Simplified polynomial formulation for the calculation of the Moment-Curvature diagram of RC rectangular sections

The seismic response of multi-span RC bridges is often based on the response of the piers, provided that deck, bearings and foundations remain elastic. The seismic response of a RC bridge pier is influenced, in general, by different mechanisms (i.e. flexure, shear, lap-splice or buckling of the longitudinal reinforcement bars, second order effects). For mechanisms different from the flexural one, simplified formulations are available in literature. On the other hand, the flexural behaviour of the pier can be characterised by means of equivalent plastic hinge length and Moment-Curvature diagram of the base section, usually carried out with a computer software. In this paper, it is proposed a simplified analytical solution to obtain the Moment-Curvature relationship for rectangular RC sections, in both principal axes. The solution is based on adjusted polynomials, fitted against a database of 800 numerical Moment-Curvature analyses of rectangular RC sections. The proposed polynomials allow to define the cross-section capacity curve through the position of 6 characteristic points and they are based on 4 input parameters: depth-towidth ratio of the cross-section, axial force ratio, longitudinal reinforcement ratio, transversal reinforcement ratio. The solution is tested through the application to a RC rectangular section case study and comparison of the resulting capacity curves to the outcome of refined numerical Moment-Curvature analyses. The results show that the proposed analytical solution is a reliable method to characterise the flexural response of RC rectangular cross-sections.