In the moment-resisting frame system, columns are under combined loading, i.e., axial force with bending moment. The member under combined loading is the so-called beam-column. In the Ultimate Limit State (ULS) design, the beam-column shall need the capacity to sustain the axial force and provide sufficient ductility when it is expected to form a plastic hinge. If the structural frame is a fixed-based column, plastic hinges are also expected to form at the bottom of the first-floor columns. Moreover, Japan's Building Standard of Law (BSL) has a design pass that allows the column and beam strength hierarchy to be checked by story level (this is so-called Route 3) instead of each joint. This means that some columns in the story can be weaker than the beams. Current design formulae for the steel beam-column compiled in the Recommendations published by the Architectural Institute of Japan (AIJ) were based on the test data conducted in the 1980s by monotonic loading. Based on this background, several real-scale tests were conducted by the author's group to confirm the accuracy of the design formulae to the different H-shaped profiles that were not included in the 1980s testing. In the recent conclusion, new design formulae were proposed based on several section profiles, i.e., deep to shallow H-shaped sections, but only for the single moment-curvature bending. In this paper, the numerical simulation using the finite element analysis was also conducted to interpolate the results to derive the new design formulae with different moment distributions, including the double curvature bending. The monotonic and cyclic loadings were challenged in the numerical simulation, and valuable results were obtained after confirming the validity with the test results. Finally, the proposed design formulae were evaluated by the axial force level, slenderness ratio for in-plane and out-of-plane. Moreover, when the out-of-plane slenderness ratio was calculated, the lateral-torsional buckling behaviour was considered, and a new evaluation index was proposed.