Two Different Approaches for Collapse of Nonsymmetric Masonry Arches: Monasterio’s Treatment versus Limit Equilibrium Analysis

Abstract

This research can be viewed as a development of the critical review of the Monasterio’s manuscript Nueva teórica sobre el empuje de bóvedas, proposed by the authors in previous studies; this unpublished manuscript is devoted to the collapse of nonsymmetric masonry arches, modeled as an assemblage of rigid voussoirs, infinitely resistant to compression, and characterized by nil strength to tension and finite friction. As its starting point, the current work examines the conditions identified by Monasterio for the activation of the pure sliding collapse mechanism: his approach is applied to a case study, i.e., a nonsymmetric arch of a given geometry, by showing some critical aspects related to the apparent independence of the collapse from the thickness of the arch. Thus, an alternative formulation based on an appositely developed mixed approach is proposed that allows for identifying under the hypothesis of finite friction some critical issues related to nonstandard behavior. This approach shows that the search for the various collapse mechanisms depends on the general equilibrium conditions of the arch, expressed as a function of the internal reactions—that is thrust and shear acting at the key joint—by extending Coulomb’s method of maximis and minimis to the case of nonsymmetric arches. The activation of the various collapse mechanisms—in particular those by pure sliding and mixed type—is therefore identified only after having determined the rotational equilibrium domain and its intersection with the sliding domain allowed by friction performance.