Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

22.7 Deflections 603

Fig.22.14

Shear flow (N/mm) distribution in tapered beam of Example 22.4.

or

0 =− 690726 + 72000 qs,0,I+ 144000 qs,0,II (v)

SolvingEqs.(iii)through(iv)gives

qs,0,I=4.6N/mm qs,0,II=2.5N/mm

andtheresultingshearflowdistributionisshowninFig.22.14.

22.7 Deflections............................................................................................

Deflectionsofmulticellwingsmaybecalculatedbytheunitloadmethodinanidenticalmannertothat
describedinSection19.4foropenandsingle-cellbeams.

Example 22.5
Calculate the deflection at the free end of the two-cell beam shown in Fig. 22.15, allowing for both
bending and shear effects. The booms carry all the direct stresses, while the skin panels, of constant
thicknessthroughout,areeffectiveonlyinshear.

TakeE=69000N/mm^2 and G=25900N/mm^2

Boomareas:B 1 =B 3 =B 4 =B 6 =650mm^2 B 2 =B 5 =1300mm^2

Thebeamcrosssectionissymmetricalaboutahorizontalaxisandcarriesaverticalloadatitsfree
endthroughtheshearcenter.Thedeflection atthefreeendisthen,fromEqs.(19.17)and(19.19),

=

(^2000) ∫
0
Mx,0Mx,1
EIxx
dz+
(^2000) ∫
0

⎛

⎝

∫

section

q 0 q 1

Gt

ds

⎞

⎠dz (i)

where

Mx,0=−44.5× 103 ( 2000 −z) Mx,1=−( 2000 −z)