Secondary Deflections and Lateral Stability of Beams

For members whose properties can be described in terms of one independent variable such as beams and columns, a new formulation of equations describing their elastic behavior is derived by expressing the characteristics of the twisted member in fixed coordinate system. This formulation leads to a reinterpretation of the lateral buckling of cantilevers of not-so-narrow rectangular cross sections, and to a unified approach to problems of transverse loading oblique to the principal axes of a cross section. Certain of the latter beams are found to have limiting loads analogous to the critical load associated with lateral buckling. However, the behavior of these members cannot be described as buckling since nonzero deflections and twist are predicted for all nonzero loads. In addition a limiting load dependent upon the sign of the load is found for cantilevers of angle cross section transversely loaded parallel to one leg.