set wMin $Xmin
set wMax $Xmax
} elseif {$viewPlane =="XY" || $viewPlane =="YX" } {
set wMin $Zmin
set wMax $Zmax
} elseif {$viewPlane =="XZ" || $viewPlane =="ZX" } {
set wMin $Ymin
set wMax $Ymax
} else {
return -1
}
}

set epsilon 1e-3; # make windows width or height not zero when the Max and Min values of a coordinate are the same

set uWide [expr $uMax - $uMin+$epsilon];
set vWide [expr $vMax - $vMin+$epsilon];
set uSide [expr 0.25*$uWide];
set vSide [expr 0.25*$vWide];
set uMin [expr $uMin - $uSide];
set uMax [expr $uMax + $uSide];
set vMin [expr $vMin - $vSide];
set vMax [expr $vMax + 2*$vSide]; # pad a little more on top, because of window title
set uWide [expr $uMax - $uMin+$epsilon];
set vWide [expr $vMax - $vMin+$epsilon];
set uMid [expr ($uMin+$uMax)/2];
set vMid [expr ($vMin+$vMax)/2];

# keep the following general, as change the X and Y and Z for each view plane
# next three commmands define viewing system, all values in global coords
vrp $Xo $Yo $Zo; # point on the view plane in global coord, center of local viewing system
if {$vLocal == "X"} {
vup 1 0 0; # dirn defining up direction of view plane
} elseif {$vLocal == "Y"} {
vup 0 1 0; # dirn defining up direction of view plane
} elseif {$vLocal == "Z"} {
vup 0 0 1; # dirn defining up direction of view plane
}
if {$viewPlane =="YZ" } {
vpn 1 0 0; # direction of outward normal to view plane
prp 10000. $uMid $vMid ; # eye location in local coord sys defined by viewing system
plane 10000 -10000; # distance to front and back clipping planes from eye
} elseif {$viewPlane =="ZY" } {
vpn -1 0 0; # direction of outward normal to view plane
prp -10000. $vMid $uMid ; # eye location in local coord sys defined by viewing system
plane 10000 -10000; # distance to front and back clipping planes from eye
} elseif {$viewPlane =="XY" } {
vpn 0 0 1; # direction of outward normal to view plane
prp $uMid $vMid 10000; # eye location in local coord sys defined by viewing system
plane 10000 -10000; # distance to front and back clipping planes from eye
} elseif {$viewPlane =="YX" } {
vpn 0 0 -1; # direction of outward normal to view plane
prp $uMid $vMid -10000; # eye location in local coord sys defined by viewing system
plane 10000 -10000; # distance to front and back clipping planes from eye
} elseif {$viewPlane =="XZ" } {
vpn 0 -1 0; # direction of outward normal to view plane
prp $uMid -10000 $vMid ; # eye location in local coord sys defined by viewing system
plane 10000 -10000; # distance to front and back clipping planes from eye
} elseif {$viewPlane =="ZX" } {
vpn 0 1 0; # direction of outward normal to view plane
prp $uMid 10000 $vMid ; # eye location in local coord sys defined by viewing system
plane 10000 -10000; # distance to front and back clipping planes from eye
} elseif {$viewPlane =="3D" } {
vpn 1 0.25 1.25; # direction of outward normal to view plane
prp -100 $vMid 10000; # eye location in local coord sys defined by viewing system
plane 10000 -10000; # distance to front and back clipping planes from eye
} else {
return -1
}
# next three commands define view, all values in local coord system
if {$viewPlane =="3D" } {
viewWindow [expr $uMin-$uWide/4] [expr $uMax/2] [expr $vMin-0.25*$vWide] [expr $vMax]
} else {
viewWindow $uMin $uMax $vMin $vMax
}
projection 1; # projection mode, 0:prespective, 1: parallel
fill 1; # fill mode; needed only for solid elements

if {$quadrant == 0} {
port -1 1 -1 1 # area of window that will be drawn into (uMin,uMax,vMin,vMax);
} elseif {$quadrant == 1} {
port 0 1 0 1 # area of window that will be drawn into (uMin,uMax,vMin,vMax);
} elseif {$quadrant == 2} {
port -1 0 0 1 # area of window that will be drawn into (uMin,uMax,vMin,vMax);
} elseif {$quadrant == 3} {
port -1 0 -1 0 # area of window that will be drawn into (uMin,uMax,vMin,vMax);
} elseif {$quadrant == 4} {
port 0 1 -1 0 # area of window that will be drawn into (uMin,uMax,vMin,vMax);
}

if {$ShapeType == "ModeShape" } {
display -$nEigen 0 [expr 5.*$dAmp]; # display mode shape for mode $nEigen
} elseif {$ShapeType == "NodeNumbers" } {
display 1 -1 0 ; # display node numbers
} elseif {$ShapeType == "DeformedShape" } {
display 1 2 $dAmp; # display deformed shape the 2 makes the nodes small
}
}; #
######################################################################################

vesna · Post by **vesna** » Mon Feb 28, 2011 12:17 pm

Try contacting Laura Eads, the author of the example. She should be able to help you with your problem in the shortest time.

salarmanie · Post by **salarmanie** » Tue Mar 08, 2011 12:12 pm

Tell me what the problem is ... I have run it without any problem, even for RC members ...

goase66 · Post by **goase66** » Sun Mar 13, 2011 10:10 pm

setareh20 wrote:
> Dear fmk,
>
> First of all , thank you for your attention.
