Effects of nonlinearity and temperature field on in-plane behaviour and buckling of crown-pinned steel arches

This paper investigates the effects of geometric nonlinearity and temperature field on the in-plane elastic behaviour and buckling of crown-pinned circular steel arches that is subjected to a uniform radial load. Differential equations of equilibrium are derived based on the principle of stationary potential energy, and analytic solutions for the linear and nonlinear behaviour and buckling loads are derived. It is found that the nonlinearities have significant influences on the in-plane behaviour and buckling of crown-pinned arches. The nonlinear bending actions produced by the uniform radial load in crown-pinned arches are substantial, while the linear bending actions are equal to zero for three-pinned arches and are small for one-pinned arches. The nonlinear buckling loads are much lower than their linear counterparts. It is also found that the uniform temperature field influences the nonlinear elastic behaviour and buckling of crown-pinned arches, while it has no effects on the linear internal actions of three-pinned arches and small effects on those of one-pinned arches. As temperature increases, radial displacements decrease while the nonlinear buckling loads increases. It is further found that crown-pinned arches can buckle only in a symmetric mode, but not in an antisymmetric mode. Comparisons with the finite element results show that the analytical solutions derived in this paper are quite accurate.