The Design of Modern Steel Bridges - TEDI

5.5.6 Design of longitudinal web stiffeners
The critical buckling load of a longitudinally loaded orthogonally stiffened web
has been derived in Section 5.5.4 as
Pcro ¼ 2p2 E
B
Isx Isy
a b
with the notations as in that section.
For a particular ratio of the moments of inertia of the transverse and
longitudinal stiffeners I sy and I sx, see Figure 5.26, P cro will be equal to the sum
of the Euler buckling loads of the longitudinal stiffeners, i.e. when
or
2p 2 E
B
Isx Isy
a b
Isy ¼ 1 IsxbB
4
2
a3 1=2
¼ p 2 E Isx
a 2
With this value of Isy, the half-wave-length L will be
B
Isx a
1=4
b Isy
B
b
¼ ffiffiffi p
2a
1
1=2
B
b
2
B
B b
If I sy is greater than the above value, the sum of the Euler buckling loads will
be less than Pcro; there is also the possibility that there may not be a transverse
stiffener within the half-wave-length L, thus invalidating the evaluation of P cro
as above. Hence in this situation the longitudinal stiffeners should be designed
as struts with effective length equal to a.
If I sy is less than the above value, the orthotropic critical buckling load P cro
will be less than the sum of the Euler buckling loads of the longitudinal
stiffeners. Hence the longitudinal stiffeners should be designed as struts with
effective length leff greater than a and given by
wherefrom
p 2 EIsx
l 2 eff
B
b
leff ¼ B
2
Rolled Beam and Plate Girder Design 147
1 ¼ 2p2 E
B
B
b
1
Isx Isy
a b
1=2 abIsx
The axial loading on a longitudinal stiffener should include not only the
longitudinal stresses in the girder web, but should also allow for the destabilising
effects of shear stresses and any transverse stresses in the web. Thus the
applied longitudinal stress should be taken as
s1 þ 2:5ksðt þ s2Þ
Isy
1
1=2
1=2
1=4