Assessment of the response envelope of reinforced concrete members with different failure modes

The expected lateral response of reinforced concrete (RC) elements strongly depends on their failure mode. Code-conforming RC members are supposed to exhibit a flexural (F) ductile failure, with complete exploitation of their post-peak displacement/deformation capacity. However, substandard RC elements, which are typical of existing structures, may undergo a shear failure after yielding (FS) or even before yielding (S) of longitudinal reinforcement. In this case, the element is classified as “shear-sensitive” and may be characterized by an abrupt collapse after the attainment of the peak load-capacity, with a fast loss of lateral load-bearing capacity up to the onset of the progressive reduction of the axial load-bearing capacity. This condition may trigger structural collapse, as also shown from surveys of damages due to strong earthquakes in past and recent times. So, the determination of the failure mode of RC members is paramount for a reliable assessment of the seismic safety of structures. In general, static criteria are applied to pre-classify the expected failure mode of RC members and their response backbone is defined dependently on the determined failure mode. However, a comprehensive approach for modelling, with a unique set of predictive equations, the response envelope of RC members without pre-determining with a deterministic approach their failure mode is missing. In this paper membership functions are defined to determine for RC columns the possibility that they exhibit an F, an FS, or an S failure. A set of basic predictive equations are defined, based on experimental data, to define a multilinear response envelope. The proposed equations may be combined with membership functions to use a unique set of equation able to reproduce the behaviour of RC columns with different expected failure modes.