Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

602 CHAPTER 22 Wings

Fromcolumn⑥

∑^6

r= 1

Py,r=764.4N

Fromcolumn⑩

∑^6

r= 1

Px,rηr=−117846Nmm

Fromcolumn

∑^6

r= 1

Py,rξr=−43680Nmm

FromEq.(20.15),

Sx,w= 0 Sy,w= 10 × 103 −764.4=9235.6N

Also,sinceCxisanaxisofsymmetry,Ixy=0andEq.(19.6)forthe“opensection”shearflowreducesto

qb=−

Sy,w

Ixx

∑n

r= 1

Bryr

or

qb=−

9235.6

34.02× 106

∑n

r= 1

Bryr=−2.715× 10 −^4

∑n

r= 1

Bryr (ii)

“Cutting”thetopwallsofeachcellandusingEq.(ii),weobtaintheqbdistributionshowninFig.22.13.
EvaluatingδforeachwallandsubstitutinginEq.(22.10)givesthefollowing:

ForcellI,

dθ

dz

=

1

2 × 36000 G

( 760 qs,0,I− 180 qs,0,II− 1314 ) (iii)

ForcellII,

dθ

dz

=

1

2 × 72000 G

(− 180 qs,0,I+ 1160 qs,0,II+ 1314 ) (iv)

Takingmomentsaboutthemidpointofweb25,wehave,usingEq.(22.13),

0 =−14.7× 180 × 400 +14.7× 180 × 200 + 2 × 36000 qs,0,I+ 2 × 72000 qs,0,II

− 117846 − 43680

Fig.22.13

qb(N/mm) distribution in beam section of Example 22.4 (view alongzaxis toward C).