>
> There is a problem when I run the file by the name of Pushover_concentrated which
> is in OpenSees examples. Please guide me? (This problem goes back to the #
> rotSpring2DModIKModel.tcl )
>
> Thanks
>
>
> #
> --------------------------------------------------------------------------------------------------
> # Example: 2-Story Steel Moment Frame with Concentrated Plasticity
> # Centerline Model with Concentrated Plastic Hinges at Beam-Column Joint
> # Created by: Laura Eads, Stanford University, 2010
> # Units: kips, inches, seconds
>
> # Element and Node ID conventions:
> # 1xy = frame columns with springs at both ends
> # 2xy = frame beams with springs at both ends
> # 6xy = trusses linking frame and P-delta column
> # 7xy = P-delta columns
> # 3,xya = frame column rotational springs
> # 4,xya = frame beam rotational springs
> # 5,xya = P-delta column rotational springs
> # where:
> # x = Pier or Bay #
> # y = Floor or Story #
> # a = an integer describing the location relative to beam-column joint (see
> description where elements and nodes are defined)
>
>
> ###################################################################################################
> # Set Up & Source Definition
>
> ###################################################################################################
> wipe all; # clear memory of past model definitions
> model BasicBuilder -ndm 2 -ndf 3; # Define the model builder, ndm = #dimension, ndf
> = #dofs
> source DisplayModel2D.tcl; # procedure for displaying a 2D perspective of model
> source DisplayPlane.tcl; # procedure for displaying a plane in a model
> source rotSpring2DModIKModel.tcl; # procedure for defining a rotational spring
> (zero-length element)
> source rotLeaningCol.tcl; # procedure for defining a rotational spring
> (zero-length element) with very small stiffness
>
>
> ###################################################################################################
> # Define Analysis Type
>
> ###################################################################################################
> # Define type of analysis: "pushover" = pushover
> set analysisType "pushover";
> if {$analysisType == "pushover"} {
> set dataDir Concentrated-Pushover-Output; # name of output folder
> file mkdir $dataDir; # create output folder
> }
>
>
> ###################################################################################################
> # Define Building Geometry, Nodes, and Constraints
>
> ###################################################################################################
> # define structure-geometry parameters
> set NStories 2; # number of stories
> set NBays 1; # number of frame bays (excludes bay for P-delta column)
> set WBay [expr 30.0*12.0]; # bay width in inches
> set HStory1 [expr 15.0*12.0]; # 1st story height in inches
> set HStoryTyp [expr 12.0*12.0]; # story height of other stories in inches
> set HBuilding [expr $HStory1 + ($NStories-1)*$HStoryTyp]; # height of building
>
> # calculate locations of beam/column joints:
> set Pier1 0.0; # leftmost column line
> set Pier2 [expr $Pier1 + $WBay];
> set Pier3 [expr $Pier2 + $WBay]; # P-delta column line
> set Floor1 0.0; # ground floor
> set Floor2 [expr $Floor1 + $HStory1];
> set Floor3 [expr $Floor2 + $HStoryTyp];
>
> # calculate joint offset distance for beam plastic hinges
> set phlat23 [expr 0.0]; # lateral dist from beam-col joint to loc of hinge on Floor
> 2
>
> # calculate nodal masses -- lump floor masses at frame nodes
> set g 386.2; # acceleration due to gravity
> set Floor2Weight 535.0; # weight of Floor 2 in kips
> set Floor3Weight 525.0; # weight of Floor 3 in kips
> set WBuilding [expr $Floor2Weight + $Floor3Weight];# total building weight
> set NodalMass2 [expr ($Floor2Weight/$g) / (2.0)]; # mass at each node on Floor 2
> set NodalMass3 [expr ($Floor3Weight/$g) / (2.0)]; # mass at each node on Floor 3
> set Negligible 1e-9; # a very smnumber to avoid problems with zero
>
> # define nodes and assign masses to beam-column intersections of frame
> # command: node nodeID xcoord ycoord -mass mass_dof1 mass_dof2 mass_dof3
> # nodeID convention: "xy" where x = Pier # and y = Floor #
> node 11 $Pier1 $Floor1;
> node 21 $Pier2 $Floor1;
> node 31 $Pier3 $Floor1;
> node 12 $Pier1 $Floor2 -mass $NodalMass2 $Negligible $Negligible;
> node 22 $Pier2 $Floor2 -mass $NodalMass2 $Negligible $Negligible;
> node 32 $Pier3 $Floor2;
> node 13 $Pier1 $Floor3 -mass $NodalMass3 $Negligible $Negligible;
> node 23 $Pier2 $Floor3 -mass $NodalMass3 $Negligible $Negligible;
> node 33 $Pier3 $Floor3;
>
> # define extra nodes for plastic hinge rotational springs
> # nodeID convention: "xya" where x = Pier #, y = Floor #, a = location
> relative to beam-column joint
> # "a" convention: 2 = left; 3 = right;
> # "a" convention: 6 = below; 7 = above;
> # column hinges at bottom of Story 1 (base)
> node 117 $Pier1 $Floor1;
> node 217 $Pier2 $Floor1;
> # column hinges at top of Story 1
> node 126 $Pier1 $Floor2;
> node 226 $Pier2 $Floor2;
> node 326 $Pier3 $Floor2; # zero-stiffness spring will be used on p-delta column
> # column hinges at bottom of Story 2
> node 127 $Pier1 $Floor2;
> node 227 $Pier2 $Floor2;
> node 327 $Pier3 $Floor2; # zero-stiffness spring will be used on p-delta column
> # column hinges at top of Story 2
> node 136 $Pier1 $Floor3;
> node 236 $Pier2 $Floor3;
> node 336 $Pier3 $Floor3; # zero-stiffness spring will be used on p-delta column
>
> # beam hinges at Floor 2
> node 122 [expr $Pier1 + $phlat23] $Floor2;
> node 223 [expr $Pier2 - $phlat23] $Floor2;
> # beam hinges at Floor 3
> node 132 [expr $Pier1 + $phlat23] $Floor3;
> node 233 [expr $Pier2 - $phlat23] $Floor3;
>
> # constrain beam-column joints in a floor to have the same lateral displacement using
> the "equalDOF" command
> # command: equalDOF $MasterNodeID $SlaveNodeID $dof1 $dof2...
> set dof1 1; # constrain movement in dof 1 (x-direction)
> equalDOF 12 22 $dof1; # Floor 2: Pier 1 to Pier 2
> equalDOF 12 32 $dof1; # Floor 2: Pier 1 to Pier 3
> equalDOF 13 23 $dof1; # Floor 3: Pier 1 to Pier 2
> equalDOF 13 33 $dof1; # Floor 3: Pier 1 to Pier 3
>
> # assign boundary condidtions
> # command: fix nodeID dxFixity dyFixity rzFixity
> # fixity values: 1 = constrained; 0 = unconstrained
> # fix the base of the building; pin P-delta column at base
> fix 11 1 1 1;
> fix 21 1 1 1;
> fix 31 1 1 0; # P-delta column is pinned
>
>
> ###################################################################################################
> # Define Section Properties and Elements
>
> ###################################################################################################
> # define material properties
> set Es 29000.0; # steel Young's modulus
>
> # define column section W24x131 for Story 1 & 2
> set Acol_12 38.5; # cross-sectional area
> set Icol_12 4020.0; # moment of inertia
> set Mycol_12 20350.0; # yield moment
>
> # define beam section W27x102 for Floor 2 & 3
> set Abeam_23 30.0; # cross-sectional area (full section properties)
> set Ibeam_23 3620.0; # moment of inertia (full section properties)
> set Mybeam_23 10938.0; # yield moment at plastic hinge location (i.e., My of RBS
> section, if used)
> # note: In this example the hinges form right at the beam-column joint, so using an
> RBS doesn't make sense;
> # however, it is done here simply for illustrative purposes.
>
> # determine stiffness modifications to equate the stiffness of the spring-elastic
> element-spring subassembly to the stiffness of the actual frame member
> # Reference: Ibarra, L. F., and Krawinkler, H. (2005). "Global collapse of
> frame structures under seismic excitations," Technical Report 152,
> # The John A. Blume Earthquake Engineering Research Center, Department
> of Civil Engineering, Stanford University, Stanford, CA.
