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Abstract: When a concrete member is subjected to a load its response is both instantaneous and time dependent. The influence of time dependent deformation is particularly import because it may lead to serviceability failures in structural members where deflections or crack widths are excessive. Current analysis techniques for reinforced concrete members are built around a moment–curvature (M/χ) approach that is based on the assumption of full-interaction (FI), that is, the reinforcement does not slip relative to the concrete which encases it and, consequently, the widening of cracks and their effect on deflection cannot be simulated directly. Hence in order to determine member deflection, empirically derived expressions for the flexural rigidity of a member (EIemp) are required to allow for the tension stiffening associated with cracking. In contrast to this FI M/χ approach, a moment–rotation (M/θ) approach has been developed which allows for slip between the reinforcement and concrete, that is partial-interaction (PI) and which, consequently, obviates the need for the empirically derived flexural rigidities (EIemp). The PI M/θ approach simulates directly, through partial-interaction structural mechanics, the formation and widening of cracks as the reinforcement pulls from the concrete at crack faces and, consequently, automatically allows for tension stiffening. Hence the PI M/θ approach is a useful improvement of the current FI M/χ approach as it quantifies the flexural rigidities associated with tension stiffening which can then be used in standard analysis techniques. It is also shown in this paper that the moment rotation approach can be used to derive flexural rigidities that account for the long term effects of creep and shrinkage as well as predicting the effects of creep and shrinkage on cracks widths and spacings. [Copyright &y& Elsevier]

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. [Copyright &y& Elsevier]