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Dear Vesna,

I have tried to plot the base shear against the displacement but I am having some difficulties. I read in one of your post that I should plot the second column of Dfree.out and the Rbase.out but when I ran my file, my Rbase.out contains negative number, so I plotted without the negative number and compared it to a study done before on the same column but my results are slightly different. Please help me out. I need to understand why I have negative number? If my file contain errors that caused the results to be different? I will really appreciate any input.

Thank you

wipe
# This a texas standard single bent bridge for a 28' roadway.
# The Column is circular and the bent is square shape.
# In the Future we will set up a texas standard bridge with random node
# that can change at all times
#Units in kip/ft
# column.tcl
# No overlay load was considered in this model.
# This model is a 2D model

# SET UP ----------------------------------------------------------------------------
model basic -ndm 2 -ndf 3; # 2 spacial dimensions, 3 DOF's per nodey
set dataDir Data; # set up name for data directory
file mkdir $dataDir/; # create data directory
set GMdir "../GMfiles"; # ground-motion file directory
# -----------------------------------------------------
# --------------------------------------------------------------------------------------------------
# ------------- define system of units-----------------------------------------
#
# define UNITS ----------------------------------------------------------------------------
set in 1.; # define basic units -- output units
set kip 1.; # define basic units -- output units
set sec 1.; # define basic units -- output units
set LunitTXT "inch"; # define basic-unit text for output
set FunitTXT "kip"; # define basic-unit text for output
set TunitTXT "sec"; # define basic-unit text for output
set ft [expr 12.*$in]; # define engineering units
set ksi [expr $kip/pow($in,2)];
set psi [expr $ksi/1000.];
set lbf [expr $psi*$in*$in]; # pounds force
set pcf [expr $lbf/pow($ft,3)]; # pounds per cubic foot
set psf [expr $lbf/pow($ft,3)]; # pounds per square foot
set in2 [expr $in*$in]; # inch^2
set in4 [expr $in*$in*$in*$in]; # inch^4
set cm [expr $in/2.54]; # centimeter, needed for displacement input in MultipleSupport excitation
set PI [expr 2*asin(1.0)]; # define constants
#set g [expr 32.2*$ft/pow($sec,2)]; # gravitational acceleration
set g 386.4; # g.
set Ubig 1.e10; # a really large number

# Superstructure Weight+Rail+ Haunch; We neglected the bearing pad weight
# build important quantities from input paramters
set span [expr 120]; #forward and backward total span length
set triblength [expr $span/2]
set ngir 4; # the number of girder
set roadway 38; # roadway width
set girderw 0.851; # Standard Tx54 girder in ksi
set bentcap 3.5 ; #rectangular bent cap
set deckwidth 40; # width of the deck
set deck [expr 8.5/12] ; # Typical deck thickness in Texas
set trib [expr $deck*$triblength*$deckwidth]; # tributary area
set haunch 1.1; # factor for haunch dead load to be considered
set gamma 0.15; # the unit weight of concrete is in kcf)
set P1 [expr $haunch*$trib*$gamma]; # deck weight
set P2 [expr $ngir*$girderw*$triblength]; # girder weight kip/ft
set capweight [expr $bentcap*$bentcap*$roadway*$gamma]
set rwt [expr 2*0.382*$triblength]; # Standard T551 rail used in texas
#set P [expr $P1+$rwt+$P2+$capweight]; # superstructure weight

set P 800; # Load used by Choe and al.2008

# define section geometry
set Dcol [expr 5.5*$ft]; # Column Diameter
set LCol [expr 25*$ft]; # column length
set Weight [expr $P]
# calculated parameters
set Mass [expr $P/$g]; # nodal mass

# nodal coordinates:
node 1 0 0; # node#, X, Y
node 2 0 $LCol

# Single point constraints -- Boundary Conditions
fix 1 1 1 1; # node DX DY RZ

# nodal masses:
mass 2 $Mass 1e-9 0.;

# we need to set up parameters that are particular to the model.
set IDctrlNode 2; # node where displacement is read for displacement control
set IDctrlDOF 1; # degree of freedom of displacement read for displacement control
set iSupportNode "1"; # define support node, if needed.

