In the previous paper, simplified theory was proposed in which unified method for computing the elasto-plastic behaviour of beam-columns subjected to axial force and also to bi-axial moment by neglecting torsion effect and adopting a new concept with respect to bending stiffness of a section was introduced. Refined such a method described above, a general method is presented here, by which the effect of torsion and warping strains due to non-uniform torsion on beam-columns with thin walled open cross section subjected to elasto-plastic bi-axial bending can be treated. In this analysis, force, bi-axial bending moment and torsional moment are applied on beam-columns at each end. A good correlation between theory and experimental results with respect to the maximum load is obtained.