7.10 Numerical Examples
249
Fig. 7.13 Thin-walled steel
section
2a
2a
a
A 1
q 2
q 1
A 2
t
t
t
t
A 2 = (2a × 2a) = 4a
2
For Cell (1),
a 1 =
ds
t
(Including the web)
a 1 =
πa + 2a
t
For Cell (2),
a 2 =
ds
t
=
2a
t
+
2a
t
+
2a
t
+
2a
t
∴ a 2 =
8a
t
For web,
a 12 =
2a
t
Now,
For Cell (1),
2Gθ =
1
A 1
(a 1 q 1 − a 12 q 2 )
=
2
πa 2
(πa + 2a)
t
q 1 −
2a
t
q 2
=
2a
π ta 2 [(2 + π )q 1 − 2q 2 ]
∴ 2Gθ =
2
π at
[(π + 2)q 1 − 2q 2 ]
(a)
For Cell (2),