Buckling of spherical cap gridshells: A numerical and analytical study revisiting the concept of the equivalent continuum

• Different gridshell topologies and curvatures can have the same structural efficiency.
• Many definitions of the equivalent continuum can provide quick estimates for the buckling load.
• An equivalent continuum defined by axial stiffness provides a conservative buckling load.
• Triangular gridshells are sensitive to geometric imperfections; quadrilaterals are not.

The use of gridshell structures in architecture and structural engineering has risen in the past decade, yet fundamental research on the mechanics of such structures is lacking. The majority of gridshells built use either quadrilateral or triangular grids. In this paper, we assess the effect of the grid shape (triangular or quadrilateral), the grid spacing, and the span-to-height ratio on the failure load of spherical cap gridshells. The failure load is calculated using finite element methods and analytical methods derived from the equivalent continuum. Both a linear eigenvalue and a nonlinear analysis using geometric imperfections are performed and compared. While a triangular grid is expected to be greater in structural capacity, it is found that for shallower shells there is less of a structural advantage to using a triangular grid. Further, the triangular grid is highly sensitive to imperfections whereas a quadrilateral grid is not. The equivalent continuum defined by area equivalence provides a conservative estimate for the buckling load and multiple definitions of the equivalent continuum can be used to establish a practical design tool in the early phases of design. By understanding the fundamental mechanical behavior of gridshells, design guidelines aimed to maximize their capacity and efficiency and intended to facilitate the discussion between architect and engineer are proposed.