A novel graphical assessment approach for compressed curved structures under vertical loading

Geometry forms the basis for the study of equilibrium of masonry structures. The dependence of the stability of masonry structures on geometry rather than on material strength was well known to the ancient builders who, over time, empirically worked out rules of proportion for good structural building design. We propose a new graphical approach to assess, the equilibrium in compression for planar and non-planer arches and curves according to the Safe Theorem of Limit Analysis. The approach extends an existing two-dimensional funicular polygon strategy into three dimensions for the first time. The method finds robust applications in the study of masonry flying staircases made of monolithic blocks, giving an alternative for equilibrium to the pure torsional solution. The advantage of the presented approach is that it can be solved solely graphically. The approach is demonstrated by assessing the equilibrium of the main flying or open-well staircase in the Palazzo delle Poste (Trapani, 1924, designed and constructed by Francesco La Grassa), an expressive yet poorly understood structure.