Partial-interaction time dependent behaviour of reinforced concrete beams

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.