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This paper presents a methodology to assess the stability of vaulted masonry structures using Thrust Network Analysis (TNA). It offers a new numerical strategy to compute the Geometric Safety Factor (GSF) of a given structure by directly evaluating its minimum thickness. Moreover, it provides an approach for tracing the vault’s stability domain based on its extreme thrust values, which indicates the robustness of the structure. Together, these outcomes represent a proper measure of the safety level of masonry structures. Such results are obtained from constrained nonlinear optimisation problems (NLPs) with appropriate objective functions and constraints enforcing the limit analysis’ admissibility criteria. Networks with fixed horizontal projection are considered, for which the spatial geometry is a function of the independent force densities and the height of the support vertices. A faster, interactive procedure is proposed to improve the selection of such independent force densities. The range of applications of the present method includes arbitrary network topologies and different support conditions. Beyond analytically described geometries, the method can deal with geometries obtained numerically (e.g. from point clouds). The presented strategy is implemented in a Python-based package, and relevant applications illustrate the method’s potential in assessing the stability of three-dimensional historic vaulted structures.
Avelino et al. (Mon,) studied this question.