> # calculate modified section properties to account for spring stiffness being in
> series with the elastic element stiffness
> set n 10.0; # stiffness multiplier for rotational spring
>
> # calculate modified moment of inertia for elastic elements
> set Icol_12mod [expr $Icol_12*($n+1.0)/$n]; # modified moment of inertia for
> columns in Story 1 & 2
> set Ibeam_23mod [expr $Ibeam_23*($n+1.0)/$n]; # modified moment of inertia for beams
> in Floor 2 & 3
> # calculate modified rotational stiffness for plastic hinge springs
> set Ks_col_1 [expr $n*6.0*$Es*$Icol_12mod/$HStory1]; # rotational stiffness of
> Story 1 column springs
> set Ks_col_2 [expr $n*6.0*$Es*$Icol_12mod/$HStoryTyp]; # rotational stiffness of
> Story 2 column springs
> set Ks_beam_23 [expr $n*6.0*$Es*$Ibeam_23mod/$WBay]; # rotational stiffness of
> Floor 2 & 3 beam springs
>
> # set up geometric transformations of element
> set PDeltaTransf 1;
> geomTransf PDelta $PDeltaTransf; # PDelta transformation
>
> # define elastic column elements using "element" command
> # command: element elasticBeamColumn $eleID $iNode $jNode $A $E $I $transfID
> # eleID convention: "1xy" where 1 = col, x = Pier #, y = Story #
> # Columns Story 1
> element elasticBeamColumn 111 117 126 $Acol_12 $Es $Icol_12mod $PDeltaTransf; #
> Pier 1
> element elasticBeamColumn 121 217 226 $Acol_12 $Es $Icol_12mod $PDeltaTransf; #
> Pier 2
> # Columns Story 2
> element elasticBeamColumn 112 127 136 $Acol_12 $Es $Icol_12mod $PDeltaTransf; #
> Pier 1
> element elasticBeamColumn 122 227 236 $Acol_12 $Es $Icol_12mod $PDeltaTransf; #
> Pier 2
>
> # define elastic beam elements
> # eleID convention: "2xy" where 2 = beam, x = Bay #, y = Floor #
> # Beams Story 1
> element elasticBeamColumn 212 122 223 $Abeam_23 $Es $Ibeam_23mod $PDeltaTransf;
> # Beams Story 2
> element elasticBeamColumn 222 132 233 $Abeam_23 $Es $Ibeam_23mod $PDeltaTransf;
>
> # define p-delta columns and rigid links
> set TrussMatID 600; # define a material ID
> set Arigid 1000.0; # define area of truss section (make much larger than A of frame
> elements)
> set Irigid 100000.0; # moment of inertia for p-delta columns (make much larger than
> I of frame elements)
> uniaxialMaterial Elastic $TrussMatID $Es; # define truss material
> # rigid links
> # command: element truss $eleID $iNode $jNode $A $materialID
> # eleID convention: 6xy, 6 = truss link, x = Bay #, y = Floor #
> element truss 622 22 32 $Arigid $TrussMatID; # Floor 2
> element truss 623 23 33 $Arigid $TrussMatID; # Floor 3
>
> # p-delta columns
> # eleID convention: 7xy, 7 = p-delta columns, x = Pier #, y = Story #
> element elasticBeamColumn 731 31 326 $Arigid $Es $Irigid $PDeltaTransf; # Story 1
> element elasticBeamColumn 732 327 336 $Arigid $Es $Irigid $PDeltaTransf; # Story 2
>
> # display the model with the node numbers
> DisplayModel2D NodeNumbers
>
>
> ###################################################################################################
> # Define Rotational Springs for Plastic Hinges
>
> ###################################################################################################
> # define rotational spring properties and create spring elements using
> "rotSpring2DModIKModel" procedure
> # rotSpring2DModIKModel creates a uniaxial material spring with a bilinear response
> based on Modified Ibarra Krawinkler Deterioration Model
> # references provided in rotSpring2DModIKModel.tcl
> # input values for Story 1 column springs
> set McMy 1.05; # ratio of capping moment to yield moment, Mc / My
> set LS 1000.0; # basic strength deterioration (a very large # = no cyclic
> deterioration)
> set LK 1000.0; # unloading stiffness deterioration (a very large # = no cyclic
> deterioration)
> set LA 1000.0; # accelerated reloading stiffness deterioration (a very large # =
> no cyclic deterioration)
> set LD 1000.0; # post-capping strength deterioration (a very large # = no
> deterioration)
> set cS 1.0; # exponent for basic strength deterioration (c = 1.0 for no
> deterioration)
> set cK 1.0; # exponent for unloading stiffness deterioration (c = 1.0 for no
> deterioration)
> set cA 1.0; # exponent for accelerated reloading stiffness deterioration (c = 1.0
> for no deterioration)
> set cD 1.0; # exponent for post-capping strength deterioration (c = 1.0 for no
> deterioration)
> set th_pP 0.025; # plastic rot capacity for pos loading
> set th_pN 0.025; # plastic rot capacity for neg loading
> set th_pcP 0.3; # post-capping rot capacity for pos loading
> set th_pcN 0.3; # post-capping rot capacity for neg loading
> set ResP 0.4; # residual strength ratio for pos loading
> set ResN 0.4; # residual strength ratio for neg loading
> set th_uP 0.4; # ultimate rot capacity for pos loading
> set th_uN 0.4; # ultimate rot capacity for neg loading
> set DP 1.0; # rate of cyclic deterioration for pos loading
> set DN 1.0; # rate of cyclic deterioration for neg loading
> set a_mem [expr ($n+1.0)*($Mycol_12*($McMy-1.0)) / ($Ks_col_1*$th_pP)]; # strain
> hardening ratio of spring
> set b [expr ($a_mem)/(1.0+$n*(1.0-$a_mem))]; # modified strain hardening ratio
> of spring (Ibarra & Krawinkler 2005, note: Eqn B.5 is incorrect)
>
> # define column springs
> # Spring ID: "3xya", where 3 = col spring, x = Pier #, y = Story #, a =
> location in story
> # "a" convention: 1 = bottom of story, 2 = top of story
> # command: rotSpring2DModIKModel id ndR ndC K asPos asNeg MyPos
> MyNeg LS LK LA LD cS cK cA cD th_p+ th_p- th_pc+ th_pc-
