A no-tension model for the analysis of combined masonry vaults

The lower bound theorem of limit analysis and masonry vaults made with notension materials is the starting point of this paper. Statically admissible stress field, concentrated on surfaces and their folds contained into the masonry vault are taken into account. These ideal surfaces have the form of Dirac delta lines and surfaces for the stress field and can be considered as membranes/arches, in which the singular stress field represents the generalized stress surface. The unilateral assumptions give as a result a membrane contained in the thickness of the vault (the surface lies between extrados and intrados of the vault) and generalized compressive stress on the surface, i.e. a concave stress function. The equilibrium of the membrane can be written in the Pucher form, so that both the scalar stress function and shape function can be determined by the transverse equilibrium and unilateral conditions. The model can be generally applied to no-tension materials, such as masonry and concrete. The paper examines the classical combination of two vaults present in several architectural examples since the Roman age: a domical vault and a barrel vault. Particular attention is given to the fold between the two vaults. The case study is a Roman concrete combination in the plaster room in the Villa dei Papiri at Ercola.