Page 340 - Aircraft Stuctures for Engineering Student

9.6 Torsion of open section beams 321

i,

8.04mm
2.5mm
t-
1.5 mrn
4
s3

M

Fig. 9.40 Determination of points of zero warping.

warping is not known but may be found using the method described in Section 1 1.5
for the restrained warping of an open section beam. From the derivation of Eq.
(1 1.56) we see that

(9.69)

in which ARqO is the area swept out by a generator rotating about the centre of twist
from some convenient origin and Ak is the value of AR,O at the point of zero warping.
As an illustration we shall apply the method to the beam section of Example 9.8.
Suppose that the position of the centre of twist (i.e. the shear centre) has already
been calculated and suppose also that we choose the origin for s to be at the point
1. Then, in Fig. 9.40

tds = 2 x 1.5 x 25 +2.5 x 50 = 2O0mm2

In the wall 12
A12 = 4 x 25sl (ARo for the wall 12)
from which

A2 = 4 x 25 x 25 = 312.5m’
Also
A23 = 312.5 - 4 x 8.04~2 (ii)
and

A3 = 312.5 -4 x 8.04 x 50 = 111.5mm’