This study presents a practical method for three-dimensional static equilibrium analysis for masonry vaults using funicular networks. The method, a nonlinear extension of Thrust Network Analysis, is explained, and through three exemplary case studies, the potential of this new research is demonstrated. These examples discuss different assumptions on the "flow of forces" in Gothic quadripartite vaults; visualize the flat-vault equilibrium of rose windows under wind loading; and provide a stability analysis of the intricate nave vaults of Sherborne Abbey, Dorset, England. The presented approach provides insights in structural redundancy of unreinforced masonry structures by quantifying lower bounds on the geometric safety factors. The method for efficient funicular analysis of complex vault geometries furthermore provides the foundation for a fully three-dimensional funicular analysis implementation, extending thrust line analysis to three-dimensional thrust networks, for historic masonry. Keywords: unreinforced masonry structuresGothic vaultsGothic rose windowsflow of forcesequilibrium analysislimit analysisfunicular analysisthrust network analysisgeometric safety factor ACKNOWLEDGMENT The first author is thankful for the discussions with Prof. John Ochsendorf on the case studies in Sections 4.1 and 4.2.1 during his doctoral studies at MIT.
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