The maximum modulus eccentricities surface for masonry vaults and limit analysis

This paper presents a constitutive equation tbr masonry vaults which associates to each pair of generalized strains (A . K), with A the strains and K the curvature changes of the mean surface, the pair of generalized internai forces (N, M), with N and M the normal forces and bending moments per unit length. respectively. The maximum modulus eccentricities surface, which plays a role analogous to that of the line of thrust for arches. is defined and its main propertìes are proved. Subsequently, thè limit analysis for masonry vaults is set forth and the static and kinematic theorems stated. The theory is then applied to determination of the collapse load for both a plate subjected to a lateral pressure and an increasing vertical force, and a spherical vault subjected to its own weight and a point load applied at the crown.