Page 345 - Aircraft Stuctures for Engineering Student

326 Open and closed, thin-wailed beams

172.5
Fig. 9.43 Shear flow distribution in beam of Example 9.9 (all shear flows in Wmm).

1.5mrn 1 2 rnm

I
2 4
I 600 mm -1

Fig. 9.44 Wing section of Example 9.10.

It may be assumed, in a simplified approach, that the torsional rigidity GJ of the
complete section is the sum of the torsional rigidities of the open and closed portions.
For the closed portion the torsional rigidity is, from Eq. (9.52)
4A2G 4 x 200002 x 25000
(GJ)cl = = (900 + 300)/1.5
which gives
(GJ),, = 5000 x lo7 Nmm2
The torsional rigidity of the open portion is found using Eq. (9.59), thus

st3 25000 x 900 x Z3
(GJ),, = G - =
3 3
i.e.

(GJ),, = 6 x 107Nmm2