Between stereotomy and mechanics: joints inclination and minimum thickness in frictionless pointed and circular arches

This research is inspired by an issue strictly linked to the art of stereotomy and rarely tackled in the contributions on the statics of arches and vaults, i.e., the search of the inclination to be assigned to each joint able to ensure the respect of the equilibrium conditions when the friction between the voussoirs is absent, by assuming that the intrados and extrados curves are known. After presenting some brief notes on the state-of-the-art on this subject, both a numerical and an analytical approach, based on the maxima and minima Coulomb method revisited through a re-edition of Durand-Clayes method, is developed in order to determine the inclination of the joints as well as the minimum archs thickness compatible with equilibrium. The analysis is performed for frictionless pointed and circular arches for different values of the embrace angle (i.e., the complement of springing angle).