Stability analysis of steel structures under elevated temperatures remains a challenging design problem because of the uncertainties associated with fire loads, temperature-dependent material properties, non-uniform heating of structural members, and large deformational demands on the steel frames. The challenge is further aggravated if the stability of the system is also influenced by the permanent lateral deformation due to the earthquake preceding the thermal loads. The present study discusses a framework for assessing the stability of steel columns under inter-story drift imposed by the earthquake followed by fire loads. A nonlinear finite element formulation is proposed to analyze the stability of steel columns subjected to permanent lateral deformations caused by earthquake and fire loads. The finite element formulation takes into account the effects of longitudinal temperature variation in first- and second-order stiffness matrices of a beam-column element, residual stresses, and initial geometric imperfections. The results indicate an excellent agreement with available strength design equations of steel columns at ambient and elevated temperatures. A set of equations is then proposed to predict the critical buckling stress in steel columns under fire and fire following an earthquake. The proposed equations can be implemented to investigate the performance of steel structures under fire and fire following earthquake considering stability as engineering demand parameter.
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