The Design of Modern Steel Bridges - TEDI

Rolled Beam and Plate Girder Design 125
Figure 5.18 Buckling behaviour of plates with initial out-of-plane deviations.
(a) Ideally flat plate; (b) plate with initial out-of-plane deviations.
quantitative effects of initial out-of-plane deviations depend on:
(1) the magnitude of the deviations
(2) the pattern of the deviations
(3) the type of the applied stresses on the plate
(4) the in-plane and out-of-plane edge conditions of the plate
(5) the slenderness (i.e. the width-to-thickness ratio) of the plate and to a
lesser extent its aspect ratio (i.e. the ratio of length to width).
Obviously, the larger the deviations, the worse are the effects. Initial
deviations in the pattern of the elastic critical buckling mode of the plate have
the worst effects. For example, in a plate with an aspect ratio of 3, subjected to
compression on the shorter edges, the worst pattern of initial deviations will be
the one with one sine wave across the width and three sine waves in the form
of ripples along the length. Plates subjected to in-plane compression along one
or both directions are most affected by initial deviations; plates in shear are
least affected. In-plane restraints on the edges reduce the effects of initial
deviations. But the beneficial effects of out-of-plane edge fixities (i.e. clamped
against rotation) are less pronounced in the case of initially curved plates than
the improvement in the elastic critical buckling stress of a perfectly flat plate.
Plates with low slenderness, e.g. the width–thickness ratio less than, say, 20 in
the case of longitudinal in-plane compression or 50 in the case of in-plane
bending or shear, are able to reach their squash loading, i.e. applied stress can
be as high as the yield stress, in spite of any out-of-plane deviations. A more