Prebuckling deflections and lateral buckling: Theory

When the ratio of the minor axis flexural stiffness to the major axis flexural stiffness is not small, classic analysis may lead to inaccurate predictions of the lateral buckling loads of beams and beam-columns because the effects of prebuckling deformations are not considered. The energy equation for the elastic lateral buckling of monosymmetric beam-columns including the effects of prebuckling deformations is derived, and the buckling differential equilibrium equations are obtained. A finite element algorithm for the prediction of the lateral buckling loads of monosymmetric beam-columns including the effects of prebuckling deformations is developed from the energy equation. This includes the effects of second order moments due to the prebuckling displacements and the axial loads. An iterative procedure for determining the lateral buckling loads is recommended. The finite element results given in a companion paper show that the classic predictions of the lateral buckling loads of beams and beam-columns are generally conservative, but that the predictions by the linearized procedure are overestimated. The predictions by the recommended nonlinear iteration procedure agree well with experimental results.