Load-slip relationship of tension reinforcement in reinforced concrete members

Abstract

An accurate evaluation of the moment-rotation relationship of reinforced concrete members at both serviceability and ultimate limit states is a very important aspect as rotation has a significant contribution to the deflection of the member and also has a direct impact on the magnified moment, the ability to absorb energy and the redistribution of moments. The rotation in the un-cracked or homogenous parts of a reinforced concrete member can be determined by integrating the curvature using standard procedures. However, in the cracked or non-homogenous regions, rotations are found to have sudden or discrete changes at each crack between their crack faces. This can be quantified by the crack opening produced by the slip Δ between the reinforcement and the concrete at the crack face induced by the force in the reinforcing bar P. In this paper, closed form solutions are derived for the P–Δ relationships which are applicable to any type and shape of reinforcement. It is then shown how these closed form solutions can be conveniently used to derive the moment-rotation relationship at a crack.