Buckling of Frames under Various Torsional Loadings

A bending or torsional moment may be generated internally as the stress resultant of a cross section or externally by mechanical devices. Depending on how the moments are generated, they do not exhibit identical behaviors when subjected to three‐dimensional rotations. In the buckling analysis of space frames, all types of moments, whether internal or external, must be specified in the buckling position. This is particularly important in writing the equilibrium conditions for internal joints with members meeting at angles and in setting up the natural boundary conditions for external joints subjected to loadings of the moment type. Emphasis of the paper is placed on the effects of torsional loadings generated by external mechanisms, which may be of the semitangential type or of the quasitangential type (first kind or second kind), on the buckling of structural frames and members. The solutions presented herein are exact and are useful for theoretical as well as for practical purposes.