New procedure for determining the moment–curvature relationship of a reinforced concrete section

Abstract

The moment–curvature relationship is fundamental for inelastic analysis of structures to predict sectional strength, flexural stiffness, sectional ductility and energy dissipation capacity. Here, a new procedure for determining the moment–curvature relationship is developed through calculating the internal force by deformation. This method improves on the traditional iterative procedure by presenting and using the regulations of strain distributions on the moment–curvature curve as well as employing more analytical approaches. Based on possible strain distributions in the ultimate state, three possible strain distribution cases are considered, giving a clear view of the change process of strain distributions over the whole curve. Algorithms are then proposed to calculate the strain distributions of the first and last points on the curve, which greatly benefits the rate of convergence. Furthermore, according to constitutive relationships, equilibrium and deformation compatibility, analytical expressions with respect to two strains are derived to calculate the internal forces of an arbitrary stress state, which may include the ultimate; this is normally done by numerical methods. By computer programming, the influences of axial force on the moment–curvature relationship are analysed, along with the influences of curvature on the moment–axial force relationship.