Page 403 - Aircraft Stuctures for Engineering Student

384 Stress analysis of aircraft components

- -
w - q R - 1 ~R-~R+I
3 4
qR
Fig. 10.19 Shear flow distribution in the Rth cell of an N-cell wing section.

Consider the Rth cell of the wing section shown in Fig. 10.18. The rate of twist in
the cell is, from Eq. (9.42)

(10.23)

The shear flow in Eq. (10.23) is constant along each wall of the cell and has the values
shown in Fig. 10.19. Writing Jds/t for each wall as 6, Eq. (10.23) becomes

or, rearranging the terms in square brackets

In general terms, this equation may be rewritten in the form

(10.24)

in which 6R-I,R is J&/t for the wall common to the Rth and (R - 1)th cells, 6, is
J&/t for all the walls enclosing the Rth cell and ~5,+,,~ is Jds/t for the wall
common to the Rth and (R + 1)th cells.
The general form of Eq. (10.24) is applicable to multicell sections in which the cells
are connected consecutively, that is, cell I is connected to cell 11, cell I1 to cells I and I11
and so on. In some cases, cell I may be connected to cells I1 and I11 etc. (see problem
P.10.9) so that Eq. (10.24) cannot be used in its general form. For this type of section
the term $q(&/t) should be computed by considering Jq(ds/t) for each wall of a
particular cell in turn.
There are N equations of the type (10.24) which, with Eq. (10.22), comprise the
N + 1 equations required to solve for the N unknown values of shear flow and the
one unknown value of do/&.
Frequently, in practice, the skin panels and spar webs are fabricated from materials
possessing different properties such that the shear modulus G is not constant. The
analysis of such sections is simplified if the actual thickness t of a wall is converted
to a modulus-weighted thickness t* as follows. For the Rth cell of an N-cell wing