Simplified closed-form solution for the determination of the moment-curvature response of a circular RC section

A seismic vulnerability analysis of a multi-span simply supported bridge is often based on the seismic response of the most critical pier. This response is influenced by different collapse modes (flexural, shear, second order effects, lap-splice of longitudinal bars or their buckling). Among these the flexural behaviour is important and it's known if the equivalent plastic hinge length and the Moment-Curvature law of the fixed end are given. This paper provides a closed-form dimensionless solution to obtain a 5 point Moment-Curvature diagram for circular RC section. The solution is based only on three parameters: dimensionless axial force, mechanical percentage of longitudinal reinforcement, geometrical percentage of transversal reinforcement. A numerical example is presented to test the solution comparing it with a FEM analysis.