Buckling of elastically restrained steel columns under longitudinal non-uniform temperature distribution

Columns under natural fire conditions are usually exposed to a non-uniform temperature distribution in the longitudinal direction. The motivation for this study stems from zone modeling of a compartment fire where the gas layers are artificially divided into two zones, namely the hotter upper zone and the cooler lower zone. However, for field modeling of a compartment fire, more detailed information of the temperature distribution can be obtained. Depending on the required accuracy, two different idealizations of temperature distributions are analyzed in this paper, namely linear distribution from zone modeling and piece-wise step distribution from field modeling in the longitudinal direction. Compared to a column with uniform temperature distribution, both of them represent more realistically the thermal response of a column, which experiences greater temperature with increasing height. The difference in temperature between the top and bottom ends of a column can be quite significant, particularly prior to the flashover condition. Advantage can be made of this in a performance-based approach to ascertain the stability of a column subjected to a prescribed fire size. In this paper, the stability of a pin-ended steel column under a non-uniform temperature distribution is studied. Although the formulations are based on linear elastic assumptions, the paper explores the validity aspect of the approach and shows that it can be applied to columns with a minimum slenderness ratio where plasticity is negligible. Across a section, the temperature is assumed to be uniform. Two linear elastic springs connected to the column ends simulate the axial restraints from the adjoining unheated structure. The objective is to derive closed-form solutions to enable engineers to quickly ascertain the column stability under a non-uniform temperature distribution, without recourse to finite element modeling.