In‐Plane Instability of Parabolic Arches under Uniformly Distributed Vertical Load Coupled with Temperature Gradient Field

Abstract

In civil engineering, arches, such as steel arch roofs and arch bridges, are often subjected to linear temperature gradient field. It is known that the in‐plane instability of parabolic arches is caused by the significant axial force. The arch under the linear temperature gradient field produces complex axial force, and so the instability of arches would be affected by temperature gradient field significantly. However, the analytical solutions of in‐plane instability of parabolic arches being subjected to the uniformly distributed vertical load and the temperature gradient field are not solved in the opening literature. In this paper, in‐plane instability of a fixed steel parabolic arch under linear temperature gradient field and vertical uniform load is analyzed theoretically. Firstly, the cross‐sectional effective centroid and effective stiffness of the cross section for arches under the linear temperature gradient field are derived. Secondly, the preinstability internal force analysis of the parabolic arch under the linear temperature gradient field and the vertical uniform load is carried out based on the force methods. Novel theoretical solutions for in‐plane instability load for fixed steel parabolic arches under the linear temperature gradient field and the vertical uniform load are obtained. It is found that the gradient temperature, slenderness, and rise‐span ratio have important influences on the critical in‐plane instability load of the shallow parabolic arch, while there is no significant effect on the deep parabolic arch.