Multi-Hinge Failure Mechanisms of Masonry Arches Subject to Self-Weight as Derived from Minimum Thickness Analysis

The present study investigates the relation between the optimal geometry (quantified via the minimum thickness) and the number of concurrent hinges at the masonry arch's limit state. The Heymanian assumptions regarding material behavior are adopted, and only constant thickness arches subject to static (i.e., self-weight) loading are considered. First, the only numerically verified completeness of the failure mode types (including 6 and even 7 hinges) of gothic arches is analytically proven. Next, it is investigated whether a higher number of hinges can concurrently occur for arbitrary, symmetric concave arches. A numerical procedure is presented which generates suitable arch geometries corresponding to a k-hinge mechanism, where k is an arbitrary odd integer not smaller than 5. For the generated class of arches, a higher number of concurrent hinges leads to lower minimum thickness values. However, it is explicitly proven that a higher number of hinges is not necessary for lower minimum thickness values. A small database about the geometry of the transversal arches of English and French medieval gothic cathedrals concludes the first part to allow comparison with the derived results. In the second part of the paper, existing literature results on the limit state analysis of gothic arches are extended by the effect of stereotomy on the failure mode type and minimum thickness value.