Rocking Mechanism of Masonry Portals with Circular Arches

Abstract

Unreinforced masonry (URM) structures represent most of the world architectural heritage, whose vulnerability has been also highlighted by damages and collapses occurred after recent seismic events. Numerous studies regarding the seismic capacity of masonry walls, arches and portals have been carried out by applying the so-called equivalent static analysis method, neglecting their dynamic behaviour. A proper evaluation of the dynamic response of masonry elements can be done analytically considering the dynamic equation of rigid bodies not resistant to the tensile stresses. Some studies are available in literature regarding the dynamic behaviour of walls and arches. In this framework, the paper aims to develop an analytical model, able to describe the dynamic behaviour of portals with circular arches, subjected to a base motion. Starting point of the analysis is the evaluation of the mechanism (local, semi-global or global) governing the activation of the motion of the structure, performed in the context of Limit Analysis. Subsequently the equation of motion of the system of rigid bodies is derived applying the Lagrange Equation. Finally a numerical application is carried out.