Influence of in-plane and out-of-plane stiffness on the stability of free-edge gridshells: A parametric analysis

Gridshells are form-resistant structures, which are suitable for covering large spans, especially when lightness and transparency are respectively relevant architectural and functional requirements. The majority of built gridshells are characterised by one ore more free-edges, which derive from trimming the gridshell reference surface in order to provide building access or to integrate the gridshell within existing structures. Up to now, only few scientific systematic studies have been devoted to the effects of elastic boundary structures on the stability of gridshells. This study aims at filling some gaps about this issue. To do so, an ideal free-edge bending-inactive hybrid single-layer gridshell is analysed. The gridshell sensitivity to the flexural stiffness of the boundary arch and to the shear stiffness of the gridshell are investigated through an extensive parametric analysis, which was performed by means of numerical experiments. Results are first discussed in terms of the well-established load factor and buckling shape. Then a complementary mechanical reading is provided by introducing ad-hoc conceived local metrics of the in-plane and out-of-plane deformations at collapse. Three different mechanical regimes at collapse are outlined. In conclusion, a range-finding chart within the design parameter space is proposed to orient the structural analyst in the choice of the preferred regime.