Simplified analytical Moment-Curvature relationship for hollow circular RC cross-sections

The seismic vulnerability analysis of multi-span bridges can be based on the response of the piers, provided that deck, bearings and foundations remain elastic. The lateral response of an RC bridge pier can be affected by different mechanisms (i.e., flexure, shear, lap-splice or buckling of the longitudinal reinforcement bars, second order effects). In the literature, simplified formulations are available for mechanisms different from the flexure. On the other hand, the flexural response is usually calculated with a numerically-based Moment-Curvature diagram of the base section and equivalent plastic hinge length. The goal of this paper is to propose a simplified analytical solution to obtain the Moment-Curvature relationship for hollow circular RC sections. This based on calibrated polynomials, fitted against a database comprising 720 numerical Moment-Curvature analyses. The section capacity curve is defined through the position of 6 characteristic points and they are based on four input parameters: void ratio of the hollow section, axial force ratio, longitudinal reinforcement ratio, transversal reinforcement ratio. A case study RC bridge pier is assessed with the proposed solution and the results are compared to a refined numerical FEM analysis, showing good match.