> Res+ Res- th_u+ th_u- D+ D-
> # col springs @ bottom of Story 1 (at base)
> rotSpring2DModIKModel 3111 11 117 $Ks_col_1 $b $b $Mycol_12 [expr -$Mycol_12] $LS
> $LK $LA $LD $cS $cK $cA $cD $th_pP $th_pN $th_pcP $th_pcN $ResP $ResN $th_uP $th_uN
> $DP $DN;
> rotSpring2DModIKModel 3211 21 217 $Ks_col_1 $b $b $Mycol_12 [expr -$Mycol_12] $LS
> $LK $LA $LD $cS $cK $cA $cD $th_pP $th_pN $th_pcP $th_pcN $ResP $ResN $th_uP $th_uN
> $DP $DN;
> #col springs @ top of Story 1 (below Floor 2)
> rotSpring2DModIKModel 3112 12 126 $Ks_col_1 $b $b $Mycol_12 [expr -$Mycol_12] $LS
> $LK $LA $LD $cS $cK $cA $cD $th_pP $th_pN $th_pcP $th_pcN $ResP $ResN $th_uP $th_uN
> $DP $DN;
> rotSpring2DModIKModel 3212 22 226 $Ks_col_1 $b $b $Mycol_12 [expr -$Mycol_12] $LS
> $LK $LA $LD $cS $cK $cA $cD $th_pP $th_pN $th_pcP $th_pcN $ResP $ResN $th_uP $th_uN
> $DP $DN;
>
> # recompute strain hardening since Story 2 is not the same height as Story 1
> set a_mem [expr ($n+1.0)*($Mycol_12*($McMy-1.0)) / ($Ks_col_2*$th_pP)]; # strain
> hardening ratio of spring
> set b [expr ($a_mem)/(1.0+$n*(1.0-$a_mem))]; # modified strain hardening ratio
> of spring (Ibarra & Krawinkler 2005, note: there is mistake in Eqn B.5)
> # col springs @ bottom of Story 2 (above Floor 2)
> rotSpring2DModIKModel 3121 12 127 $Ks_col_2 $b $b $Mycol_12 [expr -$Mycol_12] $LS
> $LK $LA $LD $cS $cK $cA $cD $th_pP $th_pN $th_pcP $th_pcN $ResP $ResN $th_uP $th_uN
> $DP $DN;
> rotSpring2DModIKModel 3221 22 227 $Ks_col_2 $b $b $Mycol_12 [expr -$Mycol_12] $LS
> $LK $LA $LD $cS $cK $cA $cD $th_pP $th_pN $th_pcP $th_pcN $ResP $ResN $th_uP $th_uN
> $DP $DN;
> #col springs @ top of Story 2 (below Floor 3)
> rotSpring2DModIKModel 3122 13 136 $Ks_col_2 $b $b $Mycol_12 [expr -$Mycol_12] $LS
> $LK $LA $LD $cS $cK $cA $cD $th_pP $th_pN $th_pcP $th_pcN $ResP $ResN $th_uP $th_uN
> $DP $DN;
> rotSpring2DModIKModel 3222 23 236 $Ks_col_2 $b $b $Mycol_12 [expr -$Mycol_12] $LS
> $LK $LA $LD $cS $cK $cA $cD $th_pP $th_pN $th_pcP $th_pcN $ResP $ResN $th_uP $th_uN
> $DP $DN;
>
> # create region for frame column springs
> # command: region $regionID -ele $ele_1_ID $ele_2_ID...
> region 1 -ele 3111 3211 3112 3212 3121 3221 3122 3222;
>
> # define beam springs
> # Spring ID: "4xya", where 4 = beam spring, x = Bay #, y = Floor #, a =
> location in bay
> # "a" convention: 1 = left end, 2 = right end
> # redefine the rotations since they are not the same
> set th_pP 0.02;
> set th_pN 0.02;
> set th_pcP 0.16;
> set th_pcN 0.16;
> set a_mem [expr ($n+1.0)*($Mybeam_23*($McMy-1.0)) / ($Ks_beam_23*$th_pP)]; # strain
> hardening ratio of spring
> set b [expr ($a_mem)/(1.0+$n*(1.0-$a_mem))]; # modified strain hardening
> ratio of spring (Ibarra & Krawinkler 2005, note: there is mistake in Eqn B.5)
> #beam springs at Floor 2
> rotSpring2DModIKModel 4121 12 122 $Ks_beam_23 $b $b $Mybeam_23 [expr -$Mybeam_23]
> $LS $LK $LA $LD $cS $cK $cA $cD $th_pP $th_pN $th_pcP $th_pcN $ResP $ResN $th_uP
> $th_uN $DP $DN;
> rotSpring2DModIKModel 4122 22 223 $Ks_beam_23 $b $b $Mybeam_23 [expr -$Mybeam_23]
> $LS $LK $LA $LD $cS $cK $cA $cD $th_pP $th_pN $th_pcP $th_pcN $ResP $ResN $th_uP
> $th_uN $DP $DN;
> #beam springs at Floor 3
> rotSpring2DModIKModel 4131 13 132 $Ks_beam_23 $b $b $Mybeam_23 [expr -$Mybeam_23]
> $LS $LK $LA $LD $cS $cK $cA $cD $th_pP $th_pN $th_pcP $th_pcN $ResP $ResN $th_uP
> $th_uN $DP $DN;
> rotSpring2DModIKModel 4132 23 233 $Ks_beam_23 $b $b $Mybeam_23 [expr -$Mybeam_23]
> $LS $LK $LA $LD $cS $cK $cA $cD $th_pP $th_pN $th_pcP $th_pcN $ResP $ResN $th_uP
> $th_uN $DP $DN;
>
> # create region for beam springs
> region 2 -ele 4121 4122 4131 4132;
>
> # define p-delta column spring: zero-stiffness elastic spring
> #Spring ID: "5xya" where 5 = leaning column spring, x = Pier #, y = Story
> #, a = location in story
> # "a" convention: 1 = bottom of story, 2 = top of story
> # rotLeaningCol ElemID ndR ndC
> rotLeaningCol 5312 32 326; # top of Story 1
> rotLeaningCol 5321 32 327; # bottom of Story 2
> rotLeaningCol 5322 33 336; # top of Story 2
>
> # create region for P-Delta column springs
> region 3 -ele 5312 5321 5322;
>
> ############################################################################
> # Eigenvalue Analysis
> ############################################################################
> set pi [expr 2.0*asin(1.0)]; # Definition of pi
> set nEigenI 1; # mode i = 1
> set nEigenJ 2; # mode j = 2
> set lambdaN [eigen [expr $nEigenJ]]; # eigenvalue analysis for nEigenJ modes
> set lambdaI [lindex $lambdaN [expr 0]]; # eigenvalue mode i = 1
> set lambdaJ [lindex $lambdaN [expr $nEigenJ-1]]; # eigenvalue mode j = 2
> set w1 [expr pow($lambdaI,0.5)]; # w1 (1st mode circular frequency)
> set w2 [expr pow($lambdaJ,0.5)]; # w2 (2nd mode circular frequency)
> set T1 [expr 2.0*$pi/$w1]; # 1st mode period of the structure
> set T2 [expr 2.0*$pi/$w2]; # 2nd mode period of the structure
> puts "T1 = $T1 s"; # display the first mode period in the command
> window
> puts "T2 = $T2 s"; # display the second mode period in the command
> window
>
> ############################################################################
> # Gravity Loads & Gravity Analysis
> ############################################################################
> # apply gravity loads
> #command: pattern PatternType $PatternID TimeSeriesType
> pattern Plain 101 Constant {
>
> # point loads on leaning column nodes
> # command: load node Fx Fy Mz
