Parametric investigation on the dynamic behaviour of masonry pointed arches

In the evaluation of the vulnerability of built cultural heritage, a comprehensive literature addresses circular arches, while few works consider pointed arches and none of them deals with seismic actions. This paper reports a parametric analysis of the dynamic behaviour of pointed arches made of two circular arcs. The analysis considers variations of arch slenderness and sharpness that result from different positions of centres of circular arcs on a set of 48 arches. The arch is modelled as a rigid macroblock system, and limit analysis with the kinematic approach is exploited to determine the collapse acceleration through nonlinear programming optimization. The pattern of hinges at collapse differs considerably from the one that occurs for circular arches. Moreover, the effect of arch slenderness on collapse accelerations turns out to be significantly conditioned by sharpness. Acceleration necessary to initiate motion grows with the rise, as opposed to what occurs for circular shapes. Dynamic behaviour of pointed arches for rectangular- shaped and harmonic inputs is investigated as well transforming arch mechanisms into four-bar linkages. Failure domains for the rocking arch in the framework of linearized motion revealed the impossibility to model the driving failure mode, which occurs after the first impact and, thus, requires consecutive integrations of the full nonlinear version of the distinctive ODE. Failure during the second half cycle of motion for harmonic inputs, especially for low and medium frequencies, is found to be deeply influenced by the adopted impact model and, more importantly, by the position of hinges. A dedicated sensitivity analysis validates the procedure predicting the failure of circular arches as a particular case of pointed.