# Define ELEMENTS & SECTIONS -------------------------------------------------------------
set ColSecTag 1; # assign a tag number to the column section

# Define Column geometry
set coverSec [expr 1.5*$in]; # Column cover to reinforcing steel NA.
set numBarsSec 40; # number of longitudinal-reinforcement bars in the column section
set barAreaSec [expr 1.56*$in*$in] ; # area of longitudinal-reinforcement bars #11
set fy [expr 65*$ksi]; # STEEL yield stress

# MATERIAL parameters -------------------------------------------------------------------
set IDconcC 1; # material ID tag -- confined core concrete
set IDconcU 2; # material ID tag -- unconfined cover concrete
set IDreinf 3; # material ID tag -- reinforcement

# nominal concrete compressive strength
set fc [expr 4.0*$ksi]; # CONCRETE Compressive Strength (+Tension, -Compression)
set E [expr (57*sqrt($fc*1000/$ksi))*$ksi]; # Concrete Elastic Modulus

# Define uniaxial materials

# Mander concrete model for confined and unconfined concrete
# requires rhos_trans = 4 Asp / (ds s)
# where Asp = cross sectional area of spiral reinforcement
# ds = center to center diameter inside spirals
# s = center to center spacing of spiral
set trans_bar 6.0
set As $barAreaSec
set rhos_trans 0.007
set pi [expr acos(-1.0)]
set epss 0.005
set eps0 0.002
set epsu 0.02
set f1 [expr 1.0/2.0*$rhos_trans*$fy]
set dcs [expr $Dcol-2.0*$coverSec-($trans_bar/8.0)]
set rho_cc [expr $As/($pi/4.0*pow($dcs,2))]
set spacing [expr $pi*pow($trans_bar/8.0,2)/$rhos_trans/$dcs]
set ke [expr (1.0-($spacing-$trans_bar/8.0)/2.0/$dcs)/(1.0-$rho_cc)]
set fcc [expr $fc*(-1.254+2.254*sqrt(1.0+7.94*$ke*$f1/$fc)-2.0*$ke*$f1/$fc)]
if { $fcc > 2.23*$fc } {
set fcc [expr 2.23*$fc]
}
set epsc [expr $eps0*(1.0+5.0*($fcc/$fc-1.0))]
set ecr [expr $E/($E-$fcc/$epsc)]
set fcu [expr $fcc*$epsu/$epsc*$ecr/($ecr-1.0+pow($epsu/$epsc,$ecr))]

# Cover concrete
# tag -f'c -epsco -f'cu -epscu
uniaxialMaterial Concrete01 1 -$fc -$eps0 0.0 -$epss
# Core concrete
uniaxialMaterial Concrete01 2 -$fcc -$epsc -$fcu -$epsu


# ----------- Reinforcing Steel --------
set Es [expr 29000.*$ksi]; # modulus of steel
set Esh [expr 2000.0*$ksi]; # Initial Hardening Modulus (estimated)
set Bs 0.01; # strain-hardening ratio
set R0 18; # control the transition from elastic to plastic branches
set cR1 0.925; # control the transition from elastic to plastic branches
set cR2 0.15; # control the transition from elastic to plastic branches

uniaxialMaterial Steel02 $IDreinf $fy $Es $Bs $R0 $cR1 $cR2;

# Generate a circular reinforced concrete section
# with one layer of steel evenly distributed around the perimeter and a confined core.
# confined core.
# by: Michael H. Scott, 2003
#
#
# Notes
# The center of the reinforcing bars are placed at the inner radius
# The core concrete ends at the inner radius (same as reinforcing bars)
# The reinforcing bars are all the same size
# The center of the section is at (0,0) in the local axis system
# Zero degrees is along section y-axis
#
set ri 0.0; # inner radius of the section, only for hollow sections
set ro [expr $Dcol/2]; # overall (outer) radius of the section
set nfCoreR 96; # number of radial divisions in the core (number of "rings")
set nfCoreT 36; # number of theta divisions in the core (number of "wedges")
set nfCoverR 24; # number of radial divisions in the cover
set nfCoverT 36; # number of theta divisions in the cover


# Define the fiber section
section fiberSec $ColSecTag {
set rc [expr $ro-$coverSec]; # Core radius
patch circ $IDconcC $nfCoreT $nfCoreR 0 0 $ri $rc 0 360; # Define the core patch
patch circ $IDconcU $nfCoverT $nfCoverR 0 0 $rc $ro 0 360; # Define the cover patch
set theta [expr 360.0/$numBarsSec]; # Determine angle increment between bars
layer circ $IDreinf $numBarsSec $barAreaSec 0 0 $rc $theta 360; # Define the reinforcing layer
}


# define geometric transformation: performs a linear geometric transformation of beam stiffness and resisting force from the basic system to the global-coordinate system
set ColTransfTag 1; # associate a tag to column transformation
set ColTransfType Linear ; # options, Linear PDelta Corotational
geomTransf $ColTransfType $ColTransfTag ;

