The Design of Modern Steel Bridges - TEDI

Rolled Beam and Plate Girder Design 127
for the stress pattern under consideration. Generally this coincided with the
elastic critical buckling mode for the stress pattern. The main reason for
relating the imperfection to the yield stress sy was that the non-dimensional
imperfection parameter
pffiffiffiffiffiffiffiffiffiffiffiffiffiffi
d/t could be related to the non-dimensional slenderness
parameter (b/t) ðsy=EÞ as follows:
d b
¼ 0:145
t t
rffiffiffiffiffi
sy
E
and this allowed the non-dimensional strength parameters su/sy to be obtained
from the same strength graphs for all strength grades of steel. It was found that
plates subjected to in-plane shear or bending pattern of stresses were not very
sensitive to initial out-of-plane deviations, but plates subjected to in-plane
compression
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
were, and especially in the slenderness range of 40 <
(b/t) ðsy=245Þ < 60. For example, in the above slenderness range, doubling
the initial imperfection amplitude from b/400 to b/200 or from b/200 to b/100
reduced the strength of the plate by up to 10%.
Regarding initial welding residual stresses, it was found that both plates
under compression and
p
plates
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
under shear were sensitive, particularly in the
slenderness range (b/t) ðsy=245Þ of 40 to 60 and 90 to 150, respectively,
though by a lesser degree in the case of shear. For example, welding residual
compressive stress equal to 10% of the yield stress caused up to 10% reduction
in the compressive strength of a plate with initial imperfection amplitude of
b/200, and an increase of welding compressive stress to 33% of the yield stress
caused another
p
10%
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
reduction in the strength of that plate. A plate of
slenderness (b/t) ðsy=245Þ ¼ 120, and initial imperfection amplitude b/200
had its shear strength reduced by 5% by welding compressive stress equal to
10% of the yield stress. Thus, even for plates that were sensitive to initial
geometric
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
imperfections and welding residual stresses, assumptions of
(b/200) ðsy=245Þ and 0.1 sy for the two parameters yielded plate strengths
that were not substantially decreased with further increase in these two
parameters. Hence for design strength, the level of welding residual
compressive stress was assumed to be 10% of the yield stress.
In these large-deflection elasto-plastic computer analyses, all four edges
were taken as simply supported, i.e. no restraint against rotation. The in-plane
loading was applied as linear displacements of the edges, the resultant of the
edge stresses being taken as the applied edge load. In the case of pure in-plane
bending applied on the transverse edges, the longitudinal edges were held in
the shape of the simple bending curvature instead of being held straight.
Plate strength curves are given in the British Standard BS 5400: Part 3 for
the two cases of:
(1) no in-plane restraint at the longitudinal edges, and
(2) longitudinal edges held straight (or in a pre-determined configuration, e.g.
for pure bending case), but allowed to move inwards in-plane for the three