The Design of Modern Steel Bridges - TEDI

148 The Design of Modern Steel Bridges
where
s 1 ¼ applied longitudinal stress on the stiffener
t ¼ shear stress in the web
s 2 ¼ transverse stress in the web
ks ¼ defined in Section 5.5.4.
5.6 Restraint at supports
The lateral buckling strength of beams has been derived in Section 5.3 on the
assumption that its cross-section at the supports is restrained fully against any
lateral deflection of its flanges. In reality the stiffeners at the support restraint
to prevent twisting of the beam section is likely to be finite. Flint[12] has
derived a reduction in the elastic critical bending strength scr of a perfect
simply supported beam as
scr
¼
scr
4 GJ
for a central concentrated load
3 LeS
¼ 2GJ for constant bending moment on the
LeS whole length of the beam:
where
GJ ¼ torsional rigidity of the beam
L e ¼ effective length of the beam
S ¼ stiffness of the support against twisting of the beam section.
The reduction s b in the limiting bending stress s b of the imperfect simply
supported beam is, taking the worse of the above two cases
sb
sb
¼ scr
scr
sb scr
scr sb
¼ 2GJ
LeS
sb scr
scr sb
If we decide to limit sb to n% ofsb, then
2GJ
LeS
sb scr
4 0:01 n
scr sb
or
S 5 200 GJ
n Le
sb scr
scr sb
ð5:45Þ
From equations (5.7) and (5.8) in Section 5.3.1, assuming k, and the shape
factor (i.e. the ratio of the plastic to elastic modulus) to be each approximately
equal to unity, scr can be expressed as
scr
sy
2 Le
¼ p
ry
rffiffiffiffiffi 2
sy
E
¼ 5700
b 2