Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

572 CHAPTER 20 Wing Spars and Box Beams

and

σz,r=

− 190 × 106

5.22× 108

yr=−0.364yr

Hence,

P 1 =P 3 =−P 4 =−P 6 =−0.364× 295 × 900 =−96642N

and

P 2 =−P 5 =−0.364× 295 × 1200 =−128856N

Atasection1.9mfromthebuilt-inend,

Mx=− 100 ×2.1=−210kNm

andthesectiondimensionsareofwidth=1.22manddepth=0.61m,so

Ixx= 4 × 900 × 3052 + 2 × 1200 × 3052 =5.58× 108 mm^4

and

σz,r=

− 210 × 106

5.58× 108

yr=−0.376yr

Hence,

P 1 =P 3 =−P 4 =−P 6 =−0.376× 305 × 900 =−103212N

and

P 2 =−P 5 =−0.376× 305 × 1200 =−137616N

Thus,thereisanincreaseincompressiveloadof103212− 96642 =6570Ninbooms1and3andan
increaseintensileloadof6570Ninbooms4and6betweenthetwosections.Also,thecompressive
loadinboom2increasesby137616− 128856 =8760N,whilethetensileloadinboom5increasesby
8760N.Therefore,thechangeinboomloadperunitlengthisgivenby

P 1 = P 3 =− P 4 =− P 6 =

6570

200

=32.85N

and

P 2 =− P 5 =

8760

200

=43.8N

ThesituationisillustratedinFig.20.9.Supposenowthattheshearflowsinthepanels12,23,34,and
soonareq 12 ,q 23 ,q 34 ,andsoon,andconsidertheequilibriumofboom2,asshowninFig.20.10,with
adjacentportionsofthepanels12and23.Thus,

q 23 +43.8−q 12 = 0