Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

612 CHAPTER 22 Wings

Fig.22.25

Correction shear flows in bay③of the wing box of Example 22.7.

Forequilibriuminthechordwisedirectionatanysectioninbay,③

800 q 21 ′′ = 800 q′′ 43

or

q 21 ′′ =q′′ 43 (v)

Finally,forverticalequilibriumatanysectioninbay,③

300 q′′ 41 + 50 q 43 ′′+ 50 q′′ 21 − 200 q′′ 23 = 0 (vi)

SimultaneoussolutionofEqs.(iii)through(vi)gives

q 21 ′′ =q′′ 43 =38.0N/mm q 23 ′′ =58.8N/mm q′′ 41 =26.6N/mm

Superimposing these correction shear flows on those shown in Fig. 22.22 gives the final shear flow
distributioninbay③asshowninFig.22.26.Theribloadsatstations2000and3000arefoundasbefore
byaddingalgebraicallytheshearflowsintheskinpanelsandsparwebsoneachsideoftherib.Thus,
atstation3000,weobtaintheshearflowsactingaroundtheperipheryoftheribasshowninFig.22.27.
Theshearflowsappliedtotheribattheinboardendofthecutoutbaywillbeequalinmagnitudebut
oppositeindirection.
Notethatinthisexample,onlytheshearloadsonthewingboxbetweenstations1000and4000are
given.Wecannotthereforedeterminethefinalvaluesoftheloadsinthesparflanges,sincewedonot
knowthevaluesofthebendingmomentsatthesepositionscausedbyloadsactingonotherpartsofthe
wing.