Page 415 - Aircraft Stuctures for Engineering Student

396 Stress analysis of aircraft components

Fig. 10.30 Shear flows giving G(dB/dz) = I for the separated cells of a two-cell wing section.

that each cell acts independently and that cell I is subjected to a constant shear flow qI
such that G(dB/dz) for cell I is equal to unity. From Eqs (9.49) and (9.52)

where

s - ds/t
1-11
Hence
24
41 = -
61
Similarly, for G(dB/dz) to be unity for cell I1

We now have the situation shown in Fig. 10.30 where the two cells are separate and

Imagine now that the two cells are rejoined with the interior web as a common part of
both cells. The action of qII is to reduce the rate of twist in cell I by applying, in effect,
a clockwise torque to cell I opposing the anticlockwise torque corresponding to qI.
Thus, G(de/dz)I is not now equal to G(dB/dz)II so that the assumption of an
undistorted cross-section is invalidated and the shear flows qr and qII are therefore
not the true shear flows.
To correct this situation we again suppose that the cells are separated and apply
constant shear flows qf and qfI around cells I and I1 respectively to counteract
the effect of qII (shown dotted) on cell I and qI on cell 11. The total shear flows
now acting on each cell are shown in Fig. 10.31. Note that the effect of a shear
flow acting on one wall of a cell, e.g. qII applied to the internal web and acting
on cell I, is counteracted by a constant shear flow applied around the complete cell.
Thus