> set P_PD2 [expr -398.02]; # Floor 2
> set P_PD3 [expr -391.31]; # Floor 3
> load 32 0.0 $P_PD2 0.0; # Floor 2
> load 33 0.0 $P_PD3 0.0; # Floor 3
>
> # point loads on frame column nodes
> set P_F2 [expr 0.5*(-1.0*$Floor2Weight-$P_PD2)]; # load on each frame node in Floor
> 2
> set P_F3 [expr 0.5*(-1.0*$Floor3Weight-$P_PD3)]; # load on each frame node in Floor
> 3
> # Floor 2 loads
> load 12 0.0 $P_F2 0.0;
> load 22 0.0 $P_F2 0.0;
> # Floor 3 loads
> load 13 0.0 $P_F3 0.0;
> load 23 0.0 $P_F3 0.0;
> }
>
> # Gravity-analysis: load-controlled static analysis
> set Tol 1.0e-6; # convergence tolerance for test
> constraints Plain; # how it handles boundary conditions
> numberer RCM; # renumber dof's to minimize band-width (optimization)
> system BandGeneral; # how to store and solve the system of equations in the
> analysis (large model: try UmfPack)
> test NormDispIncr $Tol 6; # determine if convergence has been achieved at the end
> of an iteration step
> algorithm Newton; # use Newton's solution algorithm: updates tangent stiffness
> at every iteration
> set NstepGravity 10; # apply gravity in 10 steps
> set DGravity [expr 1.0/$NstepGravity]; # load increment
> integrator LoadControl $DGravity; # determine the next time step for an analysis
> analysis Static; # define type of analysis static or transient
> analyze $NstepGravity; # apply gravity
>
> # maintain constant gravity loads and reset time to zero
> loadConst -time 0.0
> puts "Model Built"
>
> ############################################################################
> # Recorders
> ############################################################################
> # record drift histories
> # drift recorder command: recorder Drift -file $filename -iNode $NodeI_ID -jNode
> $NodeJ_ID -dof $dof -perpDirn $Record.drift.perpendicular.to.this.direction
> recorder Drift -file $dataDir/Drift-Story1.out -iNode 11 -jNode 12 -dof 1 -perpDirn
> 2;
> recorder Drift -file $dataDir/Drift-Story2.out -iNode 12 -jNode 13 -dof 1 -perpDirn
> 2;
> recorder Drift -file $dataDir/Drift-Roof.out -iNode 11 -jNode 13 -dof 1 -perpDirn 2;
>
> # record base shear reactions
> recorder Node -file $dataDir/Vbase.out -node 117 217 31 -dof 1 reaction;
>
> # record story 1 column forces in global coordinates
> recorder Element -file $dataDir/Fcol111.out -ele 111 force;
> recorder Element -file $dataDir/Fcol121.out -ele 121 force;
> recorder Element -file $dataDir/Fcol731.out -ele 731 force;
>
> # record response history of all frame column springs (one file for moment, one for
> rotation)
> recorder Element -file $dataDir/MRFcol-Mom-Hist.out -region 1 force;
> recorder Element -file $dataDir/MRFcol-Rot-Hist.out -region 1 deformation;
>
> # record response history of all frame beam springs (one file for moment, one for
> rotation)
> recorder Element -file $dataDir/MRFbeam-Mom-Hist.out -region 2 force;
> recorder Element -file $dataDir/MRFbeam-Rot-Hist.out -region 2 deformation;
>
>
> #######################################################################################
> #
> #
> # Analysis Section #
> #
> #
>
> #######################################################################################
>
> ############################################################################
> # Pushover Analysis #
> ############################################################################
> if {$analysisType == "pushover"} {
> puts "Running Pushover..."
> # assign lateral loads and create load pattern: use ASCE 7-10 distribution
> set lat2 16.255; # force on each frame node in Floor 2
> set lat3 31.636; # force on each frame node in Floor 3
> pattern Plain 200 Linear {
> load 12 $lat2 0.0 0.0;
> load 22 $lat2 0.0 0.0;
> load 13 $lat3 0.0 0.0;
> load 23 $lat3 0.0 0.0;
> }
>
> # display deformed shape:
> set ViewScale 5;
> DisplayModel2D DeformedShape $ViewScale ; # display deformed shape, the scaling
> factor needs to be adjusted for each model
>
> # displacement parameters
> set IDctrlNode 13; # node where disp is read for disp control
> set IDctrlDOF 1; # degree of freedom read for disp control (1 = x displacement)
> set Dmax [expr 0.1*$HBuilding]; # maximum displacement of pushover: 10% roof drift
> set Dincr [expr 0.01]; # displacement increment
>
> # analysis commands
> constraints Plain; # how it handles boundary conditions
> numberer RCM; # renumber dof's to minimize band-width (optimization)
> system BandGeneral; # how to store and solve the system of equations in the
> analysis (large model: try UmfPack)
> test NormUnbalance 1.0e-6 400; # tolerance, max iterations
> algorithm Newton; # use Newton's solution algorithm: updates tangent stiffness
> at every iteration
> integrator DisplacementControl $IDctrlNode $IDctrlDOF $Dincr; # use
> displacement-controlled analysis
> analysis Static; # define type of analysis: static for pushover
> set Nsteps [expr int($Dmax/$Dincr)];# number of pushover analysis steps
> set ok [analyze $Nsteps]; # this will return zero if no convergence problems were
> encountered
> puts "Pushover complete"; # display this message in the command window
> }
>
>
> wipe all;
>
>
>
>
>
> ############################################################################################
> # rotSpring2DModIKModel.tcl
> #
> # This routine creates a uniaxial material spring with deterioration
> #
> # Spring follows: Bilinear Response based on Modified Ibarra Krawinkler Deterioration
> Model
> #
> # Written by: Dimitrios G. Lignos, Ph.D.
