Abstract
In this paper, a mathematical model for predicting the stress –strain and moment curvature relations in concrete is developed. A good number of empirical equations were proposed to represent stress-strain behaviour of conventional concrete. Most of the equations can be used for the ascending portion of the curve only. In 1997 Mansur et al. have adopted Carriera and Chu (1985) model, which was based on the model proposed by Popovics (1973). As such, model proposed by Mansur et al includes both ascending and descending portions of the stress-strain curve for the confined concrete with introduction of two constants for the descending portion of the curve. Several researchers proposed various empirical equations for stress-strain behaviour as briefly reported in the previous chapter. An attempt has been made in this study to develop mathematical models for concrete in unconfined state. These analytical equations can be applied to any concrete with slight modifications. These models are developed to validate the experimental values obtained.
Highlights
Graph obtained by drawing a curve for the values of stresses and strains obtained during testing a material specimen of materials is called a stress - strain curve
Even though the stress strain relation for cement paste and aggregate when tested individually is practically linear, it is observed from the stress-strain plots of concrete that, no portion of the curves is in the form of a straight line
In conventional concrete the value of stress is maximum corresponding to a strain of about 0.002 and further goes on decreasing with the increasing strain, giving a dropping curve till it terminates at ultimate crushing strain
Summary
Graph obtained by drawing a curve for the values of stresses and strains obtained during testing a material specimen of materials is called a stress - strain curve. By testing cylinders of standard size made with concrete, under uni-axial compression values of stresses and strains are obtained and the stress-strain curves are plotted. Even though the stress strain relation for cement paste and aggregate when tested individually is practically linear, it is observed from the stress-strain plots of concrete that, no portion of the curves is in the form of a straight line. In concrete the rate of increase of stress is less than that of increase in strain because of the formation of micro cracks, between the interfaces of the aggregate and the cement paste. The stress strain curve is not linear. In conventional concrete the value of stress is maximum corresponding to a strain of about 0.002 and further goes on decreasing with the increasing strain, giving a dropping curve till it terminates at ultimate crushing strain
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