Collapse of masonry arches in Romanesque and Gothic constructions

Round and ogival (or pointed) arches are found bearing the weight of the vertical walls in many vaulted masonry structures, especially architectural designs typical of the Roman- esque and Gothic periods. It would therefore appear interesting to examine such arch-wall sys- tems and attempt to determine the stress levels as a function of the relevant geometrical and me- chanical parameters and assess their safety margin with respect to conditions of incipient collapse, as well as the actual mechanism by which such collapse would occur. A simplified ver- sion of the problem can be studied by following two different approaches, which are in fact com- plementary to each other. The first, which is based on a proper extension of Durand-Claye’s method of the stability area, aims at determining the set of statically admissible solutions within the limits imposed by the material’s ultimate compressive and tensile strengths and the limited shear capacity of the joints. When such area shrinks to a point, a limit equilibrium condition is at- tained in the arch-wall system. The second approach instead studies the stress and strain fields generated in the arch, which is considered to be made of material offering poor resistance to ten- sion and whose mechanical behaviour can be modelled, as a first approximation, via a non-linear elastic constitutive relation. In this case, the problem is addressed by studying and numerically in- tegrating systems of non-linear equations. The condition of incipient collapse is considered to be reached when the residual stiffness of the system falls below a predetermined fraction of its initial value. As will be shown, the two approaches, rather than offering two alternative paths, actually provide two complementary views of the same problem.