Between geometry and mechanics: a re-examination of the principles of stereotomy from a statical point of view

The main objective of this paper is to give a mechanical interpretation of the geometrical principies guiding the art of stereotomy for designing masonry arches. The treatises on the coupe des pierres - even those published after the birth of modern structural mechanics - deal with the design of vaulted structures from an essentially geometrical point of view. For instance, the main issue of cutting voussoirs, as concerned the inclination of the joints, was dealt with in geometrical terms without taking any statical consequences into account. With reference to this problem, the coupe des pierres develops two geometrical criteria: the first requires that the joints converge at a single point (e.g. Villard de Honnecourt); the second requires that the joints be perpendicular to the intrados of the arch (e.g. Frézier). In order to determine the degree of stability corresponding to these geometrical criteria, the present paper analyses the problem of stonecutting in statical terms by considering the equilibrium of voussoirs in the absence of friction and cohesion. The works of Coulomb, de Nieuport and Venturoli are examined and the statical formulation of the problem is extended to some stereotomic constructions.