Definition of equivalent damping for masonry structures in support of displacement based design

In the last years, several researches have established the importance to correlate design limit states to performance levels defined by displacement, in order to obtain a better control on expected damage after an earthquake. The displacement spectra proposed by code for damping values higher than the nominal value of 5% of critical are generally obtained, as in the case of Eurocode 8 and the Italian Technical Code (2008), by applying a scaling factor to the elastic response spectras 5% damped. This factor is defined as a function of equivalent viscous damping, which depends on hysteretic energy dissipation. The paper presents a procedure for determining the hysteretic damping for reinforced masonry structures. The method makes use of the equivalent linear system, whose vibration period is determined by nonlinear dynamic analysis on single degree of freedom idealized system, by using synthetic spectrum compatible time histories. The analyses are performed using an hysteretic model calibrated on experimental results obtained from cyclic shear compression tests that were carried out by the University of Padova.