Hi all,
I am modelling a nonlinear RC cantilever shear wall using fiber section and implementing section aggregator in order to include flexure-shear interaction. When I don't define shear behaviour I get a reasonable natural period T=0.034. But the problem is, when I include shear behaviour I get it extremely high, T=3.40. (Almost 100 times the other which is strange.) I was wondering if the way I couple shear and flexural behaviour is insufficient or is there anything wrong with my model or commands?
Do you have any idea or suggestions? Here is my code which I manipulated from examples:
# define GEOMETRY -------------------------------------------------------------
set LCol [expr 13*$ft]; # column length
set Weight [expr 1170.*$kip];
# define section geometry
set HCol [expr 312.*$in]; # Column Depth
set BCol [expr 10.*$in]; # Column Width
# calculated parameters
set PCol [expr $Weight]; # nodal dead-load weight per column
set Mass [expr $PCol/$g]; # nodal mass
# calculated geometry parameters
set ACol [expr $BCol*$HCol]; # cross-sectional area
set IzCol [expr 1./12.*$BCol*pow($HCol,3)]; # Column moment of inertia
# 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
# 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.
# nodal masses:
mass 2 $Mass 1e-9 0.; # node#, Mx My Mz, Mass=Weight/g, neglect rotational inertia at nodes
# Define ELEMENTS & SECTIONS -------------------------------------------------------------
set ColSecTag 1; # assign a tag number to the column section
# define section geometry
set coverCol [expr 1.75*$in]; # Column cover to reinforcing steel NA.
set numBarsCol 80; # number of longitudinal-reinforcement bars in column. (symmetric top & bot)
set barAreaCol [expr 0.44*$in2]; # area of longitudinal-reinforcement bars
# MATERIAL parameters -------------------------------------------------------------------
set IDconcU 1; # material ID tag -- unconfined cover concrete
set IDreinf 2; # material ID tag -- reinforcement
# nominal concrete compressive strength
set fc [expr -5.0*$ksi];
set Ec [expr 57*$ksi*sqrt(-$fc/$psi)];
# unconfined concrete
set fc1U $fc; # UNCONFINED concrete (todeschini parabolic model), maximum stress
set eps1U -0.003; # strain at maximum strength of unconfined concrete
set fc2U [expr 0.2*$fc1U]; # ultimate stress
set eps2U -0.01; # strain at ultimate stress
set lambda 0.1; # ratio between unloading slope at $eps2 and initial slope $Ec
# tensile-strength properties
set ftU [expr -0.14*$fc1U]; # tensile strength +tension
set Ets [expr $ftU/0.002]; # tension softening stiffness
# -----------
set Fy [expr 60*$ksi]; # STEEL yield stress
set Es [expr 29000.*$ksi]; # modulus of steel
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 Concrete02 $IDconcU $fc1U $eps1U $fc2U $eps2U $lambda $ftU $Ets; # build cover concrete (unconfined)
uniaxialMaterial Steel02 $IDreinf $Fy $Es $Bs $R0 $cR1 $cR2; # build reinforcement material
# FIBER SECTION properties -------------------------------------------------------------
# symmetric section
# RC section:
set coverY [expr $HCol/2.0]; # The distance from the section z-axis to the edge of the cover concrete -- outer edge of cover concrete
set coverZ [expr $BCol/2.0]; # The distance from the section y-axis to the edge of the cover concrete -- outer edge of cover concrete
set coreY [expr $coverY-$coverCol]
set coreZ [expr $coverZ-$coverCol]
set nfY 16; # number of fibers for concrete in y-direction
set nfZ 4; # number of fibers for concrete in z-direction
section Fiber $ColSecTag {; # Define the fiber section
patch quad $IDconcU $nfZ $nfY -$coverY $coverZ -$coverY -$coverZ $coverY -$coverZ $coverY $coverZ; # Define the concrete patch
layer straight $IDreinf $numBarsCol $barAreaCol -$coreY $coreZ -$coreY -$coreZ; # top layer reinfocement
layer straight $IDreinf $numBarsCol $barAreaCol $coreY $coreZ $coreY -$coreZ; # bottom layer reinforcement
}; # end of fibersection definition
#SHEAR BEHAVIOR
set Vyield 2700;
set Gc [expr 0.4*$Ec];
uniaxialMaterial Steel01 3 $Vyield $Gc 0.1;
section Aggregator 4 3 Vy -section $ColSecTag;
# define geometric transformation:
set ColTransfTag 1; # associate a tag to column transformation
set ColTransfType Linear ; # options, Linear PDelta Corotational
geomTransf $ColTransfType $ColTransfTag ;
# element connectivity:
set numIntgrPts 10; # number of integration points for force-based element
#element nonlinearBeamColumn 1 1 2 $numIntgrPts $ColSecTag $ColTransfTag; # using flexural behaviour only
