Studying the Dome of Pisa Cathedral via a modern reinterpretation of Durand-Claye’s method

The dome of Pisa Cathedral is a masonry structure of great interest for many aspects related to history, architecture, building techniques as well as geometry and mechanical behaviour. The Romanesque dome presents a peculiar shape with an oval base and a pointed profile. The opportunity provided by the scaffolding recently assembled for the under-way restoration works, in preparation for the 900th anniversary of the Cathedral dedication, offered a privileged context, also thanks to the cooperation of the Opera della Primaziale Pisana, which allowed for developing a research project aimed at an overall analysis of the dome, covering its shape, building details, material properties and the state of preservation of the intrados and extrados surfaces. The present contribution is part of the aforementioned research project. It focuses on a modern translation of Durand-Claye’s method, in order to perform a preliminary study of the mechanical response of the dome. In his memoir published in 1880 [2] Durand-Claye extends his stability area method - originally conceived for masonry arches - in order to assess the equilibrium of domes of revolution. As already done by the authors in some previous works on masonry arches [3], here we propose a modern reinterpretation and an enhancement of the original Durand-Claye’s method. The equilibrium problem is solved by means of an in-house, expressly developed algorithm implemented in Mathematica, which accounts for the specific shape of the dome. As a first model, each lune is assumed to be independent from the others. Then, by assuming that tensile hoop stresses are not admissible in masonry structures, we further extend the method proposed by Durand-Claye for spherical domes, by explicitly taking compressive hoop forces into account to the aim of obtaining statically admissible solutions. The results obtained seem able to provide an estimate of