Energy dissipation involved in the out-of-plane response of unreinforced masonry walls

Abstract

The assessment of the out-of-plane response of masonry has been largely investigated in literature assuming walls responding as rigid blocks or assemblies of rigid bodies. Several studies developed numerical integration of single-degree-of-freedom and multi-degree of freedom systems for the simulation of the OOP dynamic rocking response of simple mechanisms. Modelling the energy dissipation involved in such mechanisms is extremely important to capture the dependence of the damping phenomenon with the system frequency. Some studies, recurring to the classical hypothesis of the impulsive dynamics, simulated the energy dissipation by means of the coefficient of restitution assuming as the overall reduction of energy were concentrated at the instant of the impact. In other works, the damping force has been modelled as a velocity dependent acting force through a constant, variable or stiffness proportional damping ratio. The two damping models are compared highlighting advantages and shortcomings of each system. This paper proposes a numerical formulation for the direct equivalence of the two damping approaches for simple OOP one-way bending mechanisms assuming as force-displacement relationship nonlinear elastic tri-linear curves.