Masonry domes. Comparison between some solutions under no-tension hypothesis

The first work that is concerned with equilibrium problem of vaults and domes dates back to May 19th 1734; the author of this work was the mathematician Pierre Bouguer (Bouguer 1734). Also being the first author to be concerned with the subject Bouguer’s treatment of the problem contains, even if only in qualitative way, the consideration of the main of the characteristic of the behaviour of these structures: the two-dimensionality. In practical Bouguer realizes that the behaviour of the structure cannot be always reduced to a series of arches approached each other, but a transmission of stresses also along the parallels of the solid of revolution exists. The author deals with the two characteristic topics of the problem: the search of a geometry shape of the vault with an assigned thickness and the dual case in which, in case that the lower surface is assigned, the aim is to determine the variation of the thickness. In commenting on the various types of suggested meridian curvature (conical domes, conical vaults and spire vaults), Bouguer asserts that the resultant of the actions transmitted from the upper part of the vault can intercept the joint of interface with a non orthogonal angle. This hypothesis, added to the absence of friction one, coincides with the statement that the stability of the structure depends not only on interactions along the meridian line, but also along the parallel line. In fact Bouguer writes that if the resultant of the actions transmitted from the upper part of the vault intercepts the joint of interface with an angle that points out the tendency of the voussoir to slip towards the inside of the dome “& c’est ce qui ne peut point arriver, puisque tous les autres Voussoirs de la meme assise s’y opposent, en faisant un égal effort” (Bouguer 1734, 150).