Abstract: This paper analyzed the flexural-torsional buckling of beam-columns under linearly varying bending moments and axial forces.The Ritz method was adopted， in which both the lateral deflection and the twisting angle were represented by three terms， leading to results close to the exact solutions.The equivalent bending moment coefficient was derived， and new formulas with high accuracy and slight conservativeness were proposed.The results obtained using the proposed formulas in the standard design equations for the out-of-plane stability check of beam-columns were compared with those from current specifications.The results showed that the proposed formulas yielded a slightly higher flexural capacity when stability governed the design.