Non-linear Behavior of Reinforced Concrete Cross-Sections with Dimensionless Equations in Closed Form

Reinforced concrete is one of the most used construction material worldwide. Analysis of reinforced concrete elements is conducted usually looking at the cross sections with simplified assumptions or by means of iterative research of the neutral axis. In this paper, a solution is proposed to resolve the non-linear behavior of reinforced concrete rectangular cross-sections by the means of closed form equations and, therefore, iterative procedures are prevented. The equations are reported in a dimensionless form in order to offer generalizable results. The constitutive behavior of the reinforcement is assumed as linear-elastic and bi-linear in order to consider the effects of the hardening. The analysis results are discussed by means of dimensionless parametric investigations in terms of P-M domains and bending moment-curvature diagrams in order to analyze the effects of the hardening of the reinforcement in terms of ductility and bending moment capacity of the cross section. The proposed approach aims at simplifying the cross-section analysis process in complex algorithms where a large amount of cross-section evaluations are performed in order to reduce the analysis efforts without losing the accuracy of the results.