H-shaped steel beams in frame structures are rotationally restrained at both ends by connecting columns or beams. It is well known that the elastic lateral buckling strength is affected by both the boundary conditions at the beam ends and the moment distribution. Although there have been many reports on the elastic lateral buckling strength of such beams, the combined effects on lateral buckling of restraints on the amount of lateral bending and beam-end warping are still unknown.
The purpose of this study is to develop a formula for evaluating the lateral buckling strength of H-shaped steel beams with arbitrary restraints on the amount of lateral bending and beam-end warping. Firstly, we propose a useful displacement function which is applicable to approximation analysis based on the energy criterion. An elastic lateral buckling strength approximation formula is then derived for the case of a uniform moment distribution using a Galerkin method. Finally, a lateral buckling strength formula that is valid for any boundary conditions, sectional shape or moment distribution, is proposed.
The results obtained in this study are as follows.
1) Displacement functions were derived for structural members undergoing flexural buckling under arbitrary boundary conditions, including pinned-pinned, fixed-fixed, and pinned-fixed members. These functions were found to accurately describe the buckling mode shape for members with different rotational rigidities that are supported at both ends.
2) A parameter R, determined by the sectional shape and the member length, was introduced to evaluate the lateral buckling strength of H-shaped steel beams. It was shown that as R increases, the effect of the warping restraint on the buckling strength decreases. By including this parameter, the lateral buckling strength could be determined with Eq. (34) for arbitrary boundary conditions by Eq. (35).
3) An additional moment gradient modification factor C1 was also introduced for the cases that the rotational stiffness of one end having larger moment is also larger than the other end with Eq. (48) through Eq. (51).
