Limit analysis by linear programming of 3D masonry structures with associative friction laws and torsion interaction effects

In this paper, a formulation for limit analysis of three-dimensional masonry structures discretized as rigid block assemblages interacting through no-tension and frictional contact interfaces is developed. Linear and piecewise linearized yield functions are used for rocking, sliding and torsion failure. A simple yield condition has been defined to take into account interaction effects of shear force with torsion and bending moment. Associative flow rules are considered for strain rates. On the basis of the developed governing equations, the limit analysis problem has been formulated as a nonlinear mathematical program. An iterative solution procedure based on linear programming is used to solve the limit analysis problem and to take into account nonlinearities due to the influence of bending moments and shear stresses on torsion strength. The results of experimental investigations on out-of-plane masonry walls constrained at one edge and different examples from literature were considered for validation. Comparison with existing formulations is carried out.