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

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