The Design of Modern Steel Bridges - TEDI

Stiffened Compression Flanges of Box and Plate Girders 181
(c) If orthotropic behaviour of the whole flange is taken into account:
E
Dx ¼
64 840 298
¼ 172 907E
375
E
Dy ¼
12
253
0:91
¼ 1431E
H ¼ 0:4E 253 375 25
þ 0:3
6 375 25 þ 3454
¼ð1042 þ 313ÞE ¼ 1355E
1431E
p
scro ¼
2E 3456 3 25 þ 1500
172 907 1431 30002
þ
30002 15004 2 1355
þ
15002 ¼ p2 205 000
½0:0192 þ 0:0025 þ 0:0012Š
25 þ 6:912
¼ 1452 N=mm 2
¼ 10:05 mm
sa ¼ 145:6N=mm 2
The magnification of initial imperfection under the applied stress s a is given
by the relationship
sa ¼ scro
scro
m
2 E
þ ðm2
L2 Since this is a cubic equation, a method of successive approximation could be
used. The first trial value for m is
m1 ¼ scro
¼
scro sa
1Þ
1452
¼ 1:111
1452 145:6
The corresponding applied stress s a1 is calculated from the above relationship
as 145.61 N/mm 2 . Derivative
dsa
dm
¼ scro
m 2 1
The next approximation for m is
m2 ¼ m1
þ 2E 2 m1
L 2
sa1 sa
dso
dm
The longitudinal stress along a central stiffener is
sc ¼ sa
2E 2
L 2 ðm 2
¼ 1181:5
1:111
1Þ ¼144:5N=mm 2
The longitudinal stress along a stiffener near the box edge is
2 2E
se ¼ sa þ
L2 ðm 2
1Þ ¼146:7N=mm 2