A no-tension analysis for a brick masonry vault with lunette

A large class of analysis methods has been developed during the last century for the study of masonry structures. Among them, the so-called unilateral no-tension model plays a fundamental role. Starting from the pioneer papers by Heyman in the second half of sixties, a new definition of the safety factor based on the equilibrium of the masonry structure as a no-tension body has been considered. The safety of the structure is mainly determined by its geometry rather than its material strength. The funicular analysis largely used in the 19th century has been improved in light of Heyman’s approach to obtain computational methods based on lower-bound solutions. Heyman’s hypotheses are the basis of the rigid no-tension continuous approach presented and applied to a barrel vault with lunette in the San Barbaziano church in Bologna. The masonry vault is modelled as a membrane (thrust surface) subjected to compressive stresses only, contained within extrados and intrados surfaces, and carrying uniform applied loads. The geometry of the unilateral membrane, described as an unknown smooth surface, and the associated admissible stress field are determined via a concave stress function necessary for equilibrium and unilateral constraints fulfillment. Special attention has been devoted to the singular stress field arising in the curves at the intersection of the vaults.