#Remember for Linear PDelta
# element connectivity:
set numIntgrPts 5; # number of integration points for force-based element
element nonlinearBeamColumn 1 1 2 $numIntgrPts $ColSecTag $ColTransfTag; # self-explanatory when using variables

# Column- Pile element connectivity:

# Create recorder
recorder Node -file $dataDir/DFree.out -time -node 2 -dof 1 2 3 disp; # displacements of free nodes
recorder Node -file $dataDir/DBase.out -time -node 1 -dof 1 2 3 disp; # displacements of support nodes
recorder Node -file $dataDir/RBase.out -time -node 1 -dof 1 2 3 reaction; # support reaction
recorder Drift -file $dataDir/Drift.out -time -iNode 1 -jNode 2 -dof 1 -perpDirn 2 ; # lateral drift
recorder Element -file $dataDir/FCol.out -time -ele 2 globalForce; # element forces -- column
recorder Element -file $dataDir/ForceColSec1.out -time -ele 1 section 1 force; # Column section forces, axial and moment, node i
recorder Element -file $dataDir/DefoColSec1.out -time -ele 1 section 1 deformation; # section deformations, axial and curvature, node i
recorder Element -file $dataDir/ForceColSec$numIntgrPts.out -time -ele 1 section $numIntgrPts force; # section forces, axial and moment, node j
recorder Element -file $dataDir/DefoColSec$numIntgrPts.out -time -ele 1 section 1 deformation; # section deformations, axial and curvature, node j
recorder Element -xml $dataDir/PlasticRotation.out -time -ele 1 plasticRotation; # section deformations, axial and curvature, node j

# define GRAVITY -------------------------------------------------------------
pattern Plain 1 Linear {
load 2 0 -$P 0
}

# Gravity-analysis parameters -- load-controlled static analysis
set Tol 1.0e-8; # convergence tolerance for test
constraints Plain; # how it handles boundary conditions
numberer Plain; # renumber dof's to minimize band-width (optimization), if you want to
system BandGeneral; # how to store and solve the system of equations in the analysis
test NormDispIncr $Tol 6 ; # determine if convergence has been achieved at the end of an iteration step
algorithm Newton; # use Newton's solution algorithm: updates tangent stiffness at every iteration
set NstepGravity 1; # apply gravity in 10 steps
set DGravity [expr 1./$NstepGravity]; # first 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

print -node 2

puts "Model Built"

# --------------------------------------------------------------------------------------------------
# Example 3. 2D Cantilever -- Static Pushover
# Silvia Mazzoni & Frank McKenna, 2006
# execute this file after you have built the model, and after you apply gravity
#

#source coltest.tcl;


# characteristics of pushover analysis
set Dmax [expr 0.05*$LCol]; # maximum displacement of pushover. push to 10% drift.
set Dincr [expr 0.001*$LCol]; # displacement increment for pushover. you want this to be very small, but not too small to slow down the analysis

# create load pattern for lateral pushover load
set Hload [expr $Weight]; # define the lateral load as a proportion of the weight so that the pseudo time equals the lateral-load coefficient when using linear load pattern
pattern Plain 200 Linear {; # define load pattern -- generalized
load 2 $Hload 0.0 0.0
}

# STATIC-ANALYSIS parameters
# CONSTRAINTS handler -- Determines how the constraint equations are enforced in the analysis (http://opensees.berkeley.edu/OpenSees/m ... al/617.htm)
# Plain Constraints -- Removes constrained degrees of freedom from the system of equations (only for homogeneous equations)
# Lagrange Multipliers -- Uses the method of Lagrange multipliers to enforce constraints
# Penalty Method -- Uses penalty numbers to enforce constraints --good for static analysis with non-homogeneous eqns (rigidDiaphragm)
# Transformation Method -- Performs a condensation of constrained degrees of freedom
set constraintsType Plain; # default;
constraints $constraintsType

# DOF NUMBERER (number the degrees of freedom in the domain): (http://opensees.berkeley.edu/OpenSees/m ... al/366.htm)
# determines the mapping between equation numbers and degrees-of-freedom
# Plain -- Uses the numbering provided by the user
# RCM -- Renumbers the DOF to minimize the matrix band-width using the Reverse Cuthill-McKee algorithm
numberer Plain

# SYSTEM (http://opensees.berkeley.edu/OpenSees/m ... al/371.htm)
# Linear Equation Solvers (how to store and solve the system of equations in the analysis)
# -- provide the solution of the linear system of equations Ku = P. Each solver is tailored to a specific matrix topology.
# ProfileSPD -- Direct profile solver for symmetric positive definite matrices
# BandGeneral -- Direct solver for banded unsymmetric matrices
# BandSPD -- Direct solver for banded symmetric positive definite matrices
# SparseGeneral -- Direct solver for unsymmetric sparse matrices
# SparseSPD -- Direct solver for symmetric sparse matrices
# UmfPack -- Direct UmfPack solver for unsymmetric matrices
system BandGeneral

