A Multi-Pier MP procedure for the non-linear analysis of in-plane loaded masonry walls

Several simplified and advanced methods have been proposed to evaluate the behavior of masonrywalls under in-plane loads, but their implementation in standard commercial software remains still an exception. In this paper, a novel 1D approach called Multi-Pier MP method, which has the advantage that can be used in a commercial software and requires only truss elements with a non-linear softening behavior, is presented. In the model, a masonry structure in-plane loaded is transformed in an assemblage of piers (vertical trusses) and diagonal connecting elements (braces), ensuring by elastic stiffness equivalence that a masonry representative element of volume behaves in the same manner as the 1D system constituted by two vertical trusses and two diagonal braces. After a validation at a unit cell level, where geometric and mechanical properties of the trusses are set in order to reproduce correctly masonry behavior respectively under axial loads, combined shear and compression stresses and bending and shear actions, four masonry full scale shear walls with different length to width ratios and presence or absence of openings are analyzed in the non-linear static range. In addition to experimental results, two Heterogeneous Discrete Element and Finite Element Methods were used with validation purposes. Excellent match among MP Method results, experimental evidences and alternative advanced numerical heterogeneous approaches is found, as far as the prediction of ultimate load, post peak behavior, initial stiffness and failure mechanisms is concerned. The model is also capable to follow at each step of loading the spreading and position of tensile and shear cracks.