Improved accuracy for the Cm factor of steel beam-columns

• Basic difference between the two Cm factors for in-plane instability checking and section yielding checking is clarified.
• The ratio P/Pe is introduced into the Cm formula for beam-columns subject to end moments.
• For members subject to transverse loading, the Cm formulas are given to avoid the conservative value of 1.0.
• Simple and accurate formulas are obtained for combined transverse loading and end moments.
• The proposed formulas agree well with FEM results.

The Cm factor acting originally as equivalent moment factor for stability checking of beam-columns, assumes an additional function as part of the magnification factor B1 since the AISC–LRFD specification adopted a single equation for beam-column strength calculation. This article first clarifies the difference between the two roles of Cm for in-plane instability checking and section yielding checking and establishes the relationship between the two Cm. As there is no distinction between the two Cm, some confusion occurs in the current AISC specification, and Cm as equivalent moment factor is not accurately evaluated in many cases. In the present study, the ratio P/Pe is introduced into the Cm formula for beam-columns subject to end moments to enhance its precision. For members subject to transverse loading, formulas based on rational analysis are given in order to avoid the use of conservative value of 1.0. By making use of the principle of superposition, simple and accurate formulas are obtained for the case of transverse loading combined with end moments. The proposed formulas are compared with the calculation by finite element method to ensure their feasibility for designing elastic–plastic members with initial imperfections. The results are satisfactory.