The Design of Modern Steel Bridges - TEDI

longitudinal compression is given by
Pcro ¼ p2
B
Dx
f 2 þ Dyf 2 þ 2H
where Dx and Dy are the flexural rigidities in the orthogonal directions, H is the
torsional rigidity of the panel, and f is the aspect ratio L/B of the buckled
panel, L being the buckling half-wave-length in the x-direction.
For minimum value of Pcro, the half-wave-length L ¼ B (Dx/Dy) 1/4 and the
minimum Pcro ¼ 2p 2 /B [Dx Dy) 1/2 þ H].
For orthogonally stiffened web
Dx ¼ EIsx=b, and Dy ¼ EIsy=a
when Isx and Isy are the moments of inertia of the longitudinal and transverse
stiffeners, and b and a are their spacing respectively.
For torsionally weak stiffeners, i.e. stiffeners of open cross-section like
tees, angles or flats, it is convenient and conservative to ignore the torsional
rigidity H. Hence
Pcro ¼ 2p2 E
B
IsxIsy
ab
But if the critical half-wave-length L ¼ B ¼fðIsx=bÞða=IsyÞg 1=4 works out
less than a, then some half-waves will not contain a transverse stiffener and
hence the above solution will not be valid. In that situation we should evaluate
Pcro by taking the lowest value for L that contain a transverse stiffener, i.e.
L ¼ a. This leads to
Pcro ¼ p2 E
B
1=2
Isx B2 b a2 þ Isy a2 a B2 As transverse stiffeners will be at the crest of the half-waves, their strain
energy will be double the strain energy of smeared stiffeners. Hence there is a
good case for doubling the second term in the bracket above.
Let us denote
m ¼ Isx a
b Isy
Then
and
Rolled Beam and Plate Girder Design 141
n ¼ a=B
if m 0:25 > n, Pcro ¼ p2 EIsy
B 2
if m 0:25 < n, Pcro ¼ p2 EIsy
B 2
2m 1=2
n
m þ n 4
n 3