# TEST: # convergence test to
# Convergence TEST (http://opensees.berkeley.edu/OpenSees/m ... al/360.htm)
# -- Accept the current state of the domain as being on the converged solution path
# -- determine if convergence has been achieved at the end of an iteration step
# NormUnbalance -- Specifies a tolerance on the norm of the unbalanced load at the current iteration
# NormDispIncr -- Specifies a tolerance on the norm of the displacement increments at the current iteration
# EnergyIncr-- Specifies a tolerance on the inner product of the unbalanced load and displacement increments at the current iteration
set Tol 1.e-8; # Convergence Test: tolerance
set maxNumIter 6; # Convergence Test: maximum number of iterations that will be performed before "failure to converge" is returned
set printFlag 0; # Convergence Test: flag used to print information on convergence (optional) # 1: print information on each step;
set TestType EnergyIncr; # Convergence-test type
test $TestType $Tol $maxNumIter $printFlag;

# Solution ALGORITHM: -- Iterate from the last time step to the current (http://opensees.berkeley.edu/OpenSees/m ... al/682.htm)
# Linear -- Uses the solution at the first iteration and continues
# Newton -- Uses the tangent at the current iteration to iterate to convergence
# ModifiedNewton -- Uses the tangent at the first iteration to iterate to convergence
set algorithmType Newton
algorithm $algorithmType;

# Static INTEGRATOR: -- determine the next time step for an analysis (http://opensees.berkeley.edu/OpenSees/m ... al/689.htm)
# LoadControl -- Specifies the incremental load factor to be applied to the loads in the domain
# DisplacementControl -- Specifies the incremental displacement at a specified DOF in the domain
# Minimum Unbalanced Displacement Norm -- Specifies the incremental load factor such that the residual displacement norm in minimized
# Arc Length -- Specifies the incremental arc-length of the load-displacement path
# Transient INTEGRATOR: -- determine the next time step for an analysis including inertial effects
# Newmark -- The two parameter time-stepping method developed by Newmark
# HHT -- The three parameter Hilbert-Hughes-Taylor time-stepping method
# Central Difference -- Approximates velocity and acceleration by centered finite differences of displacement
integrator DisplacementControl $IDctrlNode $IDctrlDOF $Dincr

# ANALYSIS -- defines what type of analysis is to be performed (http://opensees.berkeley.edu/OpenSees/m ... al/324.htm)
# Static Analysis -- solves the KU=R problem, without the mass or damping matrices.
# Transient Analysis -- solves the time-dependent analysis. The time step in this type of analysis is constant. The time step in the output is also constant.
# variableTransient Analysis -- performs the same analysis type as the Transient Analysis object. The time step, however, is variable. This method is used when
# there are convergence problems with the Transient Analysis object at a peak or when the time step is too small. The time step in the output is also variable.
analysis Static


# --------------------------------- perform Static Pushover Analysis
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

if {$ok != 0} {
# if analysis fails, we try some other stuff, performance is slower inside this loop
set ok 0;
set controlDisp 0.0;
set D0 0.0; # analysis starts from zero
set Dstep [expr ($controlDisp-$D0)/($Dmax-$D0)]
while {$Dstep < 1.0 && $ok == 0} {
set controlDisp [nodeDisp $IDctrlNode $IDctrlDOF ]
set Dstep [expr ($controlDisp-$D0)/($Dmax-$D0)]
set ok [analyze 1 ]
if {$ok != 0} {
puts "Trying Newton with Initial Tangent .."
test NormDispIncr $Tol 2000 0
algorithm Newton -initial
set ok [analyze 1 ]
test $TestType $Tol $maxNumIter 0
algorithm $algorithmType
}
if {$ok != 0} {
puts "Trying Broyden .."
algorithm Broyden 8
set ok [analyze 1 ]
algorithm $algorithmType
}
if {$ok != 0} {
puts "Trying NewtonWithLineSearch .."
algorithm NewtonLineSearch .8
set ok [analyze 1 ]
algorithm $algorithmType
}
}; # end while loop
}; # end if ok !0

puts "Pushover Done. Control Disp=[nodeDisp $IDctrlNode $IDctrlDOF]"

recorder display "Column" 10 10 600 600 -wipe
vup 0 1 0
prp 0 0 200
display 1 0 50
print -node 2

Dear Vesna,

I have tried to plot the base shear against the displacement but I am having some difficulties. I read in one of your post that I should plot the second column of Dfree.out and the Rbase.out but when I ran my file, my Rbase.out contains negative number, so I plotted without the negative number and compared it to a study done before on the same column but my results are slightly different. Please help me out. I need to understand why I have negative number? If my file contain errors that caused the results to be different? I will really appreciate any input.

