Civil Engineering Reference
In-Depth Information
for a steel with
E
=
210000N/mm
2
and
ν
=
0.3. (The yield stress
f
y
in
equation 4.6 and in all of the similar equations which appear later in this chapter
must be expressed in N/mm
2
.)
The values of the buckling coefficient
k
σ
shown in Figure 4.6 indicate that the
use of intermediate transverse stiffeners to increase the elastic buckling stress of
a plate in compression is not effective, except when their spacing is significantly
less than the plate width. Because of this, it is more economical to use interme-
diate longitudinal stiffeners which cause the plate to buckle in a number of half
wavesacrossitswidth.Whensuchstiffenersareused,equation4.3stillholds,pro-
vided
b
istakenasthestiffenerspacing.Longitudinalstiffenershaveanadditional
advantagewhentheyareabletotransfercompressivestresses,inwhichcasetheir
cross-sectional areas may be added to that of the plate.
An intermediate longitudinal stiffener must be sufficiently stiff flexurally to
prevent the plate from deflecting at the stiffener. An approximate value for the
minimum second moment of area
I
st
of a longitudinal stiffener at the centre line
of a simply supported plate is given by
I
st
=
4.5
bt
3
1
+
2.3
A
st
bt
1
+
0.5
A
st
bt
(4.7)
in which
b
is now the half width of the plate and
A
st
is the area of the stiffener.
This minimum increases with the stiffener area because the load transmitted by
thestiffeneralsoincreaseswithitsarea,andtheadditionalsecondmomentofarea
is required to resist the buckling action of the stiffener load.
Stiffeners should also be proportioned to resist local buckling. A stiffener is
usually fixed to one side of the plate rather than placed symmetrically about the
mid-plane, andinthiscaseitseffectivesecondmomentofareaisgreaterthanthe
value calculated for its centroid. It is often suggested [2, 3] that the value of
I
st
can be approximated by the value calculated for the mid-plane of the plate, but
this may provide an overestimate in some cases [4-6].
The behaviour of an edge stiffener is different from that of an intermediate
stiffener, in that theoretically it must be of infinite stiffness before it can provide
an effective simple support to the plate. However, if a minimum value of the
second moment of area of an edge stiffener of
I
st
=
2.25
bt
3
1
+
4.6
A
st
bt
1
+
A
st
bt
(4.8)
isprovided,theresultingreductionintheplatebucklingstressisonlyafewpercent
[5]. Equation 4.8 is derived from equation 4.7 on the basis that an edge stiffener
only has to support a plate on one side of the stiffener, while an intermediate
stiffener has to support plates on both sides.
Theeffectivenessoflongitudinalstiffenersdecreasesastheirnumberincreases,
and the minimum stiffness required for them to provide effective lateral support
increases. Some guidance on this is given in [3, 5].
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