Danila Aita

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

AbstractThis 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 valu...

Notes on Limit and Nonlinear Elastic Analyses of Masonry Arches

This chapter is a critical presentation of studies over the last 10 years on the mechanical response of masonry arches and vaults. More precisely, we focus on a study of masonry arches conducted in parallel via both nonlinear elastic and limit analyses. The one-dimensional elastic model for masonry arches incorporates a simple but effective nonlinear constitutive law. In turn, collapse analysis is performed by the so-called ‘method of stability areas’, originally proposed by Durand-Claye in 1867. Rather than offering two alternative paths, the approaches may be considered complementary points of view on the same problem. A reasoned illustration of the concepts in question is furnished by the topics addressed: an analysis of the possible failure mechanisms of a pointed arch subject to its own weight; the search for explicit solutions to the equilibrium problem of a depressed arch subject to a uniformly distributed load; the study of arches of different shapes subject to their own weight and the weight of a superimposed wall.

Analysis of rotational and sliding collapse modes of masonry arches via Durand-Claye’s method

In this paper the mechanical behavior of circular and pointed masonry arches subject to their own weight is examined in order to determine their collapse modes. Different arch’s shapes and thicknesses are considered; the influence of the friction coefficient on the arch collapse is analyzed as well. The safety level of arches is investigated by suitably reworking in semi-analytical form the stability area graphical method proposed by a renowned 19th century French scholar, Durand-Claye. Our analysis enables accounting for any given eccentricity of the thrust at the crown; furthermore, also the strength of masonry is taken into account. According to Durand-Claye’s method, the arch is safe if along any given joint both the bending moment and the shear force do not exceed some given limit values. It is shown that attainment of a limit condition according to Durand-Claye corresponds to the onset of a collapse mechanism characterized by either relative rotation or sliding between masonry units. All possible sy...