A numerical tool for assessing the stability of masonry arches and domes via Durand-Claye’s method

This paper reports on a numerical tool addressing both masonry arches and domes; developed by the authors, it is based on a revised and enhanced version of the historical method proposed by Durand-Claye (1867). Durand-Claye’s method is one of the graphical procedures formulated in the 19th century for determining the line of thrust in masonry arches. It aims at defining the so-called area of stability at the crown section of a symmetric arch, that is to say, the locus of points formed by the extremes of the vectors representing admissible crown thrusts (i.e. those satisfying both the equilibrium of the structure and the strength of masonry). In the enhanced version developed by the authors, Durand-Claye’s method is able to account for a nonlinear stress distribution both in tension and in compression. More specifically, the original method has been modified by assuming that the limit condition of each joint is reached when a bi-rectangular distribution of the stresses occurs, which corresponds to the attainment of a limit value for the bending moment. In 1880 Durand-Claye extends his stability area method - originally conceived for masonry arches - in order to assess the equilibrium of domes of revolution. The authors have re-visited Durand-Claye’s approach in order to assess the stability of masonry domes by significantly modifying it in order to adequately account for the presence of hoop forces and ensure kinematic compatibility as well. The present paper illustrates some results obtained via an expressly developed numerical tool based on a modern re-visitation of Durand-Claye’s stability area method. Furthermore, the flow chart, as well as the numerical procedure developed working within the Mathematica® software package, are accurately described. The modern version of this method turns out to be a particularly simple means for assessing the stability of masonry arches and domes, as it enables accounting for the masonry compressive strength, the friction coefficient, and the geometrical parameters.