The Design of Modern Steel Bridges - TEDI

164 The Design of Modern Steel Bridges
The well-known Perry strut equation can be used to obtain the limiting value
of the longitudinal stress that can be applied on the effective strut:
ssu
s0 ¼
y
1
1 þð1þ ZÞ
2
sE
s0 ( )
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1 þð1þ ZÞ
y
sE
s0 ( ) 2
4sE
y s0 2
v
3
u
6
t
7
4
5 ð6:2Þ
y
where
ssu ¼ limiting value of the applied longitudinal stress on the strut
sE ¼ Euler buckling stress of the strut
Z ¼ y/r 2
y
¼ maximum initial eccentricity and imperfection, i.e. (e1 þ e2) ¼ distance of the extreme compressive fibre from the centroid of the
effective strut cross-section
r ¼ radius of gyration of the effective strut cross-section
s0 y ¼ available yield stress at the extreme compressive fibre (see Section 6.4).
Because of the asymmetry of the cross-section about the horizontal centroidal
axis, equation (6.2) must be applied to both the flange plate and the tip
of the stiffening rib, with appropriate values for , y and s 0 y .
6.4 Allowance for shear and transverse stress in flange plate
According to Hencky–Mises’ criterion of yielding (see Chapter 2), the presence
of shear stress in the flange plate reduces its effective yield stress to
s 0 y ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
3t2 q
ð6:3Þ
s 2 y
The flange shear stress t is caused by (i) the vertical shear force on the crosssection
of the main girder, and (ii) in the case of a box girder, by applied
torsion on the girder. The stress due to (i) varies linearly from a maximum
value over the main girder web to zero mid-way between a pair of such webs,
and hence only half the maximum value needs to be taken along with the full
value due to (ii) for t in equation (6.3) for the flange plate initiated failure. For
failure initiated by the tip of the stiffeners, the full value of the material yield
stress of the tip is available in equation (6.2).
In addition to the above influence on yield stress, shear stress due to torsion
on a box girder also causes a destabilising effect on the longitudinal flange
stiffeners. An allowance for this may be made in the form of an additional
notional axial load in the same way as derived for web stiffeners in Chapter 5.
Transverse stresses in the flange plate are caused by the flexure of the
transverse flange stiffeners, and crossframes and diaphragms in box girders. As
the centroid of the cross-section of a transverse stiffener is very near the flange
plate, the magnitude of the transverse stress is small. When this transverse
stress is compressive, it may in fact increase the effective yield stress in