Studying the dome of Pisa cathedral via a modern reinterpretation of Durand-Claye’s method

A Parametric Study of Masonry Domes Equilibrium via a Revisitation of the Durand-Claye Method

“…According to Durand-Claye, the hoop forces in the anneau are responsible for a further reduction of the stability area, since they would call for additional limit conditions on the masonry compressive and tensile strength. As already observed by the authors in [2,3], this result is incorrect: the hoop forces could be distributed over the lateral lune's surfaces, not only at the anneau and, more importantly, hoop forces could modify the shape of the thrust surface by providing stabilizing effects. Another critical issue related to Durand-Claye's method in its original formulation is that it does not adequately consider the kinematic aspects related to the limit equilibrium condition for the entire dome.…”

“…In previous contributions, the authors have Claye's method in its original form as well as the stability of symmetrical masonry a 3]. With reference to masonry domes, t proposed by the authors in [2,3] axial force and bending moment, method has been suitably extended in order to assess the stability of the entire dome, suming nil tensile hoop forces.…”

“…In previous contributions, the authors have provided a detailed descri in its original form as well as re-elaborated versions enabling symmetrical masonry arches [6][7][8] and, more recently, domes With reference to masonry domes, the modern formulation of Durand proposed by the authors in [2,3], expresses the complex graphical construction in terms of g moment, in order to draw the stability area for a single lune. suitably extended in order to assess the stability of the entire dome, es.…”

“…To assess the stability of the entire dome while taking into account the critical remarks advanced in Section 2, the original stability area method has been further modified by accounting for the action of hoop forces in order to find statically admissible solutions. This involves applying the procedure described in detail in [2,3], where hoop forces are estimated by imposing equilibrium conditions. It should be noted that an analogous approach has been adopted also in historical [11][12][13] as well as recent [14] contributions.…”

“…According to the Durand-Claye method applied to masonry arches, if infinite friction is assumed, and the stability area reduces to a single point, the arch is in a limit condition and a kinematically admissible mechanism is triggered. In [2,3] the authors have shown that this last statement does not generally hold for domes; nevertheless the method is still considered worth of attention, as it enables checking in a comparatively easy way the existence of statically admissible solutions for a given dome.…”