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A triangular parabolic cross vault, that was designed by Musmeci in the 1950s as a reinforced concrete structure but remained unbuilt, is revisited from the original perspective of its reinvention as a masonry structure. In the framework of static limit analysis under classical Heyman's assumptions, a generalized thrust network analysis is adopted for a structural safety assessment. The performances of the vault, subject to its self-weight, are investigated through minimum-thrust and minimum-thickness analyses by conforming to the original geometry and assuming the vault thickness as the only design parameter. Further insight is achieved by exploring a more general class of triangular parabolic masonry cross vaults, whose rise-to-span ratio is an additional design parameter. The static efficiency of the smart and unconventional geometry proposed by Musmeci is thus proven, motivating the possibility of bringing it to new life in the form of a masonry structure. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]