Closed-form approximation of the axial force-bending moment interaction diagram for hollow circular reinforced concrete cross-sections

This paper proposes a simple closed-form approximation of the axial force-bending moment interaction diagram for solid and hollow circular reinforced concrete (RC) cross-sections with an arbitrary number of layers of longitudinal reinforcement. The implemented nonlinear material models are those of the European building code. Specifically, the parabola-rectangular strain-stress relation and the stress-block model are considered for the concrete in compression. On the other hand, the elastic-perfectly plastic behavior is assumed for the reinforcing steel bars. The proposed semi-exact closed-form approximation involves one parameter only, which is calibrated by means of a numerical optimization procedure taking into account a large database of cross-sections. Moreover, an efficient procedure is developed for the design of the outer layer of longitudinal reinforcement in solid or hollow circular RC cross-sections under combined axial force and bending moment (the mechanical ratio of any other layers of longitudinal reinforcement is considered as known function of the mechanical ratio of the outer layer of longitudinal reinforcement). Finally, several numerical examples are included to demonstrate the accuracy of the approximated axial force-bending moment interaction diagram and the effectiveness of the derived design procedure.