Page 416 - Aircraft Stuctures for Engineering Student

10.3 Wings 397

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Fig. 10.31 First correction shear flows applied to give G(dB/dz) = 1 for the separated cells of a two-cell wing
section.

where = Jds/t for the wall common to cells I and 11. Hence

4,II
4: = 411 - (10.32)
61
Similarly

(10.33)

Since 4 and qfI are expressed in terms of the shear flows in adjacent cells they are
referred to as correction carry over shearflow. The factors 61.11/61 and 61,1~/6~~ are
known as correction carry over factors and may be written as
6I:II 6I:Il (10.34)
CIJI = - 1 %,I = -
611 61
We are now in a similar position to that at the beginning of the example with the wing
section divided into two separate cells in which G(dB/dz) = 1 but which are now
subjected to shear flows of, in cell I, qI, qII (on the internal web) and qf and, in cell
11, qII, qr (on the internal web) and qfI. On rejoining the cells we see that qfI from
cell I1 acts on the internal web wall of cell I and qf from cell I acts on the internal
web wall of cell I1 thereby destroying the equality and unit value of G(dB/dz) for
each cell. We therefore apply second correction shear flows 4fl and d1 completely
around the separated cells I and I1 respectively where, from Eqs (10.32), (10.33)
and (10.34)

4: = qf1C11,1, q:1 = 4CI:II
Clearly the second correction shear flows are smaller than the first so that if the
procedure is repeated a number of times the correction carry over shear flows rapidly
become negligible. In practice, the number of corrections made depends on the
accuracy required. The final shear flows in each cell corresponding to G(dB/dz) M 1
are then
qI(fina1) = 41 + 4; + d + d" + . .
*
qII(find) = 411 + 41 + 4'1 + d'i + . . .