Thank you

wipe
# This a texas standard single bent bridge for a 28' roadway.
# The Column is circular and the bent is square shape.
# In the Future we will set up a texas standard bridge with random node
# that can change at all times
#Units in kip/ft
# column.tcl
# No overlay load was considered in this model.
# This model is a 2D model

# SET UP ----------------------------------------------------------------------------
model basic -ndm 2 -ndf 3; # 2 spacial dimensions, 3 DOF's per nodey
set dataDir Data; # set up name for data directory
file mkdir $dataDir/; # create data directory
set GMdir "../GMfiles"; # ground-motion file directory
# -----------------------------------------------------
# --------------------------------------------------------------------------------------------------
# ------------- define system of units-----------------------------------------
#
# define UNITS ----------------------------------------------------------------------------
set in 1.; # define basic units -- output units
set kip 1.; # define basic units -- output units
set sec 1.; # define basic units -- output units
set LunitTXT "inch"; # define basic-unit text for output
set FunitTXT "kip"; # define basic-unit text for output
set TunitTXT "sec"; # define basic-unit text for output
set ft [expr 12.*$in]; # define engineering units
set ksi [expr $kip/pow($in,2)];
set psi [expr $ksi/1000.];
set lbf [expr $psi*$in*$in]; # pounds force
set pcf [expr $lbf/pow($ft,3)]; # pounds per cubic foot
set psf [expr $lbf/pow($ft,3)]; # pounds per square foot
set in2 [expr $in*$in]; # inch^2
set in4 [expr $in*$in*$in*$in]; # inch^4
set cm [expr $in/2.54]; # centimeter, needed for displacement input in MultipleSupport excitation
set PI [expr 2*asin(1.0)]; # define constants
#set g [expr 32.2*$ft/pow($sec,2)]; # gravitational acceleration
set g 386.4; # g.
set Ubig 1.e10; # a really large number

# Superstructure Weight+Rail+ Haunch; We neglected the bearing pad weight
# build important quantities from input paramters
set span [expr 120]; #forward and backward total span length
set triblength [expr $span/2]
set ngir 4; # the number of girder
set roadway 38; # roadway width
set girderw 0.851; # Standard Tx54 girder in ksi
set bentcap 3.5 ; #rectangular bent cap
set deckwidth 40; # width of the deck
set deck [expr 8.5/12] ; # Typical deck thickness in Texas
set trib [expr $deck*$triblength*$deckwidth]; # tributary area
set haunch 1.1; # factor for haunch dead load to be considered
set gamma 0.15; # the unit weight of concrete is in kcf)
set P1 [expr $haunch*$trib*$gamma]; # deck weight
set P2 [expr $ngir*$girderw*$triblength]; # girder weight kip/ft
set capweight [expr $bentcap*$bentcap*$roadway*$gamma]
set rwt [expr 2*0.382*$triblength]; # Standard T551 rail used in texas
#set P [expr $P1+$rwt+$P2+$capweight]; # superstructure weight

set P 800; # Load used by Choe and al.2008

# define section geometry
set Dcol [expr 5.5*$ft]; # Column Diameter
set LCol [expr 25*$ft]; # column length
set Weight [expr $P]
# calculated parameters
set Mass [expr $P/$g]; # nodal mass

# nodal coordinates:
node 1 0 0; # node#, X, Y
node 2 0 $LCol

# Single point constraints -- Boundary Conditions
fix 1 1 1 1; # node DX DY RZ

# nodal masses:
mass 2 $Mass 1e-9 0.;

# we need to set up parameters that are particular to the model.
set IDctrlNode 2; # node where displacement is read for displacement control
set IDctrlDOF 1; # degree of freedom of displacement read for displacement control
set iSupportNode "1"; # define support node, if needed.

