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The authors highly recommend that the user define variables and use these variables for the input commands. Variables can be defined using the Tcl "set" command:
set Radius 5; # define radius of section
set Diameter [expr $Radius/2.]; # define section diameter
Therefore, it is recommended that the user define all material and geometric properties, as variables:
set fc -5000;
set fy 60000;
Because OpenSees does not use internal units, the user must keep track of the types of units being used. For example, the user must define all length units in either inches or meters, etc., consistently throughout.
The Tcl feature of being able to handle variables enables the user to define units as variables, and hence use them in building the model. Here is an example:
First of all, the basic units need to be defined. The OpenSees output will be in these units:
set in 1.; # define basic unit -- length
set sec 1.; # define basic unit -- time
set kip 1.; # define basic unit -- weight (or define force, but not both)
The basic units must be independent of each other. Once they have been defined, additional units that are made up of these basic units can be defined:
set ksi [expr $kip/pow($in,2)]; # define engineering units
set psi [expr $ksi/1000.];
set ft [expr 12.*$in];
It is a good idea to define constants at the same time that units are defined:
set g [expr 32.2*$ft/pow($sec,2)]; # gravitational acceleration
set PI [expr 2*asin(1.0)]; # define constants
set U 1.e10; # a really large number
set u [expr 1/$U]; # a really small number
Once the units have been defined, model variables can be defined in terms of these units and, hence, they don't all have to be defined in the basic units:
set fc [expr -5500*$psi]; # CONCRETE Compressive Strength, ksi (+Tension, -Compression)
set Ec [expr 57000.*sqrt(-$fc/$psi)];# Concrete Elastic Modulus
set Fy [expr 68.*$ksi]; # STEEL yield stress
set Es [expr 29000.*$ksi]; # modulus of steel
set epsY [expr $Fy/$Es]; # steel yield strain
It is also a good idea to use variables for IDtags of materials, sections, elements, etc. This is done to ensure that the same ID tag is not used when defining the input. Also, it makes it easier in writing the input to use a variable name that makes sense. Here is an example:
# set up parameters for column section and element definition
set IDcore 1; # ID tag for core concrete
set IDcover 2; # ID tag for cover concrete
set IDsteel 3; # ID tag for steel
For the example structural model, the following variables need to be defined:
# define GEOMETRY variables
set Hcol [expr 6.*$ft]; # column diameter
set Lcol [expr 36*$ft]; # column length
set GrhoCol 0.015; # column longitudinal-steel ratio
set Weight [expr 3000.*$kip]; # superstructure weight
set Rcol [expr $Hcol/2]; # COLUMN radius
set Acol [expr $PI*pow($Rcol,2)]; # column cross-sectional area
set cover [expr 6*$in]; # column cover width
set G $U; # Torsional stiffness Modulus
set J 1.; # Torsional stiffness of section
set GJ [expr $G*$J]; # Torsional stiffness
# define COLUMN REINFORCEMENT variables
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
# define GRAVITY variables
set Mass [expr $Weight/$g]; # mass of superstructure
set Mnode [expr $Mass]; # nodal mass for each column joint
# define DAMPING variables from $xDamp --SDOF system, use stiffness proportional damping only
set xDamp 0.02; # modal damping ratio
# ------ set analysis variables
set DxPush [expr 0.1*$in]; # Displacement increment for pushover analysis
set DmaxPush [expr 0.05*$Lcol]; # maximum displamcement for pushover analysis
set gamma 0.5; # gamma value for newmark integration
set beta 0.25; # beta value for newmark integration
set DtAnalysis [expr 0.005*$sec]; # time-step Dt for lateral analysis
set DtGround [expr 0.02*$sec]; # time-step Dt for input grond motion
set TmaxGround [expr 50.*$sec]; # maximum duration of ground-motion analysis
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