# Parametric stability analysis of groin vaults

Maia Avelino R., Iannuzzo A., Van Mele T. and Block P.
Applied Sciences
MDPI
2021
doi: 10.3390/app11083560

This paper presents a parametric stability study of groin, or cross vaults, a structural element widely used in old masonry construction, particularly in Gothic architecture. The vaults’ stability is measured using the Geometric Safety Factor (GSF), computed by evaluating the structure’s minimum thickness through a Thrust Network Analysis (TNA). This minimum thickness is obtained by formulating and solving a specific constrained nonlinear optimisation problem. The constraints of this optimisation enforce the limit analysis' admissibility criteria, and the equilibrium is calculated using independent force densities on a fixed horizontal projection of the thrust network. The parametric description of the vault’s geometry is defined with respect to the radius of curvature of the vault and its springing angle. This detailed parametric study allows identifying optimal parameters which improve the vaults' stability, and a comprehensive comparison of these results is made with known results available for two-dimensional pointed arches. Moreover, an investigation of different force flows, represented by different form diagrams is performed providing a better understanding of the vaults' structural behaviour, and possible collapse mechanisms are studied by observing the points where the thrust network touches the structural envelope in the limit states. Beyond evaluating the GSF, the description of the groin vault’s stability domain is carried out to give additional insights into the structural robustness. Finally, this paper shows how advances in equilibrium methods can be useful to understand and assess masonry groin vaults.

BibTeX

@article{MaiaAvelino2021,
author  = "Maia Avelino, R. and Iannuzzo, A. and Van Mele, T. and Block, P. ",
title   = "Parametric stability analysis of groin vaults",
journal = "Applied Sciences",
year    = "2021",
volume  = "11",
number  = "8",
pages   = "3560",
month   = "April",
doi     = "10.3390/app11083560",
note    = "Special Issue 'Theory and Modelling of Historic Masonry Architecture', Eds. C. Cennamo and C. Cusano",
}

Related publications

Computers and Structures,2021.submitted for review.
Proceedings of the SAHC Symposium 2020 (postponed to 2021),Barcelona,2021.
Proceedings of the SAHC Symposium 2020 (postponed to 2021),Barcelona,2021.abstract accepted .

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