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Steel prismatic elements of equal flanges double-tee section subject to major axis bending and compression, unrestrained in the out-of-plane direction between the supports, are vulnerable to buckling modes associated with minor axis flexural and torsional deformations. When end bending moments are acting alone on the quasi-straight member, the sensitivity to lateral-torsional buckling (LTB) is very much dependent upon the ratio of section minor axis to major axis moments of inertia, and additionally visibly dependent upon the major axis moment gradient ratio. In the case of major axis bending with the presence of a compressive axial force, even of rather small value in relation to the section squash resistance, there is a drastic reduction of structural elements in their realistic lengths to maintain a tendency to fail in the out-of-plane mode, governed by the large twist rotation. Increasing the load effects ratio of dimensionless axial force to dimensionless maximum major axis bending moment, the buckling mode goes away from that of lateral-torsional one, starting to become that closer to the minor axis flexural buckling (FBZ) mode. Different aspects of the flexural-torsional buckling (FTB) resistance of the typical rolled H-section beam-column with regard to the General Method (GM) formulation, developed by the authors elsewhere and based on the parametric finite element analysis, are dealt with in this paper. Investigations are concerned with different member slender ratio, different moment gradient ratios and different load effects ratio. Final conclusions are related to practical applications of the proposed format of General Method in relation to the effect of large displacements on the FTB resistance reduction factor described through the dimensionless measure of action effects and the FTB relative slenderness ratio of quasi-straight beam-columns.