Lower and upper bounds in closed form for out-of-plane strength of masonry structures with frictional resistances

This paper presents a new simplified procedure to evaluate upper and lower thresholds for the possible collapse load factor for out-of-plane loaded block masonry structures with frictional resistances, by means of limit state analysis. Bypassing a detailed discrete element analysis, it is herein assumed that the general failure involves a number of cracks which separate the structures into a few macro blocks and all the possible relative motions among micro blocks are concentrated along the cracks. A particular class of mechanisms involving out-of-plane friction forces (i.e. interaction of torsion strength and shear forces on frictional interfaces) is analysed, and two limiting conditions for the collapse load factor are kinematically computed with simple formulations in closed form, by use of minimization routines. Sets of curves of the results in relation to the shape ratios of the unit and to the friction coefficient are then presented and widely discussed.