Three-dimensional Equilibrium Analysis of Gothic Masonry Vaults

Block P. and Lachauer L.
International Journal of Architectural Heritage
doi: 10.1080/15583058.2013.826301

This paper introduces a practical method for three-dimensional equilibrium analysis for masonry vaults using funicular networks. The technical core of the method 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, adding to a long historical debate on this topic; visualize the shallow 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, based on Thrust Network Analysis, furthermore provides the foundation for a fully three-dimensional limit analysis implementation for historic masonry.


    author  = "Block, P. and Lachauer, L.",
    title   = "Three-dimensional Equilibrium Analysis of Gothic Masonry Vaults",
    journal = "International Journal of Architectural Heritage",
    year    = "2014",
    volume  = "8",
    number  = "3",
    pages   = "312--335",
    month   = "",
    doi     = "10.1080/15583058.2013.826301",
    note    = "",

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