Static Analysis of Cross Vaults: The Case of the Cathedral of Casertavecchia

In the present paper, on assuming that the material has infinite friction and no cohesion, i.e. it is No-Tension in the sense of Heyman, we study the equilibrium of cross vaults of unequal rise, such as those of some Romanesque and Gothic churches. In particular the case study of the lateral cross vaults of the Cathedral of the old town of Caserta is analyzed. The scope of the paper is not to study in detail and quantitatively any particular vault, rather we give a compressive equilibrium solution (compatible with the unilateral material assumption) for the general case of cross vaults, constructed on arches of unequal rise, and loaded by a uniform load. For the purpose of the structural analysis, the vault is modelled as a thin shell made of Rigid No-Tension material. The webs of the vault that we consider, are supported on two crossing ribs. To obtain the axial force inside the ribs, equilibrated and singular stress fields (that is stress fields concentrated on curves and balanced with the loads) are constructed. An estimate of the thrust forces transmitted by the vault to the peripheral arches and walls is also obtained, so that the stability of these structures can be checked.