Equilibrium of Masonry Domes: a case study.

The work is focused on the vicissitudes concerning the reconstruction and the repair of a Neapolitan masonry dome, damaged by two earthquakes between the end of XVII and the beginning XVIII century. The study of some documents such as tenders, reports and building yard diary gives a first general outline on the planning aspects, on the construction rules and on the reinforcement techniques. Because of the repair and strengthening works several conflicting debates on the diagnosis of the cracks were set up. The debates involved field experts and mathematicians who dealt with the topic of the domes, taking into account geometrical factors, materials and “good building” rules. In the present paper we try to give a diagnosis of the damages suffered by the dome by employing a new approach based on a no-tension model proposed by Angelillo and Fortunato. The proposed method, concerned with the equilibrium of vaults, looks for a compressive thrust surface S, in equilibrium with the applied loads, contained within the extrados and the intrados surfaces of the structure. The dome structural behaviour is investigated on the basis of classical shell theory where the stresses along the meridians and parallels projected over the planform of the dome. The membrane S is partitioned in two regions: region 1 in biaxial regime and region 2 in uniaxial regime. The boundary between region 1 and region 2 is an unknown circle depending on the external loads. The equilibrium problem is referred to a potential of the stresses projected on the dome base (Pucher’s approach). The loads are supposed to be fixed and the surface S is the relevant unknown of the equilibrium problem. S is found with an iterative procedure, starting from a tentative surface S°, contained within the dome thickness.