Flexural strength-ductility assessment of unreinforced masonry cross-sections: analytical expressions

The unreinforced masonry (URM) is a complex and variegate construction material characterized by a prominent nonlinear response. For this reason, advanced numerical simulations are required to assess URM buildings, especially in case of severe loading conditions as earthquakes. However, given the theoretical and computational difficulties of detailed non-linear analyses, linear elastic methods are still adopted in current practice. This results in conservative seismic assessments and, consequently, invasive and expensive strengthening interventions to guarantee seismic safety. Starting from these statements, the aim of the paper is to provide closed-form equations useful for a preliminary strength and ductility assessment of unreinforced masonry rectangular cross-sections. Expressions for direct calculation of M-N (bending moment – axial load) strength domains and M-χ (moment – curvature) ductility diagrams for different constitutive laws are provided. The expressions are firstly applied to a representative URM cross-section and secondarily used for the numerical simulation of a recent out-of-plane loading experimental test available in the literature. For a better comprehension of URM members behavior under axial-bending loading condition, 3D M-N-χ diagrams are presented in the paper.