Out-of-Plane Buckling of Beams Having In-Plane Elastic Restraints under Gradient Thermal Action

Abstract

When a beam is subjected to an in-plane linear temperature gradient field, the thermal effects of the temperature gradient field tend to change the curvature of the beam in the transverse direction and to expand the beam in the axial direction. The rotation and expansion of the ends of the beam may be restrained elastically by its supports or by adjacent members such as columns. The restrained thermal actions will produce bending moments and compressive forces in the beam, and when these actions reach critical values the elastically restrained beam may bifurcate from its primary in-plane equilibrium configuration to an out-of-plane buckled equilibrium configuration. This paper investigates the thermoelastic out-of-plane buckling of an elastically restrained beam with a doubly symmetric cross section that is subjected to an in-plane linear temperature gradient field. The analytical solution for the critical temperature gradient for thermoelastic out-of-plane buckling of the beam is derived. It is found that the positions of the effective centroid and shear center of a cross section subjected to a linear temperature field are different from those under mechanical loads. Beams having a doubly symmetric cross section under a linear temperature gradient field behave as beam-columns with a monosymmetric cross section, thereby rendering the thermoelastic out-of-plane buckling of an elastically restrained beam under a linear temperature gradient field more complicated than its counterpart under mechanical loading.