On elastic buckling of bisymmetric H-section steel elements under bending and compression

In this state-of-the-art paper, methods of the elastic buckling evaluation applied to perfect bisymmetric double-tee section columns, beams and beam-columns are summarized. Basic approaches for flexuraltorsional buckling of an elastic beam-column, based on retaining the trigonometric functions of the twist rotation, are formulated. The fourth order differential equilibrium equations derived from the energy equation obtained for unrestrained elements under directional moment gradient are considered. The effect of prebuckling displacements on the critical state is briefly discussed in reference to the classical approach based on the linear eigenvalue analysis, in which the critical state is evaluated using only the prebuckling stress resultants. Firstly, the exact solution of the critical state under the moment stress resultant of the constant value along the element is dealt with. Secondly, approximate solutions based on the energy method and orthogonalization method for simple and combined loading cases are discussed. A general situation of elastic instability of beam-columns under moment gradient in reference to the directional bending about the section principal axis of greater moment of inertia is obtained. Special cases of lateral-torsional buckling of beams are also discussed. Finally, conclusions with regard to the improvement made with regard to critical state evaluation are presented.