Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

590 CHAPTER 22 Wings

22.3 Torsion................................................................................................

The chordwise pressure distribution on an aerodynamic surface may be represented by shear loads
(liftanddragloads)actingthroughtheaerodynamiccentertogetherwithapitchingmomentM 0 (see
Section11.1).Thissystemofshearloadsmaybetransferredtotheshearcenterofthesectioninthe
form of shear loadsSxandSytogether with a torqueT. 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
wingsectionremainsunchangedbytheloadapplication.Intheabsenceofaxialconstraint,thereisno
developmentofdirectstressinthewingsectionsothatonlyshearstressesarepresent.Itfollowsthat
thepresenceofboomsdoesnotaffecttheanalysisinthepuretorsioncase.
The wing section shown in Fig. 22.4 comprisesNcells and carries a torqueTwhich generates
individualbutunknowntorquesineachoftheNcells.Eachcellthereforedevelopsaconstantshear
flowqI,qII,...,qR,...,qNgivenbyEq.(17.1).
Thetotalistherefore

T=

∑N

R= 1

2 ARqR (22.4)

Although Eq. (22.4) is sufficient for the solution of the special case of a single-cell section, which
is therefore statically determinate, additional equations are required for anN-cell section. These are
obtainedbyconsideringtherateoftwistineachcellandthecompatibilityofdisplacementcondition
that allNcells possess the same rate of twist dθ/dz; this arises directly from the assumption of an
undistortedcrosssection.
ConsidertheRthcellofthewingsectionshowninFig.22.5.Therateoftwistinthecellis,from
Eq.(16.22),

dθ

dz

=

1

2 ARG

∮

R

q

ds

t

(22.5)

Fig.22.4

Multicell wing section subjected to torsion.