In-plane nonlinear elastic stability of pin-ended parabolic multi-span continuous arches

Abstract

The in-plane nonlinear elastic stability of single arches has been investigated by many researchers, however, a similar research of multi-span continuous arches is not available even though they are extensively used in arch bridge engineering. This paper proposes an analytical method for the in-plane nonlinear elastic buckling and post-buckling of pin-ended parabolic multi-span continuous arches. There are four key parts in the proposed method. Firstly, the in-plane nonlinear equilibrium differential equations of each arch were derived based on the strain expression in the Cartesian coordinate system of non-circular arches and the virtual work principle. Secondly, the nonlinear equilibrium equation of continuous arches was proposed based on the deformation compatibility condition of each arch end, and three key coefficients were obtained. Thirdly, the buckling requirements were deduced according to the force balance condition in each arch end. Lastly, analytical solutions for buckling and post-buckling predictions were derived. Comparisons with the results of finite element method, including the load-displacement curve, buckling behavior and buckling predictions, demonstrate that the proposed analytical solution is equipped with high accuracy. The results of theoretical and parametric analysis show that the deformation shape of symmetric and asymmetric buckling of multi-span continuous arches is thoroughly different from the single arches, the mechanical effect of the unloaded arches is a nonlinear horizontal spring support acting on the loaded arch, and the stability parameter ratio has a significant influence on the buckling behavior of multi-span continuous arches.