Page 402 - Aircraft Stuctures for Engineering Student

10.3Wings 383

Table 10.4

165 61.2
230 85.3
200 74.2
-200 -74.2
-230 -85.3
-165 -61.2

10.3.2 Torsion

The chordwise pressure distribution on an aerodynamic surface may be represented
by shear loads (lift and drag loads) acting through the aerodynamic centre together
with a pitching moment Mo (see Section 7.2). This system of shear loads may be
transferred to the shear centre of the section in the form of shear loads S, and S,>
together with a torque T. It is the pure torsion case that is considered here. In the
analysis we assume that no axial constraint effects are present and that the shape
of the wing section remains unchanged by the load application. In the absence of
axial constraint there is no development of direct stress in the wing section so that
only shear stresses are present. It follows that the presence of booms does not
affect the analysis in the pure torsion case.
The wing section shown in Fig. 10.18 comprises N cells and carries a torque T
which generates individual but unknown torques in each of the N cells. Each cell
therefore develops a constant shear flow q~! qrI,. . . ! qR!. . . ,q~ given by Eq. (9.49).
The total is therefore
N
T = 2 ~ ~ 4 ~ (10.22)
R= 1
Although Eq. (10.22) is sufficient for the solution of the special case of a single cell
section, which is therefore statically determinate, additional equations are required
for an N-cell section. These are obtained by considering the rate of twist in each
cell and the compatibility of displacement condition that all N cells possess the
same rate of twist dO/dz; this arises directly from the assumption of an undistorted
cross-section.

Fig. 10.18 Multicell wing section subjected to torsion.