Civil Engineering Reference
In-Depth Information
isamodifiedplateslendernessforbearingbuckling(whichisofthesameformas
equation 4.5) and
t
w
h
w
2
k
F
π
2
E
12
(
1
−
ν
2
)
F
cr
=
h
w
t
w
(4.103)
is the elastic buckling load for a web of area
h
w
t
w
in bearing. The buck-
ling coefficients for plates in bearing are similar to those in Figure 4.26, with
k
F
=
6
+
2
/(
a
/
h
w
)
2
beingusedforawebofthetypeshowninFigure4.25a.The
effective loaded length used in determining the yield resistance
F
y
in bearing is
y
=
s
s
+
2
nt
f
(4.104)
in which
s
s
is the stiff bearing length and
nt
f
is the additional length assuming a
dispersion of the bearing at 1:
n
through the flange thickness. More conveniently,
thedispersioncanbethoughtofasbeingataslope1:1throughadepthof
(
n
−
1
)
t
f
into the web. For a thick web (for which
λ
F
<
0.5),
n
=
1
+
√
(
b
f
/
t
w
)
, while for
a slender web (for which
λ
F
>
0.5),
n
=
1
+
√
[
b
f
/
t
w
+
0.02
(
h
w
/
t
f
)
2
]
.
4.7.7.2 Stiffened webs
When a web alone has insufficient bearing capacity, it may be strengthened by
adding one or more pairs of load-bearing stiffeners. These stiffeners increase the
yield and buckling resistances by increasing the effective section to that of the
stiffeners together with the web lengths 15
t
w
ε
on either side of the stiffeners, if
available.Theeffectivelengthofthecompressionmemberistakenasthestiffener
length
h
w
,oras0.75
h
w
ifflangerestraintsacttoreducethestiffenerendrotations
during buckling, and curve c of Figure 3.13 for compression members should be
used.
Aworkedexampleofcheckingload-bearingstiffenersisgiveninSection4.9.9.
4.8 Appendix - elastic buckling of plate
elements in compression
4.8.1 Simply supported plates
Asimply supported rectangular plate element of length
L
, width
b
, and thickness
t
isshowninFigure4.5b.Appliedcompressiveloads
N
areuniformlydistributed
over both edges
b
of the plate. The elastic buckling load
N
cr
can be determined
by finding a deflected position such as that shown in Figure 4.5b which is one of
equilibrium.The differential equation for this equilibrium position is [1-4]
∂
4
v
∂
x
4
+
2
∂
4
v
∂
x
2
∂
z
2
+
∂
4
v
∂
2
v
∂
x
∂
z
bD
=−
N
cr
(4.105)
∂
z
4
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