A Semi-analytical Approach for Masonry Arch Dynamics

Abstract

A semi-analytical approach is proposed for modelling the plane dynamics of a masonry arch, treated as a system of rigid elements with friction and unilateral contacts at each joint. By generalising the method proposed in previous research, the analytical approach is firstly applied to the plane dynamics of a rectangular block simply supported on a moving base. In this case, where the contact although sometimes extended is unique, dynamics is formulated as a frictional contact problem, and conditions for onset of motion according to various mechanisms are fully analytically identified; moreover, criteria for evaluating contact reactions during either smooth or non-smooth dynamics are outlined. The method is then extended to the case of the arch, where each element is characterized at most by a double extended contact; criteria for the onset of motion and evaluation for each element of contact reactions during the dynamic evolution are then identified. The approach proposed constitutes a first step for performing dynamic analysis through either an event-driven or a time-stepping numerical procedure.