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.

This paper theoretical analysis the internal force of the fixed parabolic arches under radient temperature gradient field incorporating shear deformations. The effective centroid of the arch-section under linear temperature gradient is derived. Based on force method and energy method, the analytical solutions of the internal force of fixed parabolic arches at pre-buckling under linear temperature gradient field are derived. A parameter study was carried out to study the influence of linear temperature gradient on the internal force of the fixed parabolic arches with different rise-span ratio and varying slenderness ratio. It is found that the temperature gradient and the rise-span ratio has a significant influence on the internal force of the parabolic arches, the influence of shear deformation causes the bending moment increase while the axial force decreases, and the axial force of parabolic arches decreases as the rise-span ratio increases.