A Computer Program for Producing Interaction Charts of T-Column
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Date
2011-03
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Addis Ababa University
Abstract
In this study an algorism for the computation of Interaction Surface of reinforced concrete Tshaped
column subjected to axial load and biaxial bending is developed. The method is exact and
it is based on the transformation of the double equilibrium integrals into line-integrals along the
compressive perimeter of the concrete section using Green’s Theorem. For up to third degree
polynomial stress-strain relations, Gauss integration with only three sample integration points
yields exact results.
By inserting the necessary cross-sectional dimensions and material properties on the user
interface, the program locates the position of the plastic centroid of the cross section. The
coordinates of corner points and reinforcement bars will be calculated using the cross sectional
dimensions and position of the plastic centroid.
The interaction charts produced are for reinforcement ratios of 0 to 0.8 with an increment of
0.1.Parabolic-rectangular stress distribution is used for the analysis of the concrete section as is
primarily recommended by EBCS-2,1995. The capacity of the section is checked for different
positions of neutral axis. Green’s theorem transforms the double integration over the
compression area into a line-integration along the closed line that encloses the area. The line
integration along the perimeter of the compression area of the section is numerically evaluated
using Gauss integration.
The calculation of the stress and force carried by the steel is straightforward. From the strain we
calculate the corresponding stress and finally the force on each bar. Note that from the stress of
each compressive bar we subtract the stress of the concrete at the location of that bar in order to
avoid double counting the compressive concrete area displaced by the bar.
The presented method for the construction of Interaction Surfaces of concrete sections is
computationally efficient because the double integration is reduced to numerical evaluation of a
few line integrals. The number of line integrations is equal to the number of the sides of the
section in the compressive zone. Each of these integrals involves typically three sample points
thus the number of computer operations is very small.
Although the initial objective of the study was to develop interaction chart for T columns; in the
process of solving the problem other possibilities are also achieved. The program developed can
also produce interaction surface of L and rectangular columns. Six of these interaction surfaces
are shown in appendix A. It is clear that the computation time would allow the interactive use of
the method as a design tool. The program is written in visual basic programming language.
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Keywords
T-Column, Computer Program