Civil Engineering Reference
In-Depth Information
7
2
k
E
--------------------------
t/t
w
= 0.75
crl
----------------------
(
=
f
6
12(1-
2
)
b/
ff
2
)
1.00
1.25
1.50
2.00
5
4
b
f
3
2
t
w
d
f
1
t
f
0
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Width to depth ratio
b
f
/d
f
Figure 4.22
Local buckling coefficients for box section beams.
4.4.3 Ultimate strength
The ultimate strength of a thick plate in bending is governed by its yield stress
f
y
and by its plastic shape factor which is equal to 1.5 for a constant thickness plate,
as discussed in Section 5.5.2.
When the width to thickness ratio
d
/
t
exceeds 138.9/
√
(
f
y
/
235
)
, the elastic
buckling stress
σ
crl
of a simply supported plate is less than the yield stress
f
y
(see equation 4.37). Along slender plate such as this has a significant reserve of
strength after buckling, because it is able to redistribute the compressive stresses
fromthebuckledregiontotheareaclosetothesupportedcompressionedge,inthe
same way as a plate in uniform compression (see Section 4.2.2.2). Solutions for
thepost-bucklingreserveofstrengthofaplateinbendinggivenin[6,11-13]show
thataneffectivewidthtreatmentcanbeused,withtheeffectivewidthbeingtaken
over part of the compressive portion of the plate. In the more general case of the
slender plate shown in Figure 4.20 being loaded by combined bending and axial
force, the post-buckling strength reserve of the plate can be substantial. For such
plates,theeffectivewidthistakenoverapartofthecompressiveportionoftheplate.
Effectivewidthscanbeobtainedinthiswayfromthelocalbucklingstress
σ
cr
under
combinedbendingandaxialforceusingthemodifiedplateslenderness
(
f
y
/σ
cr
)
inasimilarfashiontothatdepictedinFigure4.14,althoughtheprocedureismore
complex.
4.5 Plate elements in bending and shear
4.5.1 Elastic buckling
The elastic buckling of the simply supported thin flat plate shown in Figure 4.23
which is subjected to combined shear and bending can be predicted by using the
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