ANALYTICAL DETERMINATION OF STATICALLY ADMISSIBLE THRUST SURFACES FOR THE LIMIT ANALYSIS OF MASONRY VAULTS AND DOMES

The present contribution addresses the issue of determining statically admissible stress fields in a masonry dome or vault subject to a given set of external loads. The proposed method is described in detail for the case where the masonry vault or dome is subject to axial- symmetric loads. The method makes use of suitable analytical solutions obtained for the so- called direct and inverse problems in which the vault is considered a thin shell. A stress field is fully characterized by its corresponding thrust surface, which can be thought as the natural extension of the thrust line for masonry arches. A stress field is admissible if the corresponding thrust surface is wholly contained within the vault thickness. The thrust surfaces are determined via a specifically developed iterative procedure. Iterations stop when all tensile stresses are ruled out and the surface is within the vault thickness. By means of the standard theorems of limit analysis, the thusly-determined stress fields can be used for obtaining estimation of the mechanical and geometrical safety factors for a given vault or dome. By way of example, the proposed procedure is applied to the case study repre- sented by the Pantheon’s dome in Rome.