Static analysis of a double-cap masonry dome

The present work is focused on the analysis of the double-cap dome of St. Januarius Chapel, in Naples (Italy). Three different approaches based on the limit analysis for unilateral (no-tension) material has been applied to evaluate the dome stability. In the first approach, the overall stability of the dome has been investigated through a method of graphical statics. The method is a generalization of the “thrust line analysis” used for arches and consists in finding a purely compressed membrane in equilibrium with the external loads and entirely contained in the thickness of the dome, in the spirit of safe theorem. In the second approach, which is concerned with the equilibrium of domes and vaults, a thrust surface in equilibrium with the assigned external loads is found by numerically solving the Pucher’s differential equation. This latter is nothing but the equilibrium of the unknown thrust surface along the direction of vertical, i.e. gravitational, loads, where generalized stresses are conveniently projected on the platform, that is in the horizontal plane. Again in the spirit of the safe theorem, the thrust surface must be entirely contained within the volume of the structure. The solution procedure is based on the finite difference technique and has been implemented in a Mathematica-based code. Finally, in the third approach, a three-dimensional rigid block model with no-tension, frictional interfaces is employed. The formulation and the solution procedure of the underlying limit analysis problem has been implemented in a MATLAB-based tool equipped with a graphical user interface. The obtained results allow to state that the dome, under ordinary load conditions, is safe