# Define ELEMENTS & SECTIONS -------------------------------------------------------------
set ColSecTag 1; # assign a tag number to the column section

# Define Column geometry
set coverSec [expr 1.5*$in]; # Column cover to reinforcing steel NA.
set numBarsSec 40; # number of longitudinal-reinforcement bars in the column section
set barAreaSec [expr 1.56*$in*$in] ; # area of longitudinal-reinforcement bars #11
set fy [expr 65*$ksi]; # STEEL yield stress

# MATERIAL parameters -------------------------------------------------------------------
set IDconcC 1; # material ID tag -- confined core concrete
set IDconcU 2; # material ID tag -- unconfined cover concrete
set IDreinf 3; # material ID tag -- reinforcement

# nominal concrete compressive strength
set fc [expr 4.0*$ksi]; # CONCRETE Compressive Strength (+Tension, -Compression)
set E [expr (57*sqrt($fc*1000/$ksi))*$ksi]; # Concrete Elastic Modulus

# Define uniaxial materials

# Mander concrete model for confined and unconfined concrete
# requires rhos_trans = 4 Asp / (ds s)
# where Asp = cross sectional area of spiral reinforcement
# ds = center to center diameter inside spirals
# s = center to center spacing of spiral
set trans_bar 6.0
set As $barAreaSec
set rhos_trans 0.007
set pi [expr acos(-1.0)]
set epss 0.005
set eps0 0.002
set epsu 0.02
set f1 [expr 1.0/2.0*$rhos_trans*$fy]
set dcs [expr $Dcol-2.0*$coverSec-($trans_bar/8.0)]
set rho_cc [expr $As/($pi/4.0*pow($dcs,2))]
set spacing [expr $pi*pow($trans_bar/8.0,2)/$rhos_trans/$dcs]
set ke [expr (1.0-($spacing-$trans_bar/8.0)/2.0/$dcs)/(1.0-$rho_cc)]
set fcc [expr $fc*(-1.254+2.254*sqrt(1.0+7.94*$ke*$f1/$fc)-2.0*$ke*$f1/$fc)]
if { $fcc > 2.23*$fc } {
set fcc [expr 2.23*$fc]
}
set epsc [expr $eps0*(1.0+5.0*($fcc/$fc-1.0))]
set ecr [expr $E/($E-$fcc/$epsc)]
set fcu [expr $fcc*$epsu/$epsc*$ecr/($ecr-1.0+pow($epsu/$epsc,$ecr))]

# Cover concrete
# tag -f'c -epsco -f'cu -epscu
uniaxialMaterial Concrete01 1 -$fc -$eps0 0.0 -$epss
# Core concrete
uniaxialMaterial Concrete01 2 -$fcc -$epsc -$fcu -$epsu


# ----------- Reinforcing Steel --------
set Es [expr 29000.*$ksi]; # modulus of steel
set Esh [expr 2000.0*$ksi]; # Initial Hardening Modulus (estimated)
set Bs 0.01; # strain-hardening ratio
set R0 18; # control the transition from elastic to plastic branches
set cR1 0.925; # control the transition from elastic to plastic branches
set cR2 0.15; # control the transition from elastic to plastic branches

uniaxialMaterial Steel02 $IDreinf $fy $Es $Bs $R0 $cR1 $cR2;

# Generate a circular reinforced concrete section
# with one layer of steel evenly distributed around the perimeter and a confined core.
# confined core.
# by: Michael H. Scott, 2003
#
#
# Notes
# The center of the reinforcing bars are placed at the inner radius
# The core concrete ends at the inner radius (same as reinforcing bars)
# The reinforcing bars are all the same size
# The center of the section is at (0,0) in the local axis system
# Zero degrees is along section y-axis
#
set ri 0.0; # inner radius of the section, only for hollow sections
set ro [expr $Dcol/2]; # overall (outer) radius of the section
set nfCoreR 96; # number of radial divisions in the core (number of "rings")
set nfCoreT 36; # number of theta divisions in the core (number of "wedges")
set nfCoverR 24; # number of radial divisions in the cover
set nfCoverT 36; # number of theta divisions in the cover


# Define the fiber section
section fiberSec $ColSecTag {
set rc [expr $ro-$coverSec]; # Core radius
patch circ $IDconcC $nfCoreT $nfCoreR 0 0 $ri $rc 0 360; # Define the core patch
patch circ $IDconcU $nfCoverT $nfCoverR 0 0 $rc $ro 0 360; # Define the cover patch
set theta [expr 360.0/$numBarsSec]; # Determine angle increment between bars
layer circ $IDreinf $numBarsSec $barAreaSec 0 0 $rc $theta 360; # Define the reinforcing layer
}


# define geometric transformation: performs a linear geometric transformation of beam stiffness and resisting force from the basic system to the global-coordinate system
set ColTransfTag 1; # associate a tag to column transformation
set ColTransfType Linear ; # options, Linear PDelta Corotational
geomTransf $ColTransfType $ColTransfTag ;

#Remember for Linear PDelta
# element connectivity:
set numIntgrPts 5; # number of integration points for force-based element
element nonlinearBeamColumn 1 1 2 $numIntgrPts $ColSecTag $ColTransfTag; # self-explanatory when using variables

