Stability of axially restrained steel columns under temperature action

The in-plane elastic buckling of a steel column under thermal loading is investigated. The column is pinned at its ends, with two linear elastic springs that model the restraint provided by adjacent members in a structural assemblage or an elastic foundation. Across a section, the temperature is assumed to be linearly distributed. Based on a nonlinear strain-displacement relationship, the energy method is used to obtain the equilibrium and buckling equations. Then the buckling of columns with three different thermal loading cases is studied. The results show that the analytical formulas can be used to evaluate the critical temperature for elastic buckling. The thermal gradient plays a positive role in improving the stability of columns. Comparing these predictions with uniform temperature distribution over cross section, it can be shown that the buckling load is seriously underestimated. It can also be found that axial restraints can significantly affect the column elastic buckling loads. The critical temperature decreases with an increase of restraint stiffness. Furthermore, the effect of axial stiffness increases when increasing the thermal gradients and decreasing the slenderness ratio of columns.