The Design of Modern Steel Bridges - TEDI

168 The Design of Modern Steel Bridges
load P a is given by
m ¼ Pcr
Pcr Pa
where P cr is the Euler buckling load of the strut. The following cubic equation
gives the magnification m of the initial imperfection/eccentricity of an
orthotropically stiffened panel of length L between adjacent rigid transverse
stiffeners under the action of an applied compressive stress s a
sa ¼ scro
scro
m
2 E
þ ðm2
L2 1Þ ð6:10Þ
where scro is the elastic critical buckling compressive stress of the orthotropic
panel and is the sum of the maximum initial out-of-straightness in length L
and any end eccentricity of the applied stress sa. The actual longitudinal
stresses sc and se along the longitudinal centre line and edges, respectively, of
the orthotropic plate are given by
2E 2
ðm 2
9
1Þ >=
sc ¼ sa
se ¼ sa þ
L 2
2E 2
L 2 ðm 2
>; 1Þ
A longitudinal stiffener along or near the centre line is thus subject to:
(1) an axial force s cA e, where A e is the effective stiffener cross-section
(2) a maximum bending moment at its mid-span of
4pEIe ðm 1Þ=L 2
A stiffener at or near the longitudinal edge is subject to:
(1) an axial force of s eA e
(2) a bending moment of s eA e .
ð6:11Þ
ð6:12Þ
In an orthotropic stiffened panel, it is possible that all or most of the
longitudinal stiffeners in the cross-section may have high initial imperfections
e1 of similar magnitude; the end eccentricity e2 of the applied stress due to
overall bending of the whole box and plate girder is also the same for all
longitudinal stiffeners. The first Fourier series term for a constant value of
(e 1 þ e 2) across the whole width of the cross-section is 4/p (e 1 þ e 2), and
equations (6.10) to (6.12) take account of this increase in the effective value of
the imperfection.
The effective cross-section of a central stiffener and also an edge stiffener
should be checked, with appropriate values and sign of , so that the maximum
stress due to the above longitudinal axial loads and bending moments
does not exceed the effective yield stress of the flange plate given by equation
(6.3) or the yield stress of the tip of the stiffener. The benefit of orthotropic