Equilibrium of Pointed, Circular, and Elliptical Masonry Arches Bearing Vertical Walls

Abstract

This paper addresses the long-standing problem of the equilibrium of the circular, pointed, and elliptical arches commonly found in historical masonry buildings and bridges that are subjected to their own weight and the weight of superimposed masonry walls. The equilibrium problem is studied by applying two different complementary methods: the first is a simple extension and analytical re-reading of the Durand-Claye stability area method; the second is based on the application of a nonlinear elastic one-dimensional model, already used by the authors in previous studies. It is assumed that the arch’s constituent material has limited compressive strength and null tensile strength. In addition, the load transferred to the arch by the wall is determined under the common assumption that each vertical strip of wall bears directly down on the underlying arch element. The study focuses on the maximum height that the superimposed wall can reach under equilibrium conditions while maintaining acceptable values of arch residual stiffness. One noteworthy finding is confirmation of the decidedly better behavior of pointed and elliptical flat arches compared with that of circular arches.