TN-3785

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NATIONALADVISORYCOMMITTEE;AERONAUTICS I

IFOR

TECHNICAL NOTE 3785

HANDBOOK.

PART V - COMPRESSIVE

OFSTRUCTURALSTA131LITY

STRENGTHOF FLAT STIFFENEDPMIIILS

By George Gerard

NewYork University

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#-

WashingtonAugust 1957

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TAELEOFCONTENTS

SUMMARY.. . . . . . . . . . ., ● . . .*. . . . .

LNTRODU!TION. . . . . . . . . . . . . . . . . . . .

SYMJ33LS.. . . . . . . . . . . . . . . . . . . . . .

ORIXT!LINGS!CRENGTEOFPANELSWITHX3RMEDSTIFFENERS.Generalizei-Crippling-AnalysisReview. . . . . . .Z-StiffenedPanels. . . . . . . . . . . . . . . .Hat-StiffenedPanels. . . . . . . . . .“.. . . .

CRIPPLINGSTRENGTHOFPANELSWITHEXTRUDEOSTDRFENERSAngleandT-K@peElements. . . . . . . . . . . . .Y-StiffenedPanels. . . . . . . . . . . . . . . .PanelsWithFormedStiffeners. . . . . . . . . . .

STRENGTHOFSEORTRIVE?TEDPANELS. . . . . . . .AdditionalFailureModes . . . . . . . . . . .InterrivetBuckling. . . . . . . . . . . . .Ri~vetGemetrysndStrength. . . . . . . . . .FailureinWrinklingMale... . . . . . . . .EffectiveRivetOffset. . . . . . . . . . . .WrinklingJhstabilityofPanel. . . . . . . .W&inklingFailureofSkin... . . . . . . . .WrinklingFailureofAlminum-AlloyPanels. .RivetCriteria. . . . . . . . . . . . . . . .WkinKlingFailureofPanelsofOtherMaterials

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COLtMNSTRENGTHOFS~PANELS . . . . . . . . .Colmn-StrengthRangese.. . . . . . . . . . . .TransitionRange. . . . . . . . . . . . . . . . .Direct-ReadingColumnCharts. . . . . . . . . . .

OPTIMLMSTIFFENEDPANELSOptimum-PanelTheoriesandResults. . . . . . . .Specifiedslsti!l?hickness. . . . . . . . . . . . .GeometricProportions.O . . . . . . . . . . . . .IkelssticBuckling. . . . . . . . . . . . . . . .GeneralizationsforOtherMaterials. . . . . . . .

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STIFFENED-PANELBOXCONSTRUCTK)N. . .StabilizationofCompressionCuVer.GeneralInstability. . . ... . . .Rotational+tiffnessConsiderations

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Lateral-PressureEffects. . .Efluenceofspars.... . .OptimumConstruction. . . . .

AH?ENDIXA -AEPLICATJDNSECTK)Ncrippling Stragth. . . .Angle-typeelements. .T-typeelements. . . .Shortrivetedp~els . .

ColumuStrengthofPsnelsI?oxconstruction

REFmmms..

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NATIONALADVISORYCOMMITTEEFORAERONAUTICS

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TECHNICALNWE 3785

HANDEOOKOFSTRUCTURALSTABILITY

PARTV - coMl?REssrvE

m

STRENGTHOFl&AT

GeorgeGerard

SWMARY

A generalizedcripplinganalysisforshortextrudedstiffenersispresented.Theanalysis

panelswithformedorappliestomonolithic

panels.“Criteriaaregivenforrivetedpan& whichindicateifthepanelscanbeconsideredtobehaveinamonolithicmanuer.Rivetedpanelsthataresubjecttointerrivetbucklingandwinklingorforcedcripplingdonotbehaveinthismanner.Methodsarepresentedforesti-matingthestrengthofsuchpanels.

Intermediate-lengthandlongstiffenedpanelsaresubjecttootherfailuremodes.Methmisaregivenforestimatingthecolumustrengthofpanels.Variousformsofcolmncurvesanddirect-readingchartsareconsidered.Theoryandtestdataonoptimw.ustiffenedpanelsarepre-sentedforuseinpreliminarydesignstudies.

