Limit analysis of transversally loaded masonry walls using an innovative macroscopic strength criterion

The macroscopic strength properties of masonry walls with joints of finite thickness subjected to out-of-plane loads are estimated following an approach similar to the so-called Method of Cells for fiber-reinforced composites. A typical representative volume is subdivided into a few sub-cells, and a strain-rate periodic, piecewise differentiable transverse velocity field, depending on a limited number of degrees of freedom, is defined. Upper bounds to the macroscopic strength domain of the wall in the space of the macroscopic bending and twisting moments are obtained by applying the kinematic theorem of limit analysis within the framework of homogenization theory for periodic media. The approximated macroscopic failure surfaces are in good agreement with the ‘exact’ ones, available in the literature for infinitely strong units and infinitely thin joints, and with those obtainable by accurate 2D and 3D numerical models, at a much higher computational cost, for units of limited strength and joints of finite thickness. The influence of compressive in-plane loads and of the joint thickness on the macroscopic out-of-plane strength of the wall is also numerically investigated. Finally, the proposed model is applied to the prediction of the bearing capacity of laterally loaded masonry elements: the accuracy of the numerical predictions is assessed by comparisons with available experimental results and with more refined numerical models proposed by other authors.