Shear hysteresis model for reinforced concrete elements including the post-peak range

Reinforced concrete (R/C) buildings designed according to older seismic codes represent a large part of the total building stock; hence, it is important to accurately and efficiently assess their response to actions induced by natural hazards, such as earthquake. Substandard R/C structural elements are prone to shear failure subsequent, or even prior, to yielding of their longitudinal reinforcement. This can potentially lead to loss of axial load bearing capacity of vertical elements and initiate progressive collapse of the building. So far, there have been efforts to model the full-range behaviour of such elements following a macro-modelling approach, usually based on quite a limited amount of experimental results, especially with respect to the post-peak part of their response, and adopting assumptions that are not entirely appropriate. In the present study, an extensive database of shear and flexure-shear critical rectangular R/C columns has been compiled, to the purpose of investigating R/C member post-peak response and calibrating the models mentioned below. It includes both monotonic and cyclic tests, the latter constituting the majority, it spans a broad range of design, material and loading parameters and the majority of the specimens have been tested up to axial failure. A shear macro-model is developed, which is able to capture the full hysteretic behaviour of R/C elements. In addition to the behaviour up to peak shear resistance, an effort is made to properly capture the post-peak response, calibrating an empirical model for the descending branch directly, instead of indirectly defining it through shear and axial failure that has traditionally been the case. The angle of the shear failure plane is an important parameter of this model, hence an empirical relationship has been developed for it, as well. The onset of axial failure constitutes a vital aspect of post-peak response, since it signals the initiation of a process of loss of an individual R/C element's axial load-bearing capacity simultaneously with the redistribution of vertical loads to neighbouring ones; thus, it was also closely examined and empirical models were derived.