Impacts analysis in the rocking of masonry circular arches

The in-plane rocking of a masonry arch is studied. The starting motion of the arch is assumed to take place along the four-link failure mechanism u corresponding to a constant distribution of horizontal loads proportional to the arch self-weight. During such a motion, if overturning does not occur, the arch returns to the undeformed configuration, with all the hinges of the mechanism u simultaneously closing. At such an instant, impacts occur, implying a motion exchange and a subsequent movement of the arch along a new four-link mechanism u’. A novel impact model, different from the one available in literature, is here proposed. The restitution coefficient is computed by applying the linear and angular momentum impulse theorems. The rocking mechanism u’ of the arch after the impact is determined under the condition of minimum energy expense at the impact.