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

Abstract

Abstract: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.

La escalera de ojo abierto del Palacio Di Majo en Nápoles entre geometría y equilibrio

“…The method applied in this paper is the so-called membrane equilibrium analysis (MEA), originated in the paper on vaults (27) and further developed in (28). MEA is a general tool for computing the stress field on curved membrane surfaces (41), and it has also been adopted recently by the authors to assess the equilibrium of masonry domes (32)(33)(34)(35)(36)(37)(38)(39)(40)(41)(42)(43)(44)(45)(46). In the present work, we essentially used the ideas put forward in (33,47), by applying the method to open-well staircases, treated as cloister masonry vaults.…”

“…This approach has been extended to the current staircase. The analytical MEA version of this simplified geometrical approach can be found in (37)(38). The structure of Palazzo di Majo's staircase is doubly symmetrical, therefore to study the stability and consequently define the shape, the projection of the vaults and landings on a horizontal plane has been considered (Figure 11, a), identifying the polygonal region OABCDL shown in Figure 11, b.…”

Graphical and Analytical Quantitative Comparison in the Domes Assessment: The Case of San Francesco di Paola

“…Finally, Membrane Equilibrium Analysis has been proposed for the analysis of masonry vaults with a general shape, not restricted to axis-symmetric cases. Among others, the method has been applied to the cloister vault surmounting a room in Palazzo Caracciolo di Avellino, in Naples, under different load conditions [34], to the cross vaults of the Cathedral of Caserta Vecchia (Italy) [35], and the Gustavino helical stairs [36].…”

Some laser-scanner applications in structural analysis

“…The issue is complicated by the assumption that, at present, the laser scanner allows the acquisition of the external skin of the structure, and, thus, the cloud of points is spoiled by non-structural elements (such as walls in reinforced concrete buildings, plaster, cornices, tiles, etc.). This is the reason why most of the applications in the literature refer to masonry structures, where at least the vertical bearing elements may be given by visible masonry walls, the horizontal slabs are, often, supported by visible wood beams and the vaults may be free of lining and characterised by complex curvatures (Contestabile et al, 2016).…”