The Design of Modern Steel Bridges - TEDI

116 The Design of Modern Steel Bridges
5.4.2 Post-buckling behaviour of plates
In the preceding section the magnitude of the applied in-plane stress at which
an initially flat plate first buckles has been derived for various stress patterns.
Depending on the in-plane restraints on its edges, a buckled plate can carry
stresses higher than this elastic critical stress, with the buckles growing in size
but still in a stable condition. If such stable buckles are acceptable, then
considerable gain in the strength of such plates is thus possible.
If the transverse edges of a rectangular initially flat plate approach each
other by a uniform amount across the width of the plate, then longitudinal
compressive stresses will also be uniform across the width, until the elastic
critical stress is reached and the plate buckles. After buckling, however, the
condition changes. Imagine the plate to be made up of a number of longitudinal
strips; the total distance by which the extremities of each longitudinal strip will
approach each other will be the sum of:
(1) the axial shortening of the strip due to the longitudinal compressive stress
carried by it, and
(2) the reduction in the chord length due to the bowing out-of-plane, or
buckling, of the strip.
It has been shown in the preceding section that a rectangular plate under
longitudinal compression buckles with only one half-wave across its width;
hence the longitudinal strip along the longitudinal centre line of the plate will
bow out-of-plane, or buckle, by a bigger amount than the strips nearer the
longitudinal edges. If, after the onset of buckling, the transverse edges of the
buckled plate continue to approach each other by a uniform amount across
the width, it follows therefore that a central longitudinal strip will undergo less
axial shortening and consequently carry lower longitudinal compressive stress,
than the strips nearer the longitudinal edges; this redistribution of the longitudinal
stress, i.e. a transfer of stress from the relatively flexible central region
to the two regions near the longitudinal edges, is shown in Fig. 5.11.
The conditions of in-plane restraint in the transverse direction along the two
longitudinal edges of the plate influence its post-buckling behaviour and stress
distribution. If these edges are free to move in-plane in the transverse direction,
then stresses in the transverse direction are zero along these edges and are also
small in the interior of the plate; the longitudinal edges will, however, not
remain straight but will pull in more in the crest and trough regions of the
buckles and less near the nodal lines. If the longitudinal edges are prevented
against in-plane movement in the transverse direction, then significant
transverse tensile stresses develop; these will be higher in the crest and trough
regions of the buckles and less near the nodal lines. An intermediate state of
transverse restraint along the longitudinal edges is when the edges are
constrained to remain straight though allowed to pull in, the net of average
transverse stress along the edge being zero; in this case the transverse tensile