“ lhboxtypesofconstruction,theribandsparstructuresinfluencetheccxnpressivestrengthofthestiffenedpsnel.Thevariousfactorswhichcanbeofimportanceareconsidered.

IN!CRODUX!1ON

ThispartoftheHandbookofStructuralStabilityisconcernedwiththecompressivestrengthofflatstiffenedpanelsbothintheformofindividualpanelsandascomponentsofboxstructuresunderbending.

Considerationsofthecanpressivestrengthofstiffenedpanelsaregovernedtoa largeextentbythecripplingorshort-panelstrength.Thisquantityisccmmonlydeterminedexperimentallyonpanelswithaneffectiveslendernessratiointheneighborhocxlof20. b thisregion,

. variationsinlengthhavea negligibleeffectuponthecripplingstrength.-.

IllSiswas

PartIVofthisHandbookpresenttiforindividual

(ref.1),a generalizedcrig&nganaly-formedandextrudedelements.This

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2 . . NACATN3785.

methodofanalysisis*ended topanelswithformedstiffenersinthesection“CripplingStrengthofPsnelsWithFormedStiffeners”andtopauelswithextrudedstiffenersinthesection“@ipplingStrengthof

-.

PanelsWithEx_lmud~Stiffeners”h=ein. Attheendofthelast-nsmedsection,thepertinartresultsofthegeneralizedcrippkbganalysisareSullmarizea..

Thecrippl~analysispresentedisvalidforstiffenedpanelsofmonolitJQcconstructiasuchasmachined,forged,andextrudedpanelsaudalsoforrivetedpanelsifcc3%ainrivetingrequirementsaresatis-fiea. ThestrengthofshortrivetedpanelsisdiscussedinthesectianbythatnsmeintezmsofinterrivetbuclddngE@ wrinklingorforcedcrippling.

~ utilizingthemethodsofanalysispresentedintheabuve-mentionedsections,theshort-panelstrengthmsybeestimated.Forintezmediate-lengthandlongpsnels,considerationofadditionalfailuremodesisrequ&edaspresentedh thesection“ColumnStrengthofStiffenedPanels.”VariousQpes ofcolumncurvesarediscussedanddirect-readingcolumnchartsfordeteminingmintium-weightpaneldesignsarereview~.

Foruseinpreliminarydesignstudies,itisconvenienttorepresenttheenvelopeofallminimum-weightstiffened-paneldesignsinthefomnofaptimum-panelcurves.h thesection“OptimumStiffenedPanels”uptimum- .paaeltheory-andtestdataarereviewedandtheresultsaresumarizedintermsofpanelefficiencycoefficientsfa hat,Y,audZ stiffenershapes.Finally,methodsofgeneralizingtheresultsonqptimumpanelsofone.materialtopanelsofothermaterialsarepresented.

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Theuseofstiffenedpanelsinboxconstruction,whichisrepresenta-tiveofwingaudtailstructures,reqydrestheuseofribsorformerstostiividethecompressioncoverintopauelsofreasonablelength.3kLthesection“Stiffened-Ru3elBoxConstruction”strengthandstiffiesscriteriaforthesupportingrib.structuresarepresented.Ihadditiontotheribs,thesparstructuremaycontributetothestrengthofthestiffenedpauel.A briefconsiderationofthe.perttientfactorsispresented.

ThissurveywasconductalUTIIerthecialassistanceoftheNationalAdvisory

SYMEOIS

sponsorshipandwiththefinhn-CmmitteeforAeronautics.

A

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area;forstiffenedpanel,areaofstiffenerplusareaof .sheetcorrespondingtostiffenerspac,ing,sqin.

flexuralrigidityperunitwidth,in-lb

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reqydres theuseofribsorformersto stiividethecompression coverintopauelsofreasonable length.

