Out-of-plane behaviour of single-body unreinforced-masonry wall restrained by a flexible diaphragm

Past earthquakes have shown the high vulnerability of existing masonry buildings, particularly to out-of-plane local collapse mechanisms. Out-of-plane response is one of the most debated topics in the last decades, because of its complex nature as for geometrical non-linearity, energy damping, record sensitivity. In this work is considered a monolithic wall, resting on a foundation, restrained by a flexible diaphragm. The wall rocks around two base pivots and has one degree of freedom. Its thickness is explicitly accounted for, and the diaphragm is modelled as a linear-elastic spring and a concentrated mass. The non-linear equation of motion is presented, within a lagrangian approach. The energy dissipation is associated to the impact of the wall against the foundation. The effect of size of the wall, diaphragm stiffness and mass are evaluated through parametric analyses. Neglecting the diaphragm mass, the results can be interpreted also as related to a wall restrained at the top by tie-rods.