T

(e) Square box section (closed)

Perimeter s = tube perimeter = 2n x 20 x 10~3 m

. , , 2tt x 20 x 10"3 side length =---= n x 10 m

Therefore area enclosed by median line

T _ 4 x (tt x 10"2)4G x 2 x 10"3 e ~ 1 X 2tt x 20 x 10"3 = 62 x10~9G

2Ai 2 x (n x 10"2)2 x 2 x 10"3 = 0.253 x 106r

Example 53

A thin-walled member 1.2 m long has the cross-section shown in Fig. 5.10. Determine the maximum torque which can be carried by the section if the angle of twist is limited to 10°. What will be the maximum shear stress when this maximum torque is applied? For the material of the member G = 80 GN/m2.

Fig. 5.10.

Solution

This problem is of the type considered in §5.6, a solution depending upon the length of, and the area enclosed by, the median line.

Now, perimeter of median line = s = (2 x 25 + 27r x 10) mm

= 112.8 mm area enclosed by median = A = (20 x 25 + n x 102) mm2 = 814.2 mm2

4A2 Gt

360 4(814.2 x 10~6)2 x 80 x 109 x 1 x 10"3 i.e. maximum torque possible,

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