Effects of temperature variations on the in-plane stability of steel arch bridges

The in‐plane stability of shallow parabolic arches subjected to a central concentrated load and temperature variations was investigated in this paper. The virtual work principle method was used to establish the non‐linear equilibrium and buckling equations. Analytical solutions for the non‐linear in‐plane symmetric snap‐through and antisymmetric bifurcation buckling loads were obtained. Then the effects of temperature changes on the in‐plane stability for arches with supports that stiffen under compression were studied. The results show that the influence of temperature variations on the critical loads for both buckling modes (symmetric snap‐through and anti‐symmetric bifurcation) is significant. The critical loads for the two buckling modes are higher than those only under external loads without thermal loading. Moreover, the critical loads increase with an increase of the thermal loadings. It can also be found that the effects of applying temperature field increase when either initial stiffness coefficient α or the stiffening rate β is raised. Furthermore, the effect of thermal loading on the critical load increases with the span‐rise ratio m for arches with any initial stiffness coefficient α and the stiffening rate β.