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In the Tcl scripting language variables may be used to represent numbers. Once defined, these variables can be use instead of numbers in Tcl and OpenSees commands. When they are being recalled, the variables are precedented by the symbol $. If this symbol is not used, the variable name is interpreted as a string command and an error may result.
A few examples are given:
MATERIAL PARAMETERS:
# -----MaterialParameters.tcl-------------------------------------------------------
set fc [expr -4.0*$ksi]; # nominal compressive strength of concrete
set Ec [expr 57*$ksi*sqrt(-$fc/$psi)]; # Concrete Elastic Modulus
set fc1C [expr 1.26394*$fc]; # CONFINED concrete (mander model), max stress
set eps1C [expr 2.*$fc1C/$Ec]; # strain at maximum stress
set fc2C $fc; # ultimate stress
set eps2C [expr 2.*$fc2C/$Ec]; # strain at ultimate stress
set fc1U $fc; # UNCONFINED concrete (parabolic model), max stress
set eps1U -0.003; # strain at maximum stress
set fc2U [expr 0.1*$fc]; # ultimate stress
set eps2U -0.006; # strain at ultimate stress
set Fy [expr 70.*$ksi]; # STEEL yield stress
set Es [expr 29000.*$ksi]; # elastic modulus of steel
set epsY [expr $Fy/$Es]; # steel yield strain
set Fy1 [expr 95.*$ksi]; # steel stress post-yield
set epsY1 0.03; # steel strain post-yield
set Fu [expr 112.*$ksi]; # ultimate stress of steel
set epsU 0.08; # ultimate strain of steel
set Bs [expr ($Fu-$Fy)/($epsU-$epsY)/$Es]; # post-yield stiffness ratio of steel
set pinchX 1.0; # pinching parameter for hysteretic model
set pinchY 1.0; # pinching parameter for hysteretic model
set damage1 0.0; # damage parameter for hysteretic model
set damage2 0.0; # damage parameter for hysteretic model
set betaMUsteel 0.0; # degraded unloading stiffness for hysteretic material based on MU^(-beta)
set betaMUjoint 0.0; # degraded unloading stiffness for hysteretic material based on MU^(-beta) -- timoshenko value of 0.5
set betaMUph 0.0; # degraded unloading stiffness for hysteretic material based on MU^(-beta) -- timoshenko value of 0.5
set G $U; # Torsional stiffness Modulus
set J 1.; # Torsional stiffness of section, place here just to keep with G
set GJ [expr $G*$J]; # Torsional stiffness
ELEMENT PARAMETERS:
# -----ElementParameters.tcl----------------------------------------------------
set Hcol [expr 5.*$ft]; # column diameter
set Lcol [expr 36*$ft]; # column length
set Hbeam [expr 8.*$ft]; # beam depth
set Lbeam [expr 36.*$ft]; # beam length
set GrhoCol 0.0125; # column longitudinal-steel ratio
set Weight [expr 2000.*$kip]; # superstructure weight
set Bbeam $Hcol; # beam width
set Rcol [expr $Hcol/2]; # COLUMN radius
set Acol [expr $PI*pow($Rcol,2)]; # column cross-sectional area
set cover [expr $Hcol/15]; # column cover width
set IgCol [expr $PI*pow($Rcol,4)/4]; # column gross moment of inertia, uncracked
set IyCol $IgCol; # elastic-column properties
set IzCol $IgCol; # elastic-column properties
set IzBeam [expr $Bbeam*pow($Hbeam,3)/12]; # beam gross moment of inertia, about horizontal Z-axis
set IyBeam [expr $Hbeam*pow($Bbeam,3)/12]; # beam gross moment of inertia, about the vertical Y-axis
set Abeam [expr $Hbeam*$Bbeam*10000]; # beam cross-sectional area, make it very very stiff
# define COLUMN section parameters
set NbCol 20; # number of column longitudinal-reinforcement bars
set AsCol [expr $GrhoCol*$Acol]; # total steel area in column section
set AbCol [expr $AsCol/$NbCol]; # bar area of column longitudinal reinforcement
set riCol 0.0; # inner radius of column section
set roCol $Rcol; # outer radius of column section
set IDcore 1; # ID tag for core concrete
set IDcover 2; # ID tag for cover concrete
set IDsteel 3; # ID tag for steel
set nfCoreR 8; # number of radial fibers in core
set nfCoreT 16; # number of tangential fibers in core
set nfCoverR 2; # number of radial fibers in cover
set nfCoverT 16; # number of tangential fibers in cover
set IDcolFlex 2; # ID tag for column section in flexure, before aggragating torsion
set IDcolTors 10; # ID tag for column section in torsion
set IDcolSec 1; # ID tag for column section
set IDcolTrans 1; # ID tag for column transformation, defining element normal
set IDbeamTrans 2; # ID tag for beam transformation, defining element normal
set np 5; # Number of integration points
GRAVITY PARAMETERS:
# -----GravityParameters.tcl----------------------------------------------------
# define GRAVITY paramters
set Pdl [expr $Weight/2]; # gravity axial load per column
set Wbeam [expr $Weight/$Lbeam]; # gravity dead load distributed along beam length
set Mdl [expr $Wbeam*pow($Lbeam,2)/12]; # nodal moment due to distributed dl
set Mass [expr $Weight/$g]; # mass of superstructure
set Mnode [expr $Mass/2]; # nodal mass for each column joint
ANALYSIS PARAMETERS:
# -----AnalysisParameters.tcl----------------------------------------------------
set DxPush [expr 0.1*$in]; # Displacement increment for pushover analysis
set DmaxPush [expr 0.05*$Lcol]; # maximum displamcement for pushover analysis
set DtAnalysis [expr 0.005*$sec];# time-step Dt for lateral analysis
set DtGround [expr 0.02*$sec]; # time-step Dt for input grond motion
set TmaxGround [expr 35 *$sec]; # maximum duration of ground-motion analysis
set gamma 0.5; # gamma value for newmark integration
set beta 0.25 # beta value for newmark integration