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–MP–M curves). Codes and standards recommend the use of uniform average temperature for establishing the P–MP–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–MP–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–MP–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–MP–M diagram is computed by adjusting the P–MP–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.