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Some element types require that the element cross section be defined a-priori, this is done using the section command. The section is used to represent force-deformation (or resultant stress-strain) relationships at beam-column and plate sample points.
While there are many types of sections available, the fiber section will be used to define the cross section of the column in the structure under consideration. A fiber section has a general geometric configuration formed by subregions of simpler, regular shapes (e.g. quadrilateral, circular and triangular regions) called patches. In addition, individual or layers of reinforcement bars can be specified.The fiber section can be defined as a combination of the following:
fiber -- a single fiber can be defined, such as a single reinforcing bar. The coordinates, associated area and material tag are prescribed with the fiber. (The coordinates are given with respect to the plane of the cross section, a coordinate transformation is later defined in the input using the transformation command)
patch -- a patch defines an area that has a regular shape: quadrilateral or circular. A different material can be associated with each patch.
layer (Straight Layer Command, Circular Layer Command) -- a layer defines a layer of reinforcement that has a regular shape: straight or circular. A different material can be associated with each layer.
The circular cross section of reinforced concrete will be defined using the patch and layer commands. First of all, it is important to define the variables:
# 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 IDcolFlex 2; # ID tag for column section in flexure, before aggregating torsion
set riCol 0.0; # inner radius of column section
set roCol $Rcol; # outer radius of column section
set nfCoreR 8; # number of radial fibers in core (number of "rings")
set nfCoreT 16; # number of tangential fibers in core (number of "wedges")
set nfCoverR 2; # number of radial fibers in cover
set nfCoverT 16; # number of tangential fibers in cover
# cover - cover thickness, has been defined with the geometry
# IDcore - material tag for the core patch, has been defined with the materials
# IDcover - material tag for the cover patches, has been defined with the materials
# IDsteel - material tag for the reinforcing steel, has been defined with the materials
# NbCol # number of column longitudinal-reinforcement bars, has been defined with the geometry
# AbCol # bar area of column longitudinal reinforcement, has been defined with the geometry
The fiber cross section is defined as follows:
section fiberSec $IDcolFlex {
set rc [expr $roCol-$cover]; # Core radius
patch circ $IDcore $nfCoreT $nfCoreR 0 0 $riCol $rc 0 360; # Define the core patch
patch circ $IDcover $nfCoverT $nfCoverR 0 0 $rc $roCol 0 360; # Define the cover patch
set theta [expr 360.0/$NbCol]; # Determine angle increment between bars
layer circ $IDsteel $NbCol $AbCol 0 0 $rc $theta 360; # Define the reinforcing layer
}
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