Equilibrium of masonry vaults and open stairs

In this paper the unilateral model for masonry is applied to explain the equilibrium of vaults. In particular, the present study is concerned with the application of the safe theorem of limit analysis to spiral vaults, that is, curved constructions modeled as continuous unilateral bodies. On allowing for singular stresses in the form of line or surface Dirac deltas, statically admissible stress fields concentrated on surfaces (and on their folds) lying inside the masonry, are considered. The unilateral restrictions require that the membrane surface lies in between the extrados and intrados surfaces of the vault and that the stress function, representing the stress, be concave. Such a constraint is, in general, not satisfied on a given shape for given loads: in such a case, the shape has to be modified to fit the constraint. A particular application, namely the double spiral stair of Sanfelice’ palace in Naples, is considered.