ABSTRACT
The classical energy formulation dedicated to the lateral-torsional buckling of I-section steel members is based on the so-called linear buckling approach (LBA) and inclusion the prebuckling stress resultants in the energy equation. As a result, the buckling analysis may be converted to the linear eigenproblem analysis (LEA). The “exact” closed-form solution of the differential equilibrium equation is obtained only for uniform bending. Moment gradient cases need approximate analytical or numerical methods to be used. Investigations presented in this paper deal with the energy formulation in which the classical energy equation is modified in the way proposed by Timoshenko, so that such an energy approach is named the Timoshenko’s energy method. It leads to the nonlinear eigenproblem analysis (NEA). Using this method, practical approximate solutions may be obtained for any asymmetric transverse loading conditions that produce a moment gradient. The stability criterion in this paper is formulated for a general case of transverse loading, the solution of which is obtained by treating the general loading patterns and corresponding moment diagrams as a superposition of symmetric and antisymmetric components. The results are presented in a table format for considered simple loading cases. For combined loading cases, results are presented in the form of nomograms. Solutions obtained for selected combined loading cases are verified with use of LTBeam software.
