Limit analysis of cloister vaults: the case study of Palazzo Caracciolo di Avellino

The equilibrium of cloister masonry vaults, treated as composed of unilateral material in the sense of Heyman, is the topic of the present work. For such a material, the safe and the kinematic theorems of limit analysis can be employed to detect equilibrium and nonequilibrium. In the spirit of the safe theorem, the structure is stable if a statically admissible stress field can be detected. On allowing for singular stresses, here we consider statically admissible stress fields concentrated on surfaces or lines lying inside the masonry vault. Such structures are unilateral membranes, whose geometry is described a la Monge, and the equilibrium of them is formulated in Pucher form, that is, in terms of the so-called projected stresses over the planform Ω. The problem, under purely parallel loads, is reduced to a single partial differential equation of the second-order, in two space variables, where the shape function f and the stress function F appear symmetrically. The unilateral restrictions require that the membrane surface S lies in between the extrados and intrados surfaces of the vault and that the stress function be concave. In the present work, by starting with a sensible choice of a concave stress function F, the transverse equilibrium equation is solved for f by imposing suitable boundary conditions. A cloister vault of Palazzo Caracciolo di Avellino, a XIV century building located along via dell'Anticaglia in Naples, is the case study. For two load conditions, membrane surfaces and geometrical safety factors are identified.