Page 301 - Aircraft Stuctures for Engineering Student

282 Open and closed, thin-walled beams

Example 9.1
A beam having the cross-section shown in Fig. 9.5 is subjected to a bending moment
of 1500 N m in a vertical plane. Calculate the maximum direct stress due to bending
stating the point at which it acts.

8omLL
I'

"

8
rnmq
F-

Fig. 9.5 Cross-section of beam in Example 9.1.

The position of the centroid of the section may be found by taking moments of
areas about some convenient point. Thus
(120~8+80~8)J= 120~8~4+80~8~48
giving

J = 21.6mm
and
(120 x 8 +80 x 8)X= 80 x 8 x 4+ 120 x 8 x 24

giving
X=16~
The next step is to calculate the section properties referred to axes Cxy. Hence

120 ('I3 + 120 x 8 x ( 17.6)2 + 8 x (80)3
rxx = 12 12 + 80 x 8 x (26.4)2
= 1.09 x 106mm4

ryy = (120)3 + 120 x 8 x (8)2 + 80 x (8)3 +80 x 8 x (12)2
12 12
= 1.31 x 106mm4

Ixy = 120 x 8 x 8 x 17.6 + 80 x 8 x (-12) x (-26.4)
= 0.34 x 106mm4