> #
> # Variables
> # $eleID = Element Identification (integer)
> # $nodeR = Retained/master node
> # $nodeC = Constrained/slave node
> # $K = Initial stiffness after the modification for n (see Ibarra and Krawinkler,
> 2005)
> # $asPos = Strain hardening ratio after n modification (see Ibarra and Krawinkler,
> 2005)
> # $asNeg = Strain hardening ratio after n modification (see Ibarra and Krawinkler,
> 2005)
> # $MyPos = Positive yield moment (with sign)
> # $MyNeg = Negative yield moment (with sign)
> # $LS = Basic strength deterioration parameter (see Lignos and Krawinkler, 2009)
> # $LK = Unloading stiffness deterioration parameter (see Lignos and Krawinkler,
> 2009)
> # $LA = Accelerated reloading stiffness deterioration parameter (see Lignos and
> Krawinkler, 2009)
> # $LD = Post-capping strength deterioration parameter (see Lignos and Krawinkler,
> 2009)
> # $cS = Exponent for basic strength deterioration
> # $cK = Exponent for unloading stiffness deterioration
> # $cA = Exponent for accelerated reloading stiffness deterioration
> # $cD = Exponent for post-capping strength deterioration
> # $th_pP = Plastic rotation capacity for positive loading direction
> # $th_pN = Plastic rotation capacity for negative loading direction
> # $th_pcP = Post-capping rotation capacity for positive loading direction
> # $th_pcN = Post-capping rotation capacity for negative loading direction
> # $ResP = Residual strength ratio for positive loading direction
> # $ResN = Residual strength ratio for negative loading direction
> # $th_uP = Ultimate rotation capacity for positive loading direction
> # $th_uN = Ultimate rotation capacity for negative loading direction
> # $DP = Rate of cyclic deterioration for positive loading direction
> # $DN = Rate of cyclic deterioration for negative loading direction
> #
> # References:
> # Ibarra, L. F., and Krawinkler, H. (2005). “Global collapse of frame structures
> under seismic excitations,” Technical Report 152, The John A. Blume Earthquake
> Engineering Research Center, Department of Civil Engineering, Stanford University,
> Stanford, CA.
> # Ibarra, L. F., Medina, R. A., and Krawinkler, H. (2005). “Hysteretic models that
> incorporate strength and stiffness deterioration,” International Journal for
> Earthquake Engineering and Structural Dynamics, Vol. 34, No.12, pp. 1489-1511.
> # Lignos, D. G., and Krawinkler, H. (2010). “Deterioration Modeling of Steel Beams
> and Columns in Support to Collapse Prediction of Steel Moment Frames”, ASCE, Journal
> of Structural Engineering (under review).
> # Lignos, D. G., and Krawinkler, H. (2009). “Sidesway Collapse of Deteriorating
> Structural Systems under Seismic Excitations,” Technical Report 172, The John A.
> Blume Earthquake Engineering Research Center, Department of Civil Engineering,
> Stanford University, Stanford, CA.
> #
>
> ############################################################################################
> #
> proc rotSpring2DModIKModel {eleID nodeR nodeC K asPos asNeg MyPos MyNeg LS LK LA LD
> cS cK cA cD th_pP th_pN th_pcP th_pcN ResP ResN th_uP th_uN DP DN} {
> #
> # Create the zero length element
> uniaxialMaterial Bilin $eleID $K $asPos $asNeg $MyPos $MyNeg $LS $LK $LA $LD
> $cS $cK $cA $cD $th_pP $th_pN $th_pcP $th_pcN $ResP $ResN $th_uP $th_uN $DP $DN;
>
> element zeroLength $eleID $nodeR $nodeC -mat $eleID -dir 6
>
> # Constrain the translational DOF with a multi-point constraint
> # retained constrained DOF_1 DOF_2 ... DOF_n
> equalDOF $nodeR $nodeC 1 2
> }
>
>
>
>
>
>
> ###########################################################################################################
> # rotLeaningCol.tcl
> # Procedure that creates a zero-stiffness elastic rotational spring for the leaning
> column
> # and constrains the translations DOFs of the spring.
> #
> # Written by: Laura Eads
> # Date: 07/16/2010
> #
> # Formal arguments
> # eleID - unique element ID for this zero length rotational spring
> # nodeR - node ID which will be retained by the multi-point constraint
> # nodeC - node ID which will be constrained by the multi-point constraint
> #
>
> ##########################################################################################################
>
> proc rotLeaningCol {eleID nodeR nodeC} {
>
> #Spring Stiffness
> set K 1e-9; # k/in
>
> # Create the material and zero length element (spring)
> uniaxialMaterial Elastic $eleID $K
> element zeroLength $eleID $nodeR $nodeC -mat $eleID -dir 6
>
> # Constrain the translational DOF with a multi-point constraint
> # retained constrained DOF_1 DOF_2
> equalDOF $nodeR $nodeC 1 2
> }
>
>
>
>
>
>
> ############################################################################################
> # rotSect2DModIKModel.tcl
> #
> # This routine creates a section with elastic axial and bilinear flexural response
> #
> # Behavior follows: Bilinear Response based on Modified Ibarra Krawinkler
> Deterioration Model
> #
> # Written by: Dimitrios G. Lignos, Ph.D.
> #
> # Variables
> # $eleID = Element Identification (integer)
> # $E = Young's modulus
> # $A = Cross-sectional area
> # $K = Initial stiffness after the modification for n (see Ibarra and Krawinkler,
> 2005)
> # $asPos = Strain hardening ratio after n modification (see Ibarra and Krawinkler,
> 2005)
> # $asNeg = Strain hardening ratio after n modification (see Ibarra and Krawinkler,
> 2005)
> # $MyPos = Positive yield moment (with sign)
> # $MyNeg = Negative yield moment (with sign)
> # $LS = Basic strength deterioration parameter (see Lignos and Krawinkler, 2009)
> # $LK = Unloading stiffness deterioration parameter (see Lignos and Krawinkler,
> 2009)
> # $LA = Accelerated reloading stiffness deterioration parameter (see Lignos and
> Krawinkler, 2009)
> # $LD = Post-capping strength deterioration parameter (see Lignos and Krawinkler,
> 2009)
> # $cS = Exponent for basic strength deterioration
> # $cK = Exponent for unloading stiffness deterioration
> # $cA = Exponent for accelerated reloading stiffness deterioration
> # $cD = Exponent for post-capping strength deterioration
> # $th_pP = Plastic rotation capacity for positive loading direction
> # $th_pN = Plastic rotation capacity for negative loading direction
> # $th_pcP = Post-capping rotation capacity for positive loading direction
> # $th_pcN = Post-capping rotation capacity for negative loading direction
> # $ResP = Residual strength ratio for positive loading direction
> # $ResN = Residual strength ratio for negative loading direction
> # $th_uP = Ultimate rotation capacity for positive loading direction
> # $th_uN = Ultimate rotation capacity for negative loading direction
> # $DP = Rate of cyclic deterioration for positive loading direction
> # $DN = Rate of cyclic deterioration for negative loading direction
> #
> # References:
> # Ibarra, L. F., and Krawinkler, H. (2005). “Global collapse of frame structures
> under seismic excitations,” Technical Report 152, The John A. Blume Earthquake
> Engineering Research Center, Department of Civil Engineering, Stanford University,
> Stanford, CA.
