Limit analysis of out-of-plane loaded running bond masonry walls under Mindlin-Reissner plate hypotheses

Earthquake surveys have demonstrated that the lack of out-of-plane strength is a primary cause of failure in many traditional forms of masonry. Moreover, bearing walls are relatively thick and, as a matter of fact, many codes of practice impose a minimal slenderness for them, as for instance the recent Italian OPCM 3431 2004, in which the upper bound slenderness is fixed respectively equal to 12 for artificial bricks and 10 for natural blocks masonry. In this context, it seems particularly attractive a formulation at failure for regular assemblages of bricks based both on homogenization and Reissner-Mindlin theory. Starting from a compatible identification, already developed in the framework of linear elasticity by Cecchi and Rizzi [1], in which a 3D system of blocks connected by elastic interfaces is identified with a 2D Reissner-Mindlin plate, in this paper a limit analysis approach for deriving the homogenized failure surfaces for masonry out-of-plane loaded is presented. On the other hand, in a previous paper by Milani et al. [2] failure surfaces for out-of-plane loaded masonry were obtained by means of a static limit analysis approach under Love-Kirchhoff plate hypotheses. In this paper, a kinematic approach is proposed under the hypotheses of Reissner-Mindlin plate theory, infinitely resistant blocks connected by interfaces (joints) with frictional-type failure surfaces. In this way, the macroscopic masonry strength domain is obtained as a function of the macroscopic bending and torsional moments and shear forces by means of a constrained minimization of the internal power dissipated, once that a subclass of possible deformation modes is a priori chosen. A meaningful example of technical relevance is presented and some comparisons with previously developed Kirchhoff-Love kinematic limit analyses [3] are reported.