Civil Engineering Reference
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region at about
d
/5 from the compression edge. This is close to the position of
the crests in the buckles of an unstiffened plate. Such a stiffener may increase the
bucklingcoefficient
k
σ
significantly,themaximumvalueof129.4beingachieved
when the stiffener acts as if rigid. The values given in [5, 6] indicate that a hypo-
thetical stiffener of zero area
A
st
will produce this effect if its second moment of
area
I
st
is equal to 4
dt
3
.This value should be increased to allow for the compres-
sive load in the real stiffener, and it is suggested that a suitable value might be
given by
I
st
=
4
dt
3
1
+
4
A
st
dt
1
+
A
st
dt
,
(4.38)
whichisofasimilarformtothatgivenbyequation4.7forthelongitudinalstiffeners
of plates in uniform compression.
4.4.2 Plate assemblies
Thelocalbucklingofaplateassemblyinbending,suchasanI-beambentaboutits
majoraxis,canbeanalysedapproximatelybyassumingthattheplateelementsare
hingedalongtheircommonboundariesinmuchthesamefashionasthatdescribed
in Section 4.2.1.4 for compression members. The elastic buckling moment can
then be approximated by using
k
σ
=
0.425 or 4 for the flanges, as appropriate,
and
k
σ
=
23.9 for the web, and determining the element which is closest to
buckling. The results of more accurate analyses of the simultaneous buckling of
the flange and web elements in I-beams and box section beams in bending are
given in Figures 4.21 and 4.22, respectively.
1.0
2
12(1-
2
----------------------
E
--------------------------
k
crl
=
t/t
w
=1.0
b/
ff
2
(
)
f
0.8
1.5
2.0
4.0
0.6
b
f
0.4
t
w
d
f
0.2
t
f
0
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Outstand width to depth ratio
b
f
/d
f
Figure 4.21
Local buckling coefficients for I-beams.
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