In-plane elastic buckling of pin-ended shallow parabolic arches

The classical buckling theory is commonly adopted to evaluate the buckling load of arches regardless of their types and shapes. For shallow arches, however, the classical buckling theory may overestimate the buckling load because of a large pre-buckling deformation. In this study, the geometrically nonlinear behavior of pin-ended shallow parabolic arches subjected to a vertically distributed load is investigated to evaluate the buckling load. The nonlinear governing equilibrium equation of the parabolic arch is adopted to derive the buckling formula for a pin-ended shallow parabolic arch. Moreover, the threshold of different buckling modes (symmetric and asymmetric) is derived in terms of the slenderness ratio and the rise-to-span ratio of such arches. Numerical examples show that the proposed formula can accurately predict the buckling load of pin-ended parabolic arches.