The Design of Modern Steel Bridges - TEDI

longitudinal compression of the longitudinal stiffeners, as per Hencky–Mises’
yield criterion. Being localised, these transverse stresses are also not likely to
cause any destabilising effects.
6.5 Orthotropic buckling of stiffened flange
Orthotropic buckling of the stiffened flange between the webs of the main
girders provides a restraining effect on the buckling of the longitudinal flange
stiffeners as individual parallel struts. This orthotropic behaviour produces two
separate effects on the stress conditions of individual longitudinal stiffeners:
(1) Under the same magnitude of the applied longitudinal compressive load
across the flange width, the magnification of the initial deflection of the
strut in an orthotropic panel is less than that of an isolated strut.
(2) As the whole flange width between girder webs buckles, the applied longitudinal
compression varies across this width, with higher stresses along the
edges (i.e. near the girder webs) and lower stresses along the central strips.
The word ‘orthotropic’ is an abbreviation of the feature ‘orthogonally anisotropic’;
in such a plate the lack of isotropy is due to different flexural rigidities
in the orthogonal directions, even though the plate is of uniform thickness. The
elastic critical buckling stress of an orthotropic plate under longitudinal compression,
i.e. the value of the applied stress at which an ideally flat residualstress-free
orthotropic panel becomes unstable and suddenly deflects from its
initially flat plane, is given by
where
Stiffened Compression Flanges of Box and Plate Girders 165
scro ¼ p2
tb 2
Dx
f 2 þ Dyf 2 þ 2H ð6:4Þ
t ¼ thickness of the orthotropic plate
b ¼ width of the orthotropic plate
a ¼ length of the orthotropic plate
Dx; Dy ¼ are the flexural rigidities in the x and y directions, respectively
H ¼ torsional rigidity
f ¼ aspect ratio of the buckled panel, i.e. a/(mb)
m ¼ number of half-waves in the longitudinal dimension a.
For a minimum value of s cro, ds cro/df ¼ 0, i.e. f 4 ¼ D x/D y, leading to
scro ¼ 2p2
tb 2
pffiffiffiffiffiffiffiffiffiffi
DxDy þ H ð6:5Þ
and the half-wavelength of buckling l in the longitudinal direction is given by
l ¼ b Dx
Dy
1=4