Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

592 CHAPTER 22 Wings

FortheRthcellofanN-cellwingsectioninwhichGvariesfromwalltowall,Eq.(22.5)takestheform

dθ

dz

=

1

2 AR

∮

R

q

ds

Gt

Thisequationmayberewrittenas

dθ

dz

=

1

2 ARGREF

∮

R

q

ds

(G/GREF)t

(22.7)

inwhichGREFisaconvenientreferencevalueoftheshearmodulus.Equation(22.7)isnowrewrittenas

dθ

dz

=

1

2 ARGREF

∮

R

q

ds

t∗

(22.8)

inwhichthemodulus-weightedthicknesst∗isgivenby

t∗=

G

GREF

t (22.9)

Then,inEq.(22.6),δbecomes

∫

ds/t∗.

Example 22.2
Calculate the shear stress distribution in the walls of the three-cell wing section shown in Fig. 22.6,
whenitissubjectedtoancounterclockwisetorqueof11.3kNm.

Wall Length (mm) Thickness (mm) G(N/mm^2 ) Cell area (mm^2 )

12 o 1650 1.22 24200 AI= 258000

12 i 508 2.03 27600 AII= 355000

13, 24 775 1.22 24200 AIII= 161000

34 380 1.63 27600

35, 46 508 0.92 20700

56 254 0.92 20700

Note: The superscript symbols o and i are used to distinguish between outer and inner walls

connecting the same two booms.

Since the wing section is loaded by a pure torque, the presence of the booms has no effect on the
analysis.

ChoosingGREF=27600N/mm^2 then,fromEq.(22.9),

t 12 ∗◦=

24200

27600

×1.22=1.07mm

Similarly,

t∗ 13 =t∗ 24 =1.07mm t∗ 35 =t∗ 46 =t∗ 56 =0.69mm