Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

598 CHAPTER 22 Wings

where,fromExample22.1,Ixx= 809 × 106 mm^4 .Thus,fromEq.(i),

qb=−

86.8× 103

809 × 106

∑n

r= 1

Bryr=−1.07× 10 −^4

∑n

r= 1

Bryr (ii)

Sinceqb=0ateach“cut,”thenqb=0fortheskinpanels12,23,and34.Theremainingqbshearflows
arenowcalculatedusingEq.(ii).Notethattheorderofthenumeralsinthesubscriptofqbindicatesthe
directionofmovementfromboomtoboom.

qb,27=−1.07× 10 −^4 × 3880 × 230 =−95.5N/mm

qb,16=−1.07× 10 −^4 × 2580 × 165 =−45.5N/mm

qb,65=−45.5−1.07× 10 −^4 × 2580 ×(− 165 )= 0

qb,57=−1.07× 10 −^4 × 3880 ×(− 230 )=95.5N/mm

qb,38=−1.07× 10 −^4 × 3230 × 200 =−69.0N/mm

qb,48=−1.07× 10 −^4 × 3230 ×(− 200 )=69.0N/mm

Therefore,asqb,83=qb,48(orqb,72=qb,57),qb,78=0.Thedistributionoftheqbshearflowsisshownin
Fig.22.11.ThevaluesofδandqbarenowsubstitutedinEq.(22.10)foreachcellinturn.

• ForcellI,

dθ

dz

=

1

2 × 265000 GREF

[

qs,0,I( 1083 + 95 + 57 )− 57 qs,0,II+ 69 × 95 + 69 × 57

]

(iii)

• ForcellII,

dθ

dz

=

1

2 × 213000 GREF

[

− 57 qs,0,I+qs,0,II( 783 + 57 + 347 + 68 )

(iv)

− 68 qs,0,III+95.5× 68 − 69 × 57

]

Fig.22.11

qbdistribution (N/mm).