Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

22.5 Shear Center 599

• ForcellIII,

dθ

dz

=

1

2 × 413000 GREF

[− 68 qs,0,II+qs,0,III( 840 + 68 + 106

(v)

+ 840 + 202 )+45.5× 202 −95.5× 68 −95.5×106]

The solely numerical terms in Eqs. (iii) through (v) represent

∮

Rqb(ds/t)for each cell. Care must be
takentoensurethatthecontributionofeachqbvaluetothistermisinterpretedcorrectly.Thepathofthe
integrationfollowsthepositivedirectionofqs,0ineachcell—inotherwords,counterclockwise.Thus,
thepositivecontributionofqb,83to

∮

Iqb(ds/t)becomesanegativecontributionto

∮

IIqb(ds/t)andsoon.
ThefourthequationrequiredforasolutionisobtainedfromEq.(22.12)bytakingmomentsabout
theintersectionofthexaxisandtheweb572.Thus,

0 =−69.0× 250 × 1270 −69.0× 150 × 1270 +45.5× 330 × 1020

(vi)

+ 2 × 265000 qs,0,I+ 2 × 213000 qs,0,II+ 2 × 413000 qs,0,III

SimultaneoussolutionofEqs.(iii)through(vi)gives

qs,0,I=5.5N/mm qs,0,II=10.2N/mm qs,0,III=16.5N/mm

Superimposing these shear flows on theqbdistribution of Fig. 22.11, we obtain the final shear flow
distribution.Thus,

q 34 =5.5N/mm q 23 =q 87 =10.2N/mm q 12 =q 56 =16.5N/mm

q 61 =62.0N/mm q 57 =79.0N/mm q 72 =89.2N/mm

q 48 =74.5N/mm q 83 =64.3N/mm

Finally,fromanyofEqs.(iii)through(v),

dθ

dz

=1.16× 10 −^6 rad/mm

22.5 ShearCenter..........................................................................................

The position of the shear center of a wing section is found in an identical manner to that described
in Section 16.3. Arbitrary shear loadsSxandSyare applied in turn through the shear center S, the
correspondingshearflowdistributionsaredetermined,andmomentsaretakenaboutsomeconvenient
point.Theshearflowdistributionsareobtainedasdescribedpreviouslyintheshearofmulticellwing
sectionsexceptthattheNequationsofthetype(22.10)aresufficientforasolution,sincetherateof
twistdθ/dziszeroforshearloadsappliedthroughtheshearcenter.