Long-span roofs: Design solutions for free-edge barrel vault gridshells

Long-span roofs have held significant importance in both architectural and engineering fields, evolving alongside technological advancements in materials and their intrinsic properties. The concept of gridshell emerged within this framework as a lightweight, form-resistant structural typology capable of spanning large distances with minimal material thickness and weight. This revolutionary aspect enabled gridshells to be widespread worldwide, especially where lightness and transparency were paramount design criteria. The membrane-like structural behaviour of gridshells involves the high degree of structural efficiency of these structures, but also results in a propensity for buckling instability, which have been studied over time. The need to adapt gridshells to existing structures as well as ensuring accessibility has led gridshells to be designed with free-edges. They are achieved by trimming the reference surface and result in breaking the continuity of their spring line. The free-edges compromise the membrane behaviour of gridshells, and involve bending internal forces and large displacements, in addition to persisting stability issues. The MSc Thesis aims to propose design solutions for free-edge gridshells and to assess their structural performances. The study takes advantages of FreeGrid benchmark focusing on the Barrel vault DBG with the aim of testing DSGs that enhance the performance of the DBG and restore the membrane behaviour. The assessments were conducted through a holistic approach, synthesized by FreeGrid into partial metrics of Structural, Buildability and Sustainability performances. The initial phase of the research focused on the ULS and SLS analyses of the DBG mechanical behaviour through a 3D FEM model. Based upon these latter analyses, several DSGs were proposed, conceived. For each DSG, a preliminary ULS and SLS analysis returned as output two main Structural performance partial metrics: the critical Load Factor from the load-displacement curve, identifying the instability regime at ULS; the maximum vertical displacements at SLS. These evaluations served as a touchstone for assessments of the Structural performances among the DSGs and with reference to the DBG. The second phase was devoted to the detailed analysis of few DSGs, selected as the most effective in terms of Structural performance. For each of these DSGs, the ULS assessment provided as outputs the load-displacement curve linked to element plasticization; the SLS assessment evaluated maximum normal and tangential displacements, axial forces and bending moments, all normalized with respect to the corresponding peak values of the DBG. Lastly, for each selected DSG, partial performance metrics as well as the overall performance metric were computed and evaluated in relation to the DBG. The analyses revealed that each DSG reinstates the dominance of membrane behaviour, thereby reducing the occurrence of fully and partially plasticized members and shifting each gridshell into a global instability regime. The selected DSGs marked an improvement in Structural performance terms with respect to the DBG, although none satisfied the displacement threshold. Each DSG exhibited an enhancement in the overall Bulk metric, despite the decrease in Buildability and Sustainability performances. In light of these assessments, the future phasis of research could involve final sizing of strucural members as well as testing further shape variations, with the aim of fulfilling the threshold set by the benchmark.