element nonlinearBeamColumn 1 1 2 $numIntgrPts 4 $ColTransfTag; # using flexural-shear behaviour
# Define RECORDERS -------------------------------------------------------------
recorder Node -file $dataDir/DFreeFIBER.out -time -node 2 -dof 1 2 3 disp; # displacements of free nodes
recorder Node -file $dataDir/DBaseFIBER.out -time -node 1 -dof 1 2 3 disp; # displacements of support nodes
recorder Node -file $dataDir/RBaseFIBER.out -time -node 1 -dof 1 2 3 reaction; # support reaction
# define GRAVITY -------------------------------------------------------------
pattern Plain 1 Linear {
load 2 0 -$PCol 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 $Tol 6 ; # determine if convergence has been achieved at the end of an iteration step
algorithm Newton; # use Newton's solution algorithm: updates tangent stiffness at every iteration
set NstepGravity 10; # apply gravity in 10 steps
set DGravity [expr 1./$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 $NstepGravity; # apply gravity
# ------------------------------------------------- maintain constant gravity loads and reset time to zero
loadConst -time 0.0
puts "Model Built"
# Uniform Earthquake ground motion (uniform acceleration input at all support nodes)
set GMdirection 1; # ground-motion direction
set GMfile "BM68elc.acc" ; # ground-motion filenames
set GMfact 1.0; # ground-motion scaling factor
# set up ground-motion-analysis parameters
set DtAnalysis [expr 0.01*$sec]; # time-step Dt for lateral analysis
set TmaxAnalysis [expr 40. *$sec]; # maximum duration of ground-motion analysis -- should be 50*$sec
constraints Transformation ;
numberer Plain
system SparseGeneral -piv
set Tol 1.e-8; # Convergence Test: tolerance
set maxNumIter 10; # 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;
set algorithmType ModifiedNewton
algorithm $algorithmType;
set NewmarkGamma 0.5; # Newmark-integrator gamma parameter (also HHT)
set NewmarkBeta 0.25; # Newmark-integrator beta parameter
integrator Newmark $NewmarkGamma $NewmarkBeta
analysis Transient
# define DAMPING--------------------------------------------------------------------------------------
# apply Rayleigh DAMPING from $xDamp
# D=$alphaM*M + $betaKcurr*Kcurrent + $betaKcomm*KlastCommit + $beatKinit*$Kinitial
set xDamp 0.05; # 2% damping ratio
set lambda [eigen 1]; # eigenvalue mode 1
set omega [expr pow($lambda,0.5)];
set Tperiod [expr 2*$PI/$omega]; # period (sec.)
puts "T=$Tperiod"
set alphaM 0.; # M-prop. damping; D = alphaM*M
set betaKcurr 0.; # K-proportional damping; +beatKcurr*KCurrent
set betaKcomm [expr 2.*$xDamp/($omega)]; # K-prop. damping parameter; +betaKcomm*KlastCommitt
set betaKinit 0.; # initial-stiffness proportional damping +beatKinit*Kini
# define damping
rayleigh $alphaM $betaKcurr $betaKinit $betaKcomm; # RAYLEIGH damping
# --------------------------------- perform Dynamic Ground-Motion Analysis
# Uniform EXCITATION: acceleration input
set IDloadTag 400; # load tag
set dt 0.01; # time step for input ground motion
set GMfatt 386.4;
set AccelSeries "Series -dt $dt -filePath $GMfile -factor $GMfatt"; # time series information
pattern UniformExcitation $IDloadTag $GMdirection -accel $AccelSeries ; # create Unifform excitation
set Nsteps [expr int($TmaxAnalysis/$DtAnalysis)];
set ok [analyze $Nsteps $DtAnalysis]; # actually perform analysis; returns ok=0 if analysis was successful
if {$ok != 0} { ; # if analysis was not successful.
# change some analysis parameters to achieve convergence
# performance is slower inside this loop
# Time-controlled analysis
set ok 0;
set controlTime [getTime];
while {$controlTime < $TmaxAnalysis && $ok == 0} {
set ok [analyze 1 $DtAnalysis]
set controlTime [getTime]
set ok [analyze 1 $DtAnalysis]
if {$ok != 0} {
puts "Trying Newton with Initial Tangent .."
test NormDispIncr $Tol 1000 0
algorithm Newton -initial
set ok [analyze 1 $DtAnalysis]
test $TestType $Tol $maxNumIter 0
algorithm $algorithmType
}
if {$ok != 0} {
puts "Trying Broyden .."
algorithm Broyden 8
set ok [analyze 1 $DtAnalysis]
algorithm $algorithmType
}
if {$ok != 0} {
puts "Trying NewtonWithLineSearch .."
algorithm NewtonLineSearch .8
set ok [analyze 1 $DtAnalysis]
algorithm $algorithmType
}
}
}; # end if ok !0
puts "Ground Motion Done. End Time: [getTime]"
Thanks!
Is there anything wrong with my model or analysis commands?
RC shear wall shear-flexure interaction problem- weird T's
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