Hinging Mechanisms of Masonry Single-Nave Barrel Vaults Subjected to Lateral and Gravity Loads

This paper investigates the limit states of a circular masonry arch supported on rectangular buttresses when subjected to lateral inertial loading in addition to gravity loading by employing the principle of stationary potential energy. Depending on the slenderness of the arch compared to the slenderness of the buttresses, the study identifies two lower failure mechanisms: (1) a four-hinge mechanism within the arch alone; and (2) hinging of the arch in three locations together with a hinge at the base of the downstream buttress. In this analysis, radial ruptures are assumed for the arch, while the buttresses may rupture either horizontally or develop an oblique elongation failure along which the compression-free portion of the buttress separates. It is concluded that the hinging mechanism that triggers an oblique elongation failure of the downstream buttress is the most critical and initiates at a lower value of the seismic coefficient than the value associated with the mechanism that involves a horizontal fracture at the buttress. Finally, it is shown that the discrete-element method (DEM) captures the results of the proposed variational method with remarkable accuracy.