> # Ibarra, L. F., Medina, R. A., and Krawinkler, H. (2005). “Hysteretic models that
> incorporate strength and stiffness deterioration,” International Journal for
> Earthquake Engineering and Structural Dynamics, Vol. 34, No.12, pp. 1489-1511.
> # Lignos, D. G., and Krawinkler, H. (2010). “Deterioration Modeling of Steel Beams
> and Columns in Support to Collapse Prediction of Steel Moment Frames”, ASCE, Journal
> of Structural Engineering (under review).
> # Lignos, D. G., and Krawinkler, H. (2009). “Sidesway Collapse of Deteriorating
> Structural Systems under Seismic Excitations,” Technical Report 172, The John A.
> Blume Earthquake Engineering Research Center, Department of Civil Engineering,
> Stanford University, Stanford, CA.
> #
>
> ############################################################################################
>
> proc rotSect2DModIKModel {eleID E A K asPos asNeg MyPos MyNeg LS LK LA LD cS cK cA cD
> th_pP th_pN th_pcP th_pcN ResP ResN th_uP th_uN DP DN} {
>
> # Create the material and section
> uniaxialMaterial Bilin $eleID $K $asPos $asNeg $MyPos $MyNeg $LS $LK $LA $LD $cS
> $cK $cA $cD $th_pP $th_pN $th_pcP $th_pcN $ResP $ResN $th_uP $th_uN $DP $DN;
> uniaxialMaterial Elastic [expr 10*$eleID + 1] [expr $E*$A]; # this is not used as a
> material, this is an axial-force-strain response
> section Aggregator $eleID [expr 10*$eleID + 1] P $eleID Mz; # combine axial and
> flexural behavior into one section (no P-M interaction here)
>
> }
>
>
>
>
> proc DisplayModel2D { {ShapeType nill} {dAmp 5} {xLoc 10} {yLoc 10} {xPixels 512}
> {yPixels 384} {nEigen 1} } {
>
> ######################################################################################
> ## DisplayModel2D $ShapeType $dAmp $xLoc $yLoc $xPixels $yPixels $nEigen
>
> ######################################################################################
> ## display Node Numbers, Deformed or Mode Shape in 2D problem
> ## Silvia Mazzoni & Frank McKenna, 2006
> ##
> ## ShapeType : type of shape to display. # options: ModeShape , NodeNumbers ,
> DeformedShape
> ## dAmp : relative amplification factor for deformations
> ## xLoc,yLoc : horizontal & vertical location in pixels of graphical window
> (0,0=upper left-most corner)
> ## xPixels,yPixels : width & height of graphical window in pixels
> ## nEigen : if nEigen not=0, show mode shape for nEigen eigenvalue
> ##
>
> #######################################################################################
> global TunitTXT; # load time-unit text
> global ScreenResolutionX ScreenResolutionY; # read global values for screen
> resolution
>
> if { [info exists TunitTXT] != 1} {set TunitTXT ""}; # set blank if it
> has not been defined previously.
>
> if { [info exists ScreenResolutionX] != 1} {set ScreenResolutionX 1024}; # set
> default if it has not been defined previously.
> if { [info exists ScreenResolutionY] != 1} {set ScreenResolutionY 768}; # set
> default if it has not been defined previously.
>
> if {$xPixels == 0} {
> set xPixels [expr int($ScreenResolutionX/2)];
> set yPixels [expr int($ScreenResolutionY/2)]
> set xLoc 10
> set yLoc 10
> }
> if {$ShapeType == "nill"} {
> puts ""; puts ""; puts "------------------"
> puts "View the Model? (N)odes, (D)eformedShape, anyMode(1),(2),(#). Press
> enter for NO."
> gets stdin answer
> if {[llength $answer]>0 } {
> if {$answer != "N" & $answer != "n"} {
> puts "Modify View Scaling Factor=$dAmp? Type factor, or press enter for
> NO."
> gets stdin answerdAmp
> if {[llength $answerdAmp]>0 } {
> set dAmp $answerdAmp
> }
> }
> if {[string index $answer 0] == "N" || [string index $answer 0] ==
> "n"} {
> set ShapeType NodeNumbers
> } elseif {[string index $answer 0] == "D" ||[string index $answer 0] ==
> "d" } {
> set ShapeType DeformedShape
> } else {
> set ShapeType ModeShape
> set nEigen $answer
> }
> } else {
> return
> }
> }
>
> if {$ShapeType == "ModeShape" } {
> set lambdaN [eigen $nEigen]; # perform eigenvalue analysis for ModeShape
> set lambda [lindex $lambdaN [expr $nEigen-1]];
> set omega [expr pow($lambda,0.5)]
> set PI [expr 2*asin(1.0)]; # define constant
> set Tperiod [expr 2*$PI/$omega]; # period (sec.)
