The Design of Modern Steel Bridges - TEDI

144 The Design of Modern Steel Bridges
shear stress and the longitudinal stress in the web. When the distribution of
longitudinal stress in the web is not purely uniform compression, but a
combination of uniform compression sl and pure in-plane longitudinal bending
sb, such that sl sb give the stresses at the edges of the web (see Fig. 5.10),
then (sIþ1 6 sb) may be taken instead of sl only in equations (5.38)–(5.40); this
is based on the observation that the elastic critical buckling coefficient k is 4
for pure compression and 24 for pure bending (see Section 5.4.1).
5.5.5 Axial compression due to tension field in web
The tension field in the web constitutes diagonal tensile stresses in it, the
vertical component of which has to be resisted by vertical web stiffeners. This
is very like the force distribution in an N-type truss and is shown in Fig. 5.27.
In Section 5.4.5 it has been postulated that when the applied shear stress
exceeds the elastic critical value, the rest of the shear stress is resisted by the
tension field mechanism. Under the combined action of shear and bending
stresses in the web, elastic critical buckling occurs when the following condition
is reached (see Section 5.4.1.4)
where
s1
s1cr
þ sB
sBcr
2
þ t
s l ¼ uniform longitudinal compressive stress in web
s B ¼ pure longitudinal bending stress in web
t ¼ shear stress in web
s1cr ¼ 4p2 E
12ð1 m 2 Þ
sBcr ¼ 24p2 E
12ð1 m 2 Þ
tcr ¼ kp2 E
12ð1 m 2 Þ
k ¼ 5:35 þ 4 b
a
tw
b
tw
b
tw
b
2
2
2
2
9
>=
>;
tcr
2
¼ 1 ð5:41Þ
(see Section 5 :4.1)
Because of imperfections and residual stresses in the web, it may be conservatively
assumed that tension field action starts when the applied stresses
exceed 80% of the elastic critical buckling values, i.e. s lcr, s Bcr and t cr above
are reduced by multiplying by 0.8.
A further simplifying and conservative step will be to assume the power of
the second term in equation (5.41) to be 1, instead of 2. This will then lead to