Vol. 13, No. 5, 2018

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Resistance of flat vaults taking their stereotomy into account

Mathias Fantin, Thierry Ciblac and Maurizio Brocato

Vol. 13 (2018), No. 5, 657–677
Abstract

We study the structural performance of flat vaults, depending on the patterns of voussoirs. For this purpose, we propose three archetypes, derived from the 18th–19th century literature on stereotomy, with fit simplifications.

The ultimate structural answer of these models are evaluated, searching numerically for statically admissible loading conditions by means of an enhanced version of the thrust network analysis, assuming failure occurring by joints’ opening, crushing or sliding, while voussoirs remain rigid.

The considered enhancements allow one to better capture the contact forces acting on the joints and to define consistently the safety factor of the structure. They are based on the introduction of additional partial branches in the thrust network that represent actions internal to the voussoirs and are essential to describe, at least in some cases, their rotational equilibrium, which is neglected by the standard analyses.

The three examples are compared by superposing their domains of statically admissible loadings, represented in terms of vertical uniformly distributed load vs. thrust. Our findings support but partly some of the conjectures presented in the 18th century and later literature, especially because of a plate effect that can be observed at the corners of these structures. They also allow us to classify flat vaults according to the local shape of the force network, as elliptical, parabolic or hyperbolic, thus opening to a new interpretation of their nature.

Keywords
vaults, stereotomy, limit analysis, thrust network analysis
Milestones
Received: 16 June 2018
Revised: 28 January 2019
Accepted: 4 February 2019
Published: 6 April 2019
Authors
Mathias Fantin
Laboratoire GSA
ENSA Paris-Malaquais
Paris
France
Thierry Ciblac
Laboratoire GSA
ENSA Paris-Malaquais
Paris
France
Maurizio Brocato
Laboratoire GSA
ENSA Paris-Malaquais
Paris
France