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 symmetric collapse modes for an arch are thoroughly described. As it was expected, pointed and circular arches show different collapse behaviors. Limit values of arch thickness and friction coefficient are assessed. The results obtained are compared with those given by Michon in 1857.