In-Plane Instability of Fixed Arches under Linear Temperature Gradient Field and Uniformly Distributed Radial Load

This paper focuses on an in-plane instability analysis of fixed arches under a linear temperature gradient field and a uniformly distributed radial load, which has not been reported in the literature. Combining a linear temperature gradient field and uniformly distributed radial load leads to the changes in axial expansion and curvature of arches, producing the complex in-plane nonuniform bending moment and axial force. Therefore, it is necessary to explore the in-plane thermoelastic mechanism behavior of fixed arches under a linear temperature gradient field and a uniformly distributed radial load in the in-plane instability analysis. Based on the energy method and the exact solutions of internal force before instability, the analytical solutions of the critical uniformly distributed radial load considering the linear temperature gradient field associated with in-plane thermoelastic instability of arches are derived. Comparisons show that agreements of analytical solutions against FE (finite element) results are excellent. Influences of various factors on in-plane instability are also studied. It is found that the change of the linear temperature gradient field has significant influences on the in-plane instability load. The in-plane instability load decreases as the temperature differential of the linear temperature gradient field increases.