Limit equilibrium analysis of masonry arches

Abstract

In this paper, we revisit the limit equilibrium analysis of masonry arches. Firstly, the major contributions during the last three centuries associated with geometric and energy formulations are discussed, and subsequently, the paper explains that the problem of determining the minimum thickness of a masonry arch capable to support its own weight has multiple solutions. The infinite many neighboring solutions for the minimum thickness of a masonry arch result from the infinite many possible directions of rupturing that an arch with finite thickness may develop when becoming a mechanism. Given this infinite number of physically admissible rupturing directions, the energy approach expressed with the principle of stationary potential energy emerges as the most powerful tool to analyze masonry arches at their limit equilibrium state. The paper concludes that vertical rupturing is the most critical rupturing direction since it results to the largest value of the minimum thickness that an elliptical arch needs to support its own weight. For the common case where there is an intrados layer of voussoirs with physical joints perpendicular to the intrados, the initial rupture has to first follow the physical joint; therefore, the broken rupture pattern reported by Lame and Clapeyron in 1823 corresponds to the larger value of the minimum allowable thickness.