Evaluation of out-of-plane stability of unreinforced masonry walls subjected to seismic excitation

The paper presents a systematic assessment of a simplified procedure to evaluate the response of unreinforced masonry walls subjected to out-of-plane seismic excitation. The nonlinear force-displacement response of a wall is idealised by means of a suitable trilinear curve. The meaningful parameters characterising the walls and different ground motions were combined for a total of 1248 case studies. For each combination of parameters, a nonlinear SDOF dynamic time-history analysis was performed, and the results were taken as the reference for a simplified "equivalent stiffness" approach. It is shown how a suitably accurate prediction of collapse can be made by using appropriate stiffness values and elastic response spectra. Among the most relevant results for applications, it appears that initial stiffness (and therefore initial period) is not crucial in determining the occurrence of collapse. Instead, collapse depends primarily on the second and third branches of the tri-linear force-displacement relationship, i.e. on maximum strength and ultimate displacement capacity. It is shown how these latter parameters are only moderately sensitive to material mechanical parameters which are usually affected by strong uncertainty when assessing an existing building, namely the elastic modulus E and the compressive strength of masonry.