Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

19.3 Effect of Idealization on the Analysis 543

Table 19.1

① ② ③ ④ ⑤

Boom y(mm) B(mm^2 ) Ixx=By^2 (mm^4 ) σz(N/mm^2 )

1 + 660 640 278 × 106 35.6

2 + 600 600 216 × 106 32.3

3 + 420 600 106 × 106 22.6

4 + 228 600 31 × 106 12.3

5 + 25 620 0.4× 106 1.3

6 − 204 640 27 × 106 −11.0

7 − 396 640 100 × 106 −21.4

8 − 502 850 214 × 106 −27.0

9 − 540 640 187 × 106 −29.0

Fig.19.6

(a) Elemental length of shear loaded open section beam with booms; (b) equilibrium of boom element.

stress-carryingthicknesstDoftheskin.Equation(16.14)maythereforeberewrittenas

qs=−

(

SxIxx−SyIxy

IxxIyy−I^2 xy

)∫s

0

tDxds−

(

SyIyy−SxIxy

IxxIyy−Ixy^2

)∫s

0

tDyds (19.3)

inwhichtD=tiftheskinisfullyeffectiveincarryingdirectstressortD=0iftheskinisassumedto
carryonlyshearstresses.AgainthesectionpropertiesinEq.(19.3)refertothedirectstress-carrying
areaofthesection,sincetheyarethosewhichfeatureinEqs.(15.18)and(15.19).
Equation(19.3)makesnoprovisionfortheeffectsofbooms,whichcausediscontinuitiesintheskin
andthereforeinterrupttheshearflow.Considertheequilibriumoftherthboomintheelementallength
of beam shown in Fig. 19.6(a) which carries shear loadsSxandSyacting through its shear center S.