A simple structural model for a masonry arch-wall system subjected to dead vertical loads

Arches of various sizes and shapes can be found bearing the weight of vertical walls in almost all ancient masonry buildings. The most common arch shapes are round, or semicircular, and pointed, the so-called ogival arch, typical of Romanesque and Gothic architecture. The aim of this work is to study such structural systems by considering them composite systems made up of an arch and an overlying wall, both made of masonry. The study applies a simple mechanical model, in which the arch and wall are schematized as one-dimensional elements, in general characterized by nonlinear elastic behavior. In the case that the displacements undergone by the arch are sufficiently small in comparison to those of the wall, it can be shown that the distribution of the loads transmitted by the wall to the arch differs considerably from the distribution deduced by assuming each vertical strip of wall to be sustained directly by the underlying arch element. Though rather small, such differences sometimes involve a critical difference in the load bearing capacity of the arch, calculated under the assumption that the arch’s constituent material cannot withstand traction and has limited compressive strength. The model enables, among other things, evaluating the effect on bearing capacity of substituting a semicircular arch with an ogival one of equal thickness and span. The results of such comparison clearly reveal the superiority of the latter arch type over the former in terms of the maximum possible height of the overlying wall under equilibrium conditions.