A simplified approach for evaluating plastic axial and moment capacity curves for beam-columns with non-uniform thermal gradients

Restrained steel members, when exposed to fire develop significant forces and this transforms the behavior of a beam (or column) into that of a beam-column. The load carrying capacity of such beam-columns is determined through axial and moment capacity curves (P-M curves). Codes and standards recommend the use of uniform average temperature for establishing the P-M curves at elevated temperatures. This assumption, though adequate for cases where temperature in steel is uniform, such as a column exposed to fire from four sides, may not be valid for columns or beams exposed to fire from 1, 2, or 3 sides since significant thermal gradients develop across the section. These thermal gradients can cause severe distortion in the P-M curves and render the capacity curves based on uniform temperature inadequate for evaluating the strength of such beam-columns. In this paper, a simplified approach is proposed for adjusting the uniform temperature plastic P-M curves to account for the shape distortion resulting from fire-induced thermal gradients. The proposed method employs a two-step process in which the cross-sectional steel temperatures are calculated first, and then the distorted P-M diagram is computed by adjusting the P-M diagrams based on a uniform "averaged" temperature. The applicability of the proposed method to a design situation is illustrated through a numerical example. It is demonstrated that the proposed approach is well suited for predicting the capacity of beam-columns that develop thermal gradient under fire.