CHAPTER 20 Wing Spars and Box Beams............................................................
InChapters15through17,weestablishedthebasictheoryfortheanalysisofopenandclosedsection
thin-walledbeamssubjectedtobending,shear,andtorsionalloads.Inaddition,inChapter19,wesaw
howcomplexstringerstiffenedsectionscouldbeidealizedintosectionsmoreamenabletoanalysis.We
shallnowextendthisanalysistoactualaircraftcomponents,including,inthischapter,wingsparsand
boxbeams.Insubsequentchapters,weshallinvestigatetheanalysisoffuselages,wings,frames,and
ribsandconsidertheeffectsofcutoutsinwingsandfuselages.
Aircraft structural components are, as we saw in Chapter 11, complex, consisting usually of thin
sheetsofmetalstiffenedbyarrangementsofstringers.Thesestructuresarehighlyredundantandrequire
somedegreeofsimplificationoridealizationbeforetheycanbeanalyzed.Theanalysispresentedhere
isthereforeapproximate,andthedegreeofaccuracyobtaineddependsonthenumberofsimplifying
assumptions made. A further complication arises in that factors such as warping restraint, structural
andloadingdiscontinuities,andshearlagsignificantlyaffecttheanalysis.Generally,ahighdegreeof
accuracycanonlybeobtainedbyusingcomputer-basedtechniquessuchasthefiniteelementmethod
(see Chapter 6). However, the simpler, quicker, and cheaper approximate methods can be used to
advantage in the preliminary stages of design when several possible structural alternatives are being
investigated;theyalsoprovideaninsightintothephysicalbehaviorofstructureswhichcomputer-based
techniquesdonot.
Major aircraft structural components such as wings and fuselages are usually tapered along their
lengthsforgreaterstructuralefficiency.Thus,wingsectionsarereducedbothchordwiseandindepth
alongthewingspantowardthetipandfuselagesectionsaftofthepassengercabintapertoprovidea
moreefficientaerodynamicandstructuralshape.
TheanalysisofopenandclosedsectionbeamspresentedinChapters15through17assumesthatthe
beamsectionsareuniform.Theeffectoftaperonthepredictionofdirectstressesproducedbybending
isminimalifthetaperissmallandthesectionpropertiesarecalculatedattheparticularsectionbeing
considered;Eqs.(15.18)through(15.22)maythereforebeusedwithreasonableaccuracy.Ontheother
hand,thecalculationofshearstressesinbeamwebscanbesignificantlyaffectedbytaper.
20.1 TaperedWingSpar...................................................................................
Consider first the simple case of a beam—for example, a wing spar—positioned in theyzplane and
comprising two flanges and a web; an elemental lengthδzof the beam is shown in Fig. 20.1. At
the sectionz, the beam is subjected to a positive bending momentMxand a positive shear forceSy.
Copyright©2010,T.H.G.Megson. PublishedbyElsevierLtd. Allrightsreserved.
DOI:10.1016/B978-1-85617-932-4.00020-8 561