Some remarks on historical sizing rules for arch-wall-piers systems

As is well known, the master builders of the Middle Ages did not follow any scientific approach in the modern sense. Despite this fact, they possessed a body of knowledge that allowed them to design safe structures. In this context, the sizing of arch-piers systems is a subject of great interest, in particular the historical rules - codified starting in the 16th Century - aimed at determining the minimum thickness of piers so as to guarantee system’s stability. The main purpose of this paper is to compare the effectiveness of some of these rules from a mechanical point of view. To this aim, the historical sizing criteria have been applied to two different examples. The first is a theoretical arch-wall-piers system dimensioned in accordance with one of the rules proposed by Rodrigo Gil de Hontañon; the second one is the magasin à poudre actually built in 1732 and collapsed before completing ribs removing, described by Frézier in his Treatise of stereotomy. This second case study is of particular interest, because Frézier not only documented a collapse condition but also gave a mechanical interpretation of it, by concluding that the collapse of the powder magazine occurred because of the weakness of its piers. The historical rules, applied to these two examples, provide different results one from the other in terms of minimum pier thickness. In order to investigate this issue, the mechanical behaviour of the two arch-wall-piers systems under examination has been studied in the framework of limit analysis, by means of a modern reinterpretation of Durand-Claye’s method. The limit thickness thus obtained has been compared to those provided by the ancient sizing criteria, with interesting implications about the safety degree provided by each of these rules as well as possible explanations for the collapse of the magasin à poudre.