300 CHAPTER 9 Thin Plates
9.5 InstabilityofStiffenedPanels......................................................................
ItisclearfromEq.(9.7)thatplateshavinglargevaluesofb/tbuckleatlowvaluesofcriticalstress.
Aneffectivemethodofreducingthisparameteristointroducestiffenersalongthelengthoftheplate,
therebydividingawidesheetintoanumberofsmallerandmorestableplates.Alternatively,thesheet
maybedividedintoaseriesofwide,shortcolumnsbystiffenersattachedacrossitswidth.Intheformer
typeofstructure,thelongitudinalstiffenerscarrypartofthecompressiveload,whileinthelatter,all
of the load is supported by the plate. Frequently, both methods of stiffening are combined to form a
grid-stiffenedstructure.
Stiffenersinearliertypesofstiffenedpanelpossessedarelativelyhighdegreeofstrengthcompared
withthethinskinresultingintheskinbucklingatamuchlowerstresslevelthanthestiffeners.Such
panelsmaybeanalyzedbyassumingthatthestiffenersprovidesimplysupportededgeconditionstoa
seriesofflatplates.
Amoreefficientstructureisobtainedbyadjustingthestiffenersectionssothatbucklingoccursin
bothstiffenersandskinataboutthesamestress.Thisisachievedbyaconstructioninvolvingclosely
spacedstiffenersofcomparablethicknesstotheskin.Sincetheircriticalstressesarenearlythesame,
thereisanappreciableinteractionatbucklingbetweenskinandstiffenerssothatthecompletepanelmust
beconsideredaunit.However,cautionmustbeexercised,sinceitispossibleforthetwosimultaneous
criticalloadstointeractandreducetheactualcriticalloadofthestructureRef.2.
Various modes of buckling are possible, including primary buckling, where the wavelength is of the
orderofthepanellength,andlocalbuckling,withwavelengthsoftheorderofthewidthoftheplate
elementsoftheskinorstiffeners.AdiscussionofthevariousbucklingmodesofpanelshavingZ-section
stiffenershasbeengivenbyArgyrisandDunne[Ref.3].
Thepredictionofcriticalstressesforpanelswithalargenumberoflongitudinalstiffenersisdifficult
andreliesheavilyonapproximate(energy)andsemiempiricalmethods.Bleich[Ref.4]andTimoshenko
(see[Ref.1],Chapter8)gaveenergysolutionsforplateswithoneandtwolongitudinalstiffenersand
alsoconsiderplateshavingalargenumberofstiffeners.GerardandBecker[Ref.5]havesummarized
muchoftheworkonstiffenedplates,andalargeamountoftheoreticalandempiricaldataarepresented
byArgyrisandDunneintheHandbookofAeronautics[Ref.3].
For detailed work on stiffened panels, reference should be made to as much as possible of the
precedingworks.Theliteratureis,however,extensivesothatherewepresentarelativelysimpleapproach
suggestedbyGerard[Ref.1].Figure9.5representsapanelofwidthwstiffenedbylongitudinalmembers
whichmaybeflats(asshown),Z-,I-,channel,or“tophat”sections.Itispossibleforthepaneltobehave
asanEulercolumn,itscrosssectionbeingthatshowninFig.9.5.Iftheequivalentlengthofthepanel
Fig.9.5
Stiffened panel.