In-Plane Stability of Circular Arch Under Uniform Vertical Load Based on the Asymptotic Method

Conventional analyses often simplify vertical loads as uniform radial loads while neglecting axial force effects in the buckling analyses of arches, leading to discrepancies between theoretical predictions and actual loading conditions. To address this issue, this research proposes a nonlinear analytical approach based on asymptotic methods, include the parameter perturbation method and the Wentzel–Kramers–Brillouin (WKB) method. The results show the following: (1) The parameter perturbation method is effective for the snap-buckling of a shallow arch, and the fifth-order solution is sufficiently accurate. (2) For shallow arches with a large modified slenderness ratio, the influence of the axial load component cannot be neglected. (3) Regardless of the rise-to-span ratio of the arch, the nonlinear bending moment is significantly larger than the linear bending moment. (4) In the anti-symmetric buckling analysis, the eigenvalue obtained using the second-order WKB method is smaller than that obtained using the third-order WKB method; therefore, the second-order solution can be used as the critical load. (5) For shallow arches with a small rise-to-span ratio, the critical load for anti-symmetric buckling closely matches the classical solution, and the results from arches subjected to a uniformly distributed radial load are reliable. For deep arches with a large rise-to-span ratio, the influence of the axial load component cannot be ignored.