Non-linear analysis of rectangular cross-sections with different reinforcements: dimensionless closed form solution

This paper presents an algorithm to solve a non-linear rectangular cross-section analysis by means of closed form equations. The equations are provided in a dimensionless form in order to provide generalizable results. The algorithm is based on the direct integration of the non-linear constitutive behaviour of the materials into the stress-block constitutive behaviour. The algorithm is based on masonry rectangular cross-sections characterized by an external axial load similar to Reinforced-Concrete cross-sections. The failure of the strengthening system and the masonry are analysed in the proposed algorithm, in an unconventional manner, analysing the behaviour even after the attainment of the ultimate strains, accounting for progressive damage. The algorithm allows to prevent the cross-section fiber analysis and the consequential iterative procedure to retrieve the neutral axis depth. Furthermore, the direct integration allows to evaluate the exact solution of the problem without numerical approximations. The results are discussed by means of several parametric analyses in terms of P–M domains and bending moment–curvature diagrams in dimensionless form. The proposed approach aims to simplify the cross-section analysis process in complex algorithms as in the risk analysis based on a large scale approach, where a large number of structures and structural members are analysed in the vulnerability process.