A mechanics solution for hinges in RC beams with multiple cracks

Abstract

The formation of hinges in reinforced concrete beams is important as hinges influence the ability of the beam and, subsequently, the frame to absorb energy and resist extreme loads such as hurricane or seismic loads. A common approach for quantifying the rotational capacity of beams at the ultimate limit is to use a strain based moment–curvature analysis combined with an empirical hinge length to determine the rotation capacity of the member. Being empirically based, this approach is very restrictive as it can only be applied within the bounds of the tests from which they were derived. In this paper, a mechanics displacement based hinge approach is described that can simulate the formation of cracks, the discrete rotation at each individual crack and the formation of wedges. Being mechanics based, this hinge model can be applied to any type of reinforced concrete, such as those with brittle reinforcement and also to all strengths of concrete. This mechanics based model is shown to have good agreement with test results and can be used at all stages of loading from serviceability to failure. Furthermore, it can also used to develop closed form solutions that do not require the moment–curvature assumption of full interaction but specifically allow for partial interaction that is slip between the reinforcement and the concrete.