The Design of Modern Steel Bridges - TEDI

wherefrom
Ms ¼ 2
3 PE P
The net bending moment at mid-span of the longitudinal stiffeners is equal to
P e1 þ
d P2
PE P
2
3
dP 2
dP 2
P 2
PE P ¼ P e1 1 þ 0:411
PEfPE Pg
since d ¼ 1.234 ðPe1=PEÞ.
If a pin-ended strut, with Euler buckling load P E and subjected to an axial
load P, had an initial imperfection e eff, then the maximum bending moment
due to buckling would be
P eeff
PE
PE P
Hence, for checking the mid-span section of the longitudinal stiffener as a
strut, we may assume the longitudinal stiffener to have an initial imperfection
e eff, given by
wherefrom
Stiffened Compression Flanges of Box and Plate Girders 171
P eeff
PE
P 2
PE P ¼ P e1 1 þ 0:411
PEfPE Pg
eeff ¼ k1e1, when k1 ¼ 1
P
PE
þ 0:411 P
The direction of eeff is the same as the direction of e1, i.e. causing compression
on flange plate.
The support section of the longitudinal stiffener needs to be checked to
ensure that yielding is not caused by the maximum fibre stress due to the axial
load P and bending moment equal to
P e1 Ms
P 2
¼ P e1 1 0:823
PEfPE Pg
¼ P e1 k2, when k2 ¼ 1 0:823
PEfPE Pg
For various ratios of P/PE, the values of k1 and k2 are tabulated below:
PE
P 2
P/P E k 1 k 2
0 1.0 1.0
0.2 0.816 0.959
0.4 0.666 0.781
0.6 0.548 0.259
0.8 0.463 1.634
2