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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’s 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 was performed with known results available for two-dimensional pointed arches. Moreover, an investigation of different force flows represented by different form diagrams was performed, providing a better understanding of the vaults’ structural behaviour, and possible collapse mechanisms were studied by observing the points where the thrust network touches the structural envelope in the limit states. Beyond evaluating the GSF, the groin vault’s stability domain was described 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.

This article discusses design strategies to improve the mechanical behavior of elastic gridshells with singularities. The advantage of meshing with one or more singularity is to allow a wider range of surfaces to be meshed with equal-length, quadrilateral meshes, known as Chebyshev nets. However, the application of this meshing process will influence the fabrication and the mechanical behavior of the structures. The erection process is simulated by means of the dynamic relaxation method, bending the bars to their final position. This simulation shows that a facetted shape is found instead of a smooth surface. This deformed shape makes the structure softer under applied gravity load. Two strategies are investigated in this paper to enable the construction of gridshells with singularities. The first consists in extending the bars close to the singularities edge-lines to have a smother gridshell after the erection process. The second strategy applies post-tension cables to the patches to increase the local curvature in the faceted zones. Both strategies increase the stiffness and buckling load of the final structure.

In recent years, our (academic/theoretical) understanding of the behaviour of unreinforced masonry (URM) structures has improved significantly, and many advanced technological solutions for conservation have been developed. However, there is still a lack of appropriate methods and tools that can be used for the assessment of URM structures in every day practice. Therefore, since 2018, the Block Research Group has been working on "Practical Stability Assessment Strategies for Vaulted Unreinforced Masonry Structures" with support of the Swiss National Science Foundation (SNSF). The goal of this research project is to create tools suitable for everyday engineering practice and to develop appropriate analysis strategies for diverse contexts and circumstances related to the availability of time, budget and available data. The main outcome is COMPAS Masonry: an open-source, Python-based computational framework for the assessment of URM structures. It provides a general purpose toolbox for working with assemblies (compas_dem) and three custom made open-access solvers that can deal with different aspects of the assessment of masonry structures: compas_tna based on Thrust Network Analysis, compas_prd based on the Piecewise Rigid Displacement method, and compas_rbe based on the Rigid Block Equilibrium. INTRODUCTIONUnreinforced masonry (URM) is one of humankind's longest-lasting construction methods and forms the structural basis for most of the residential buildings all over the world. The assessment of URM structures is an atypical mechanical problem: constructions are comprised of individual discrete elements; large displacements and deformations are common, and, particularly for historic buildings, material properties and boundary conditions are unknown or unknowable.Many of the structural analysis tools/software available today were developed for entirely different structural systems with very different materials such as steel, concrete and timber, and