Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

22.6 Tapered Wings 601

shearmodulusisconstantthroughout,theverticalwebsareall1.0mmthick,whiletheremainingwalls
areall0.8mmthick:

Boomareas:B 1 =B 3 =B 4 =B 6 =600mm^2 B 2 =B 5 =900mm^2

Atthelargercrosssection,

Ixx= 4 × 600 × 902 + 2 × 900 × 902 =34.02× 106 mm^4

ThedirectstressinaboomisgivenbyEq.(15.18),inwhichIxy=0andMy=0,thatis,

σz,r=

Mxyr

Ixx

fromwhich

Pz,r=

Mxyr

Ixx

Br

or

Pz,r=

1.65× 106 yrBr

34.02× 106

=0.08yrBr (i)

The value ofPz,ris calculated from Eq. (i) in column②of Table 22.2;Px,randPy,rfollow from
Eqs. (20.10) and (20.9), respectively, in columns⑤and⑥. The axial loadPrisgivenby[②^2 +
⑤^2 +⑥^2 ]^1 /^2 incolumn⑦andhasthesamesignasPz,r(seeEq.(20.12)).ThemomentsofPx,randPy,r
andcolumns⑩and arecalculatedforamomentcenteratthemidpointoftheinternalweb,taking
counterclockwisemomentsaspositive.

Fromcolumn⑤

∑^6

r= 1

Px,r= 0

(aswouldbeexpectedfromsymmetry).

Table 22.2

① ② ③ ④ ⑤ ⑥ ⑦ ⑧ ⑨ ⑩

Pz,r Px,r Py,r Pr ξr ηr Px,rηr Py,rξr

Boom (N)

δxr

δz

δyr

δz (N) (N) (N) (mm) (mm) (Nmm) (Nmm)

1 2619.0 0 0.0417 0 109.2 2621.3 400 90 0 43680

2 3928.6 0.0833 0.0417 327.3 163.8 3945.6 0 90 − 29457 0

3 2619.0 0.1250 0.0417 327.4 109.2 2641.6 200 90 −29466 21840

4 −2619.0 0.1250 −0.0417 −327.4 109.2 −2641.6 200 90 −29466 21840

5 −3928.6 0.0833 −0.0417 −327.3 163.8 −3945.6 0 90 − 29457 0

6 −2619.0 0 −0.0417 0 109.2 −2621.3 400 90 0 − 43680