# Column- Pile element connectivity:

# Create recorder
recorder Node -file $dataDir/DFree.out -time -node 2 -dof 1 2 3 disp; # displacements of free nodes
recorder Node -file $dataDir/DBase.out -time -node 1 -dof 1 2 3 disp; # displacements of support nodes
recorder Node -file $dataDir/RBase.out -time -node 1 -dof 1 2 3 reaction; # support reaction
recorder Drift -file $dataDir/Drift.out -time -iNode 1 -jNode 2 -dof 1 -perpDirn 2 ; # lateral drift
recorder Element -file $dataDir/FCol.out -time -ele 2 globalForce; # element forces -- column
recorder Element -file $dataDir/ForceColSec1.out -time -ele 1 section 1 force; # Column section forces, axial and moment, node i
recorder Element -file $dataDir/DefoColSec1.out -time -ele 1 section 1 deformation; # section deformations, axial and curvature, node i
recorder Element -file $dataDir/ForceColSec$numIntgrPts.out -time -ele 1 section $numIntgrPts force; # section forces, axial and moment, node j
recorder Element -file $dataDir/DefoColSec$numIntgrPts.out -time -ele 1 section 1 deformation; # section deformations, axial and curvature, node j
recorder Element -xml $dataDir/PlasticRotation.out -time -ele 1 plasticRotation; # section deformations, axial and curvature, node j

# define GRAVITY -------------------------------------------------------------
pattern Plain 1 Linear {
load 2 0 -$P 0
}

# Gravity-analysis parameters -- load-controlled static analysis
set Tol 1.0e-8; # convergence tolerance for test
constraints Plain; # how it handles boundary conditions
numberer Plain; # renumber dof's to minimize band-width (optimization), if you want to
system BandGeneral; # how to store and solve the system of equations in the analysis
test NormDispIncr $Tol 6 ; # determine if convergence has been achieved at the end of an iteration step
algorithm Newton; # use Newton's solution algorithm: updates tangent stiffness at every iteration
set NstepGravity 1; # apply gravity in 10 steps
set DGravity [expr 1./$NstepGravity]; # first 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

print -node 2

puts "Model Built"

# --------------------------------------------------------------------------------------------------
# Example 3. 2D Cantilever -- Static Pushover
# Silvia Mazzoni & Frank McKenna, 2006
# execute this file after you have built the model, and after you apply gravity
#

#source coltest.tcl;


# characteristics of pushover analysis
set Dmax [expr 0.05*$LCol]; # maximum displacement of pushover. push to 10% drift.
set Dincr [expr 0.001*$LCol]; # displacement increment for pushover. you want this to be very small, but not too small to slow down the analysis

# create load pattern for lateral pushover load
set Hload [expr $Weight]; # define the lateral load as a proportion of the weight so that the pseudo time equals the lateral-load coefficient when using linear load pattern
pattern Plain 200 Linear {; # define load pattern -- generalized
load 2 $Hload 0.0 0.0
}

# STATIC-ANALYSIS parameters
# CONSTRAINTS handler -- Determines how the constraint equations are enforced in the analysis (http://opensees.berkeley.edu/OpenSees/m ... al/617.htm)
# Plain Constraints -- Removes constrained degrees of freedom from the system of equations (only for homogeneous equations)
# Lagrange Multipliers -- Uses the method of Lagrange multipliers to enforce constraints
# Penalty Method -- Uses penalty numbers to enforce constraints --good for static analysis with non-homogeneous eqns (rigidDiaphragm)
# Transformation Method -- Performs a condensation of constrained degrees of freedom
set constraintsType Plain; # default;
constraints $constraintsType

# DOF NUMBERER (number the degrees of freedom in the domain): (http://opensees.berkeley.edu/OpenSees/m ... al/366.htm)
# determines the mapping between equation numbers and degrees-of-freedom
# Plain -- Uses the numbering provided by the user
# RCM -- Renumbers the DOF to minimize the matrix band-width using the Reverse Cuthill-McKee algorithm
numberer Plain

# SYSTEM (http://opensees.berkeley.edu/OpenSees/m ... al/371.htm)
# Linear Equation Solvers (how to store and solve the system of equations in the analysis)
# -- provide the solution of the linear system of equations Ku = P. Each solver is tailored to a specific matrix topology.
# ProfileSPD -- Direct profile solver for symmetric positive definite matrices
# BandGeneral -- Direct solver for banded unsymmetric matrices
# BandSPD -- Direct solver for banded symmetric positive definite matrices
# SparseGeneral -- Direct solver for unsymmetric sparse matrices
# SparseSPD -- Direct solver for symmetric sparse matrices
# UmfPack -- Direct UmfPack solver for unsymmetric matrices
system BandGeneral

