The Design of Modern Steel Bridges - TEDI

142 The Design of Modern Steel Bridges
For webs stiffened with vertical stiffeners only
Pcro ¼ 2p2
B ðDx DyÞ 1=2 , ignoring H
In this case Dx ¼ Et 3 /12[1
2
], and Dy ¼ EIsy/a, when t is the thickness of the
web and is the Poisson’s ratio, equal to 0.3. Hence
Pcro ¼ 6E
B
t 3 Isy
a
We may design a transverse stiffener as a strut with an effective axial load
Peq such that the ratio of this effective axial load to the Euler buckling load of
the strut, P E, is equal to the ratio of the longitudinal force on the web to the
orthotropic elastic critical buckling load P cro derived from above, i.e.
wherefrom
Peq
PE
¼ s1tB
Pcro
Peq ¼ s1tB PE
We should also take account of the fact that the destabilising forces in the
web do not cause any axial stress on the transverse stiffeners. If a strut with an
initial imperfection i is subjected to a destabilising force Peq that magnifies
the initial imperfection, but does not cause any axial stress, the limiting value
Peql of this force that will initiate yielding on an extreme fibre will be given by
which leads to
where
PE
Peq1 i
PE Peq1
Pcro
Peq1 ¼ Py
Z þ Py
PE
Z ¼ iy
r2 r ¼ radius of gyration
y ¼ extreme compressive fibre distance
A ¼ cross-sectional area
Py ¼ squash load ¼ syA:
1=2
y
¼ sy
Ar2 Peql will obviously be greater than the strut strength Ps of a normal axially
loaded strut with initial imperfections i. We can thus apply a reduction factor
P s/P eql to evaluate P eq on the transverse stiffener, thus leading to