CHAPTER 22 Wings......................................................................................
WehaveseeninChapters11and19thatwingsectionsconsistofthinskinsstiffenedbycombinationsof
stringers,sparwebs,andcapsandribs.Theresultingstructurefrequentlycomprisesone,two,ormore
cellsandishighlyredundant.However,asinthecaseoffuselagesections,thelargenumberofclosely
spacedstringersallowstheassumptionofaconstantshearflowintheskinbetweenadjacentstringers
so that a wing section may be analyzed as though it were completely idealized as long as the direct
stress-carryingcapacityoftheskinisallowedforbyadditionstotheexistingstringer/boomareas.We
shallinvestigatetheanalysisofmulticellularwingsectionssubjectedtobending,torsional,andshear
loads,although,initially,itwillbeinstructivetoexaminethespecialcaseofanidealizedthree-boom
shell.
22.1 Three-BoomShell...................................................................................
ThewingsectionshowninFig.22.1hasbeenidealizedintoanarrangementofdirectstress-carrying
boomsandshear-stress-onlycarryingskinpanels.Thepartofthewingsectionaftoftheverticalspar31
performsanaerodynamicroleonlyandisthereforeunstressed.Liftanddragloads,SyandSx,induce
shearflowsintheskinpanels,whichareconstantbetweenadjacentbooms,sincethesectionhasbeen
completelyidealized.Therefore,resolvinghorizontallyandnotingthattheresultantoftheinternalshear
flowsisequivalenttotheappliedload,wehave
Sx=−q 12 l 12 +q 23 l 23 (22.1)
Nowresolvingvertically,
Sy=q 31 (h 12 +h 23 )−q 12 h 12 −q 23 h 23 (22.2)
Finally,takingmomentsabout,say,boom3,
Sxη 0 +Syξ 0 =− 2 A 12 q 12 − 2 A 23 q 23 (22.3)
(seeEqs.(19.9)and(19.10)).Intheabove,therearethreeunknownvaluesofshearflow,q 12 ,q 23 ,q 31 ,
andthreeequationsofstaticalequilibrium.Weconcludethereforethatathree-boomidealizedshellis
staticallydeterminate.
Copyright©2010,T.H.G.Megson. PublishedbyElsevierLtd. Allrightsreserved.
DOI:10.1016/B978-1-85617-932-4.00022-1 587