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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 108
Edited by: J. Kruis, Y. Tsompanakis and B.H.V. Topping
Paper 66

Equilibrium of Masonry-Like Vaults treated as Unilateral Membranes: Where Mathematics meets History

M. Angelillo1, E. Babilio2, A. Fortunato1, M. Lippiello2 and A. Montanino3

1Dipartimento di Ingegneria Civile, University of Salerno, Italy
2Dipartimento di Strutture, University of Napoli, Federico II, Italy
3Dipartimento di Ingegneria Civile ed Architettura, University of Pavia, Italy

Full Bibliographic Reference for this paper
M. Angelillo, E. Babilio, A. Fortunato, M. Lippiello, A. Montanino, "Equilibrium of Masonry-Like Vaults treated as Unilateral Membranes: Where Mathematics meets History", in J. Kruis, Y. Tsompanakis, B.H.V. Topping, (Editors), "Proceedings of the Fifteenth International Conference on Civil, Structural and Environmental Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 66, 2015. doi:10.4203/ccp.108.66
Keywords: old masonry, masonry vaults, unilateral.

In this paper, we study the equilibrium of masonry vaults, assuming that the material has infinite friction and no cohesion (i.e. it is No-Tension in the sense of Heyman). With Heyman's assumptions, the equilibrium of a structure composed of this ideal masonry material, can be studied with limit analysis. In particular, the present study is concerned with the application of the safe theorem of limit analysis to masonry-like vaults, that is, curved constructions modelled as continuous unilateral bodies. On allowing for singular stresses in the form of line or surface Dirac deltas, statically admissible stress fields concentrated on surfaces (and on their folds) lying inside the masonry, are considered. Such surface and line structures are unilateral membranes/arches, whose geometry is described a la Monge, and their equilibrium can be formulated in Pucher form. It is assumed that the load applied to the vault is carried by such a (possibly folded) membrane structure S. The geometry of the membrane S, that is of the support of the singularities, is not fixed, in the sense that it can be displaced and distorted, provided that one keeps it inside the masonry. Two particular case studies are analyzed to illustrate the method: a cross vaults of the Gothic Cathedral of Caserta, and a modern timbrel spiral stair built by the Guastavinos in New York.

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