Double-tee shape steel beams under major axis bending (bent about the section stronger principal axis) are generally sensitive to lateral-torsional buckling (LTB), when insufficiently restrained against lateral-torsional deformations between supports. The formulation of LTB problems presented in this paper is based on the Vlasov theory of thin-walled structures, within the concept of linear buckling analysis (LBA). In the classical approach, only the effect of prebuckling bending moment is taken into account in the energy formulation, therefore the buckling analysis is converted to the linear eignenproblem analysis (LEA). When the energy term being a product of twist rotation and minor axis curvature is replaced by the term dependent upon the twist rotation (in the same way as in the Timishenko Energy Method), LTB solutions are based on the quadratic eigenproblem analysis (QEA). In this paper, the effect of prebuckling displacements is taken into account and more accurate normal strain relationship is formulated. The energy term being dependent upon the minor axis curvature and the twist rotation is decoupled and the resultant energy equation becomes dependent only upon the twist rotation and its derivatives. Moreover, any complex loading case is treated as a superposition of two components, symmetric and antisymmetric ones. Thus, the final solution for the critical moment is workable and easy to apply for any loading condition.