Impacts analysis in the rocking of masonry circular arches

Aim of the paper is the study of the rocking of the masonry arch that, hit by a horizontal impulse of acceleration, moves sideways according to a mechanism u− defined by four hinges. The arch, once reached a maximum side displacement, inverts its motion going back, still moving along the same mechanism. At a time instant t, it reaches the zero configuration and it cannot continue its motion along u− because all the hinges of this mechanism are now blocked. A reverse mechanism thus takes place. The arch mobilizes the new mechanism u+ that has the “mirror” positions of the hinges of the mechanism u−. A new impact model, alternative to the ones available in literature and pointing out all the questionable problems, is proposed in this paper. It is thus shown that impacts occur in the points where are located the hinges of this new mechanism u+: energy losses take place at these impact points. It is shown that the arch presents a coefficient of restitution lower than the one of the solid column, due to the existence of multiple impact sections. Furthermore, the energy dissipation increases with decreasing values of the angle of embrace of the arch. Then the arch, in its rocking motion, continues to move back and forth, slowing down, up to the stop of the motion. The paper will thoroughly analyze all the stages of motion evaluating, by means of the Principles of Impulse and of the Angular Momentum, the coefficient of restitution, i.e. the changing, occurring at the impacts, of the kinetic energy of the arch.