Static analysis of masonry vaults, constitutive model and numerical analysis

The paper deals with some of the explicit and numerical methods used for modeling the mechanical behaviour of masonry vaults and domes. After a brief description of the constitutive equation of masonry-like materials, a numerical method for the structural analysis of masonry vaults is presented. Then, the concept of maximum modulus eccentricity surface for masonry vaults is recalled. Subsequently, the collapse load and the corresponding mechanism are explicitly calculated for two particular cases: a circular plate subjected to a permanent load acting on the lateral surface and a variable vertical load applied to the extrados, and a spherical dome subjected to its own weight and variable point load applied to the keystone. The exact solutions are compared to the numerical results obtained via finite element analysis. Lastly, a study of the dome of the church of Santa Maria Maddalena in Morano Calabro is described. The method has enhabled the stress field and the fractures distribution in the dome to be determined and the maximum modulus eccentricity surface evaluated.