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spacing,h.

effectivewidth,h.

effectivewidthofskincorrespondingto Ui fromequation(10)

shearrigidityperunitwidth,in-lb

nuniberofcorners

rivetdismeter,in.

effectiverivetdismeter,in.

mdulusofelasticity,psi .

effectivemodulus,psi

secantmodulus,psi

tangentmodulus,psi -

ena-fixitycoefficient

effectiverivetoffset,in.

nmberofcutsplusflsnges

deflectionalspringconstant,lb/in.

bucklingcoefficient

coefficientinwrinklingmcde

columnlengthorribspacing,in.

effectivecolumnlength,Li= L/e~lp,~m

slope

10SdiIlgper unitwidth,lb/in.

rivetpitch,in.●

lateralpressure,psi

radius,in.

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NACATN3785

rivetstrength,ksi

thiclmess,in.

effectivethiclmess,in.

panelwidthorsparspacing,in.

cripplingcoefficient

panelefficiencycoefficient

cripplingcoefficientbasedoncorners

cripplingcoefficientbasedonctisplusflanges

plasticity-reductionfactorforplates

claddingreductionfactm

rotationalspringconstant,torqueperunitrotation

Poissonssratio

radiusof~ation,in.

bucklingstress,ksi

compressiveyieldstrength,ksi

Eulercolumnstress,ksi

titerrivetbuckHngstress,ksi

proportional-limitstrength,ksi

panelstrengthat L~/p= 20,ksi .

effectivestrength,psi

effectivepanelstrength,ksi

compressiveyieldstrengthh cornerofformedsection,ksi

cripplhgstrength,ksi

strengthofa shortrivetedpanel,ksi

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NACA~ 3785 . 5

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%panelstrengthunderlateralpressure,ksi

.% strengthofrivetedpanelinwrhkl@?mcde,ksi

T plasticity-reductionfactor

7 pl.astici@-reductionfactorforoptimumstiffenedpanels

Subscripts:

o optimum

r rivetorrib

s skinorsheet

St Stiffener

w stiffenerweb

av average

CRIPF!GINGSTRENGTHOFPANE.GSWITHIUIMEDSTEFENERS4. .

Considerationsofthecompressivestrengthofstiffenedpanelscanbeconvenientlydividedintoa~roximatelythreeregions:Longpanelswhichbehsveessentiallyascolumns,shortpanelswhicharesubjecttocrippling,andpanelsofintermediatelength.Thelattergenerallyfailasa resultofccmbinedcripplingandcolumnbehaviorwithtorsionaleffectsoftenevideut.

.b thepresentsection,thecripplingstrengthofstiffenedpanels

withformelstiffenersistreated.Theskinandstiffeners~e assumedtobefastenedtogetherinsuchamannerthatthepanelcanbeconsideredtobemonolithicfrcmthestandpointofcripplingstrength.Rivetingrequirementstoobtainmonolithicbehaviorareconsideredinscmedetailinthesectionentitled“StrengthofShortRivetedPanels.”

ThemethodofcripplinganalysisusedforfomedstiffenedpanelsisanextensionofthegeneralizedcripplinganalysispresentedinPartIVofthisHandbook(ref.1). Panelsutilizingextrudedstringersofcomplexcrosssection,suchasY-shapes,me consideredinthesection“CripplingStrengthofPanelsWithExtrudedStringers.4’

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6 NACATN3785

GeneralizedCrippling-AnalysisReview.

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Inreference1,thecrippltngstrengthofa varietyoff~ed sec-tionswiththreeormorecornerswasanalyzed.Itwasshownthatexcel-lentcorrelationwasobtatiedwiththefollowingfamula:

Gf [+(7]1/20.85ct2~—=fic ~ Ucy~cy

(1)

Thecoefficientf3=dependedscxnewhatintheccmnersoftheformedsection.minumallqyfonn&itoradius-thickness

. exsmple.

upontheticreasedyieldpropertiesFarmaterialssuchas2024-T4dU-ratio R/t = 3, PC= 1.3,for

IhanalyzingthecripplingstrengthofstiffenedpanelswhichconsistofformedZ-orhatsectionsattach~toa flatsheet,certainadditionalconsiderationssrisebeyondthoseencounteredintheanalysisofthestiffenersectionalone.Toavoidconsiderationofthemethdofattach-mentofsheettostiffen~s,itisassunedthatthepsnelismonolithic.Rivetstrengthrequirementstoachievethisconditionsrepresentedinthesection“StrengthofShortRivetedPanels.“ Thelineofattaclxnentofthestiffenertothesheetintroduces,ineffect,snothercorner.Therefcme,indeterminingc ineqmtion(1)forthestiffenedpanel,.somealluwanceisnecessaryfortheattadment.

