Una possibile rilettura del problema dell’arco tra geometria e meccanica

The purpose of this paper is to look into the problem of the inclination of the joints between the voussoirs of an arch. Examining the historical literature on this subject, from the treatises of stereotomy to the first mechanical theories, it is interesting to observe that only two authors, Coulomb and Venturoli, studied this thema from a statical point of view. Starting from the problem of the flat arch of Coulomb, more complicated examples are here presented and, by reference to Venturoli’s Treatise, an interpretation in differential terms is proposed, in order to found the law which governs the inclination of the joints, if the voussoirs are rigid elements without friction nor cohesion between the joints. Finally, a formulation of the problem according to the principle of virtual works is here given.