THE ANALYTICAL AND STATISTICAL APPROACHES TO LATERAL BEAM BUCKLING

摘要

A beam loaded in its stiffer principal plane without sufficient lateral stiffness or lateral support may buckle out of the plane of loading by deflecting sideways and twisting. Since the L. PRANDTL's (1899), A.G.M. MICHELL's (1899) and S.P. TMOSHENKO's (1905) first theoretical studies on beam stability the permanent attention has been paid to the problems of actual behaviour and design of beams. Different approaches to the analysis of the problem of lateral buckling of beams - see Ref. [1] to [6], for example - illustrates Fig. 1, where the relationship between bending moment M and the total lateral deflection (v) / twist (ψ) is presented (in Fig. 1 v_0 and ψ_0 are the amplitudes of initial curvature / twist of a real beam). At present, of course, stability is no longer seen as related to buckling through bifurcation of equilibrium (M_(cr)), not either to the initial yielding of the most highly strained fiber (M_y), but rather as the ultimate strength of the initially imperfect real member (M_(u,rl))- Through improved analytical and experimental techniques, all of the major and decisive parameters are now explicitly accounted for in the design requirements.