On Beam-Column Moment Amplification Factor

In designing beam-columns in a steel frame, the LRFD Specification uses two moment amplification factors (B1 and B2) to account for the second-order P—d (member instability) and P—D (frame instability) effects. For beam-columns with joint translation restricted and subjected to end moments only, the B1 factor usually underestimates the P—d effect. However, in some uncommon practical cases, under high axial compression ratio (P/Pe > 0.7) with double curvature bending, it is conservative to estimate the P—d effect. This is due mainly to the fact that, for simplicity, the LRFD Cm expression excludes the influence of the axial load ratio P/Pe. In this paper, an improved Cm expression, written in terms of both the axial load ratio P/Pe and the end moment ratio Ma/Mb, is proposed. The proposed moment amplification factor has been verified by an extensive comparison with the exact analytical solution. It is found that the P-d moment predicted by the proposed formula is more accurate than that predicted by the B1 factor in the present LRFD Specification.