# TEST: # convergence test to
# Convergence TEST (http://opensees.berkeley.edu/OpenSees/m ... al/360.htm)
# -- Accept the current state of the domain as being on the converged solution path
# -- determine if convergence has been achieved at the end of an iteration step
# NormUnbalance -- Specifies a tolerance on the norm of the unbalanced load at the current iteration
# NormDispIncr -- Specifies a tolerance on the norm of the displacement increments at the current iteration
# EnergyIncr-- Specifies a tolerance on the inner product of the unbalanced load and displacement increments at the current iteration
set Tol 1.e-8; # Convergence Test: tolerance
set maxNumIter 6; # Convergence Test: maximum number of iterations that will be performed before "failure to converge" is returned
set printFlag 0; # Convergence Test: flag used to print information on convergence (optional) # 1: print information on each step;
set TestType EnergyIncr; # Convergence-test type
test $TestType $Tol $maxNumIter $printFlag;

# Solution ALGORITHM: -- Iterate from the last time step to the current (http://opensees.berkeley.edu/OpenSees/m ... al/682.htm)
# Linear -- Uses the solution at the first iteration and continues
# Newton -- Uses the tangent at the current iteration to iterate to convergence
# ModifiedNewton -- Uses the tangent at the first iteration to iterate to convergence
set algorithmType Newton
algorithm $algorithmType;

# Static INTEGRATOR: -- determine the next time step for an analysis (http://opensees.berkeley.edu/OpenSees/m ... al/689.htm)
# LoadControl -- Specifies the incremental load factor to be applied to the loads in the domain
# DisplacementControl -- Specifies the incremental displacement at a specified DOF in the domain
# Minimum Unbalanced Displacement Norm -- Specifies the incremental load factor such that the residual displacement norm in minimized
# Arc Length -- Specifies the incremental arc-length of the load-displacement path
# Transient INTEGRATOR: -- determine the next time step for an analysis including inertial effects
# Newmark -- The two parameter time-stepping method developed by Newmark
# HHT -- The three parameter Hilbert-Hughes-Taylor time-stepping method
# Central Difference -- Approximates velocity and acceleration by centered finite differences of displacement
integrator DisplacementControl $IDctrlNode $IDctrlDOF $Dincr

# ANALYSIS -- defines what type of analysis is to be performed (http://opensees.berkeley.edu/OpenSees/m ... al/324.htm)
# Static Analysis -- solves the KU=R problem, without the mass or damping matrices.
# Transient Analysis -- solves the time-dependent analysis. The time step in this type of analysis is constant. The time step in the output is also constant.
# variableTransient Analysis -- performs the same analysis type as the Transient Analysis object. The time step, however, is variable. This method is used when
# there are convergence problems with the Transient Analysis object at a peak or when the time step is too small. The time step in the output is also variable.
analysis Static


# --------------------------------- perform Static Pushover Analysis
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

if {$ok != 0} {
# if analysis fails, we try some other stuff, performance is slower inside this loop
set ok 0;
set controlDisp 0.0;
set D0 0.0; # analysis starts from zero
set Dstep [expr ($controlDisp-$D0)/($Dmax-$D0)]
while {$Dstep < 1.0 && $ok == 0} {
set controlDisp [nodeDisp $IDctrlNode $IDctrlDOF ]
set Dstep [expr ($controlDisp-$D0)/($Dmax-$D0)]
set ok [analyze 1 ]
if {$ok != 0} {
puts "Trying Newton with Initial Tangent .."
test NormDispIncr $Tol 2000 0
algorithm Newton -initial
set ok [analyze 1 ]
test $TestType $Tol $maxNumIter 0
algorithm $algorithmType
}
if {$ok != 0} {
puts "Trying Broyden .."
algorithm Broyden 8
set ok [analyze 1 ]
algorithm $algorithmType
}
if {$ok != 0} {
puts "Trying NewtonWithLineSearch .."
algorithm NewtonLineSearch .8
set ok [analyze 1 ]
algorithm $algorithmType
}
}; # end while loop
}; # end if ok !0

puts "Pushover Done. Control Disp=[nodeDisp $IDctrlNode $IDctrlDOF]"

recorder display "Column" 10 10 600 600 -wipe
vup 0 1 0
prp 0 0 200
display 1 0 50
print -node 2

Hello

I am new to opensees. I am trying to change the spring stiffness inside the source code to using Wringler spring stiffness equation.
I would really appreciate any help.

Thank you