CHAPTER 9 Thin Plates................................................................................
We shall see in Chapter 11 when we examine the structural components of aircraft that they consist
mainlyofthinplatesstiffenedbyarrangementsofribsandstringers.Thinplatesunderrelativelysmall
compressiveloadsarepronetobuckleandsomustbestiffenedtopreventthis.Thedeterminationof
bucklingloadsforthinplatesinisolationisrelativelystraightforward,butwhenstiffenedbyribsand
stringers,theproblembecomescomplexandfrequentlyreliesonanempiricalsolution.Infact,itmay
bethestiffenerswhichbucklebeforetheplate,andthese,dependingontheirgeometry,maybuckleas
acolumnorsufferlocalbucklingof,say,aflange.
Inthischapter,weshallpresentthetheoryforthedeterminationofbucklingloadsofflatplatesand
then examine some of the different empirical approaches which various researchers have suggested.
Inaddition,weshallinvestigatetheparticularcaseofflatplateswhich,whenreinforcedbyhorizontal
flanges and vertical stiffeners, form the spars of aircraft wing structures; these are known astension
fieldbeams.
9.1 BucklingofThinPlates.............................................................................
A thin plate may buckle in a variety of modes depending on its dimensions, the loading, and the
methodofsupport.Usually,however,bucklingloadsaremuchlowerthanthoselikelytocausefailure
inthematerialoftheplate.Thesimplestformofbucklingariseswhencompressiveloadsareapplied
to simply supported opposite edges and the unloaded edges are free, as shown in Fig. 9.1. A thin
plateinthisconfigurationbehavesinexactlythesamewayasapin-endedcolumnsothatthecritical
loadisthatpredictedbytheEulertheory.Oncethiscriticalloadisreached,theplateisincapableof
supporting any further load. This is not the case, however, when the unloaded edges are supported
against displacement out of thexyplane. Buckling, for such plates, takes the form of a bulging dis-
placement of the central region of the plate, while the parts adjacent to the supported edges remain
straight. These parts enable the plate to resist higher loads, which is an important factor in aircraft
design.
Atthisstage,wearenotconcernedwiththispostbucklingbehaviorbutratherwiththeprediction
ofthecriticalloadwhichcausestheinitialbulgingofthecentralareaoftheplate.Fortheanalysis,we
mayconvenientlyusethemethodoftotalpotentialenergy,sincewehavealready,inChapter7,derived
expressionsforstrainandpotentialenergycorrespondingtovariousloadandsupportconfigurations.
Intheseexpressions,weassumedthatthedisplacementoftheplatecomprisesbendingdeflectionsonly
Copyright©2010,T.H.G.Megson. PublishedbyElsevierLtd. Allrightsreserved.
DOI:10.1016/B978-1-85617-932-4.00009-9 293