> set fmt1 "Mode Shape, Mode=%.1i Period=%.3f %s "
> set windowTitle [format $fmt1 $nEigen $Tperiod $TunitTXT]
> } elseif {$ShapeType == "NodeNumbers" } {
> set windowTitle "Node Numbers"
> } elseif {$ShapeType == "DeformedShape" } {
> set windowTitle "Deformed Shape"
> }
>
> set viewPlane XY
> recorder display $windowTitle $xLoc $yLoc $xPixels $yPixels -wipe ; # display
> recorder
> DisplayPlane $ShapeType $dAmp $viewPlane $nEigen 0
> after 2000; #pause for 2 seconds to display
> }
>
>
>
>
> proc DisplayPlane {ShapeType dAmp viewPlane {nEigen 0} {quadrant 0}} {
>
> ######################################################################################
> ## DisplayPlane $ShapeType $dAmp $viewPlane $nEigen $quadrant
>
> ######################################################################################
> ## setup display parameters for specified viewPlane and display
> ## Silvia Mazzoni & Frank McKenna, 2006
> ##
> ## ShapeType : type of shape to display. # options: ModeShape , NodeNumbers ,
> DeformedShape
> ## dAmp : relative amplification factor for deformations
> ## viewPlane : set local xy axes in global coordinates (XY,YX,XZ,ZX,YZ,ZY)
> ## nEigen : if nEigen not=0, show mode shape for nEigen eigenvalue
> ## quadrant: quadrant where to show this figure (0=full figure)
> ##
>
> ######################################################################################
>
> set Xmin [lindex [nodeBounds] 0]; # view bounds in global coords - will add padding
> on the sides
> set Ymin [lindex [nodeBounds] 1];
> set Zmin [lindex [nodeBounds] 2];
> set Xmax [lindex [nodeBounds] 3];
> set Ymax [lindex [nodeBounds] 4];
> set Zmax [lindex [nodeBounds] 5];
>
> set Xo 0; # center of local viewing system
> set Yo 0;
> set Zo 0;
>
> set uLocal [string index $viewPlane 0]; # viewPlane local-x axis in global
> coordinates
> set vLocal [string index $viewPlane 1]; # viewPlane local-y axis in global
> coordinates
>
>
> if {$viewPlane =="3D" } {
> set uMin $Zmin+$Xmin
> set uMax $Zmax+$Xmax
> set vMin $Ymin
> set vMax $Ymax
> set wMin -10000
> set wMax 10000
> vup 0 1 0; # dirn defining up direction of view plane
> } else {
> set keyAxisMin "X $Xmin Y $Ymin Z $Zmin"
> set keyAxisMax "X $Xmax Y $Ymax Z $Zmax"
> set axisU [string index $viewPlane 0];
> set axisV [string index $viewPlane 1];
> set uMin [string map $keyAxisMin $axisU]
> set uMax [string map $keyAxisMax $axisU]
> set vMin [string map $keyAxisMin $axisV]
> set vMax [string map $keyAxisMax $axisV]
> if {$viewPlane =="YZ" || $viewPlane =="ZY" } {
> set wMin $Xmin
> set wMax $Xmax
> } elseif {$viewPlane =="XY" || $viewPlane =="YX" } {
> set wMin $Zmin
> set wMax $Zmax
> } elseif {$viewPlane =="XZ" || $viewPlane =="ZX" } {
> set wMin $Ymin
> set wMax $Ymax
> } else {
> return -1
> }
> }
>
> set epsilon 1e-3; # make windows width or height not zero when the Max and Min
> values of a coordinate are the same
>
> set uWide [expr $uMax - $uMin+$epsilon];
> set vWide [expr $vMax - $vMin+$epsilon];
> set uSide [expr 0.25*$uWide];
> set vSide [expr 0.25*$vWide];
> set uMin [expr $uMin - $uSide];
> set uMax [expr $uMax + $uSide];
> set vMin [expr $vMin - $vSide];
> set vMax [expr $vMax + 2*$vSide]; # pad a little more on top, because of window
> title
> set uWide [expr $uMax - $uMin+$epsilon];
> set vWide [expr $vMax - $vMin+$epsilon];
> set uMid [expr ($uMin+$uMax)/2];
> set vMid [expr ($vMin+$vMax)/2];
>
> # keep the following general, as change the X and Y and Z for each view plane
> # next three commmands define viewing system, all values in global coords
> vrp $Xo $Yo $Zo; # point on the view plane in global coord, center of local
> viewing system
> if {$vLocal == "X"} {
> vup 1 0 0; # dirn defining up direction of view plane
> } elseif {$vLocal == "Y"} {
> vup 0 1 0; # dirn defining up direction of view plane
> } elseif {$vLocal == "Z"} {
> vup 0 0 1; # dirn defining up direction of view plane
> }
> if {$viewPlane =="YZ" } {
> vpn 1 0 0; # direction of outward normal to view plane
> prp 10000. $uMid $vMid ; # eye location in local coord sys defined by viewing
> system
> plane 10000 -10000; # distance to front and back clipping planes from eye
> } elseif {$viewPlane =="ZY" } {
> vpn -1 0 0; # direction of outward normal to view plane
> prp -10000. $vMid $uMid ; # eye location in local coord sys defined by viewing
> system
> plane 10000 -10000; # distance to front and back clipping planes from eye
> } elseif {$viewPlane =="XY" } {
> vpn 0 0 1; # direction of outward normal to view plane
> prp $uMid $vMid 10000; # eye location in local coord sys defined by viewing system
> plane 10000 -10000; # distance to front and back clipping planes from eye
> } elseif {$viewPlane =="YX" } {
> vpn 0 0 -1; # direction of outward normal to view plane
> prp $uMid $vMid -10000; # eye location in local coord sys defined by viewing system
> plane 10000 -10000; # distance to front and back clipping planes from eye
> } elseif {$viewPlane =="XZ" } {
> vpn 0 -1 0; # direction of outward normal to view plane
> prp $uMid -10000 $vMid ; # eye location in local coord sys defined by viewing
> system
> plane 10000 -10000; # distance to front and back clipping planes from eye
> } elseif {$viewPlane =="ZX" } {
> vpn 0 1 0; # direction of outward normal to view plane
> prp $uMid 10000 $vMid ; # eye location in local coord sys defined by viewing system
> plane 10000 -10000; # distance to front and back clipping planes from eye
> } elseif {$viewPlane =="3D" } {
> vpn 1 0.25 1.25; # direction of outward normal to view plane
> prp -100 $vMid 10000; # eye location in local coord sys defined by viewing system
> plane 10000 -10000; # distance to front and back clipping planes from eye
> } else {
> return -1
> }
> # next three commands define view, all values in local coord system
> if {$viewPlane =="3D" } {
> viewWindow [expr $uMin-$uWide/4] [expr $uMax/2] [expr $vMin-0.25*$vWide] [expr
> $vMax]
> } else {
> viewWindow $uMin $uMax $vMin $vMax
> }
> projection 1; # projection mode, 0:prespective, 1: parallel
> fill 1; # fill mode; needed only for solid elements
>
> if {$quadrant == 0} {
> port -1 1 -1 1 # area of window that will be drawn into (uMin,uMax,vMin,vMax);
> } elseif {$quadrant == 1} {
> port 0 1 0 1 # area of window that will be drawn into (uMin,uMax,vMin,vMax);
> } elseif {$quadrant == 2} {
> port -1 0 0 1 # area of window that will be drawn into (uMin,uMax,vMin,vMax);
> } elseif {$quadrant == 3} {
> port -1 0 -1 0 # area of window that will be drawn into (uMin,uMax,vMin,vMax);
> } elseif {$quadrant == 4} {
> port 0 1 -1 0 # area of window that will be drawn into (uMin,uMax,vMin,vMax);
> }
>
> if {$ShapeType == "ModeShape" } {
> display -$nEigen 0 [expr 5.*$dAmp]; # display mode shape for mode $nEigen
> } elseif {$ShapeType == "NodeNumbers" } {
> display 1 -1 0 ; # display node numbers
> } elseif {$ShapeType == "DeformedShape" } {
> display 1 2 $dAmp; # display deformed shape the 2 makes the nodes small
> }
> };
> #
>
> ######################################################################################
hi , are you iranian like me? i have this problem too , can you solve it at last?

goase66 · Post by **goase66** » Sun Mar 13, 2011 10:11 pm

hi , are you iranian like me? i have this problem too , can you solve it at last?can any body help me?

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