Abstract: A second-order analysis was conducted for steel beams with initial deflection and twist. Assuming the initial deformations conform to the buckling mode shape， the second-order bending moment and bi-moment were derived. Subsequently， an expression for the stability coefficient of flexural-torsional buckling in steel beams was derived by applying the edge fiber yield criterion. This expression is identical in form to the Perry-Robertson formula used for compression member buckling， thereby providing a theoretical basis for unifying the stability coefficient expressions for compression members and steel beams. Although the expressions share an identical form， the imperfection factors for steel beams equal those for compression members multiplied by the square of a specific ratio. This ratio is defined as the normalized slenderness for lateral-torsional buckling of the steel beam divided by that for flexural buckling of the compression member about its weak axis. Given that this ratio is less than 1.0， the imperfection factor for beams is smaller. Consequently， at the same normalized slenderness， the stability coefficient for steel beams is higher than that for compression members. For uniformly loaded beams and beams under a mid-span concentrated force， similar derivations were carried out， incorporating the effect of load height. The results confirmed identical formulaic forms， with only minor differences in the definition of the imperfection factors. This consistency demonstrates the general applicability of the derivation.