Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

564 CHAPTER 20 Wing Spars and Box Beams

directstress.Thebeamtaperssymmetricallyaboutitshorizontalcentroidalaxis,andthecross-sectional
areaofeachflangeis400mm^2.

TheinternalbendingmomentandshearloadatthesectionAAproducedbytheexternallyapplied
loadare,respectively,

Mx= 20 × 1 =20kNm Sy=−20kN

ThedirectstressesparalleltothezaxisintheflangesatthissectionareobtainedfromeitherEq.(15.18)
orEq.(15.19),inwhichMy=0andIxy=0.Thus,fromEq.(15.18),

σz=

Mxy

Ixx

(i)

inwhich

Ixx= 2 × 400 × 1502 + 2 × 3003 / 12

thatis,

Ixx=22.5× 106 mm^4

Hence,

σz,1=−σz,2=

20 × 106 × 150

22.5× 106

=133.3N/mm^2

Thecomponentsparalleltothezaxisoftheaxialloadsintheflangesaretherefore

Pz,1=−Pz,2=133.3× 400 =53320N

Theshearloadresistedbythebeamwebisthen,fromEq.(20.5),

Sy,w=− 20 × 103 − 53320

δy 1

δz

+ 53320

δy 2

δz

inwhich,fromFigs.20.1and20.2,weseethat

δy 1

δz

=

− 100

2 × 103

=−0.05

δy 2

δz

=

100

2 × 103

=0.05

Hence,

Sy,w=− 20 × 103 + 53320 ×0.05+ 53320 ×0.05=−14668N

TheshearflowdistributioninthewebfollowsfromeitherEq.(20.6)orEq.(20.7)andis(seeFig.20.2(b))

q 12 =

14668

22.5× 106

⎛

⎝

∫s

0

2 ( 150 −s)ds+ 400 × 150

⎞

⎠