Secondly,thethicknessofthefarmedstiffener~ maybe~ifferent “fromthat ofthesheetts. Thus,inevaluatingequation(1)itisnecessarytoaccouutforthis

Z-StiffenedPauels

Testdataonthecripplingstrengthofflat

theparameterdifferencein

tz/A inthickness.

st~fenedpanelswithZ-sectionstiffenerswereobtainedfromthreedifferentsetsofdata(refs.2 to4)listedintable1. lhthefirstset,therewasa system-aticvariationinthepsrsmeteri+/ts.b thesecondset,ninediffer=tmaterialswereusedcoveringa-wideramgeof E and Ucy values.Thethtrdgroupcoverspotential-strengthestimatesofthehighestobtainablecripplingstrengthofa lsrgegroupofrivet&1panels.Thepotentialstrengthofa rivetedpanelcorrespondsessentiallytothestrengthofamonolithicpanel.~ alltests,theslendernessratioofthepauelL*/p= 20,approximately.Furthermore,theZ-sectionstiffenerhadsub-stantiallythesamephysicalpropertiesasthoseofthesheet,exceptfor .theticreasedyieldprop-iesinthecornersoftheformedZ.

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wasanalyzed.Itwasshownthatexcellentcorrelation wasobtatied withthefollowing famula: Gf [+(7] 1/20.85 ct2~ —=fic ~ Ucy ~cy (1)

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Thecoefficient f3=depended scxnewhat intheccmners oftheformedsection. upontheticreased yieldproperties

3 NACATN3785 7.I

Thedatapresentedinfigure1 arebasedonthenomhalvaluesof .thegecmetiicparametersandonthecompressiveyieldstrengthofthe-2024S-T3material,whichwas43ksi* 7percent.Althoughtherewasawidevariationinthe ~/~ and b~/t~psrsmet=s,nosystematicvaria-tion inthecorrelatiauwasobtatiedbyaccountingfortheseparametersindependently.Thusthedataarepresentedinfigure1 withoutregard.totheseparameters.

lhequation(1),oneofthebasicparametersusedforformedsectionsiS ct2/A.lhevaluatingthisparsmeterfora stiffenedpanelitisnecessarytospecifythemsmnerinwhichthecross-sectionalareaA andthenumberofcornersc aredetermined.Also,itisnecessarytoaccountforthe tJts variations.

Thecross-sectionalareaofa stiffenedpanelistakenastheareaofthestiffenerplustheareaofsheetcmv?espondingtothestiffenerspacing.lb a Z-stiffenedpanel,thenumberofcornersforthetypicalsreaelementconsistingoftheZ stiffenerplussheetisthree:TwofortheZ andonefortherivetline.Thismethodofdet~ c isarbitrsry.Itsjustificationliesinthefactthatthe PC values-ofequation(1)obtainedinthismannersxeincloseagreementwiththoseobtainedformulticornerfomedsections.

.,, Toaccountfori+e ~/ts variationinthemostsimpleanddirect

manner,theparsmeterct2/Afortheformedelementisreplacedbyc~ts/A forthestiffenedpanel.Again,thisprocedureissomewhat.arbitrary.Itisrelativelysimpletointroducescuneweightingfactors.whichmayresultinamorerealisticevaluationofthe ct2/Aparsmeterforstiffenedpanels.However,suchfactorsleadtoadditionalcanplexityad donotimprovethecorrelationsufficientlytowarranttheiruse.

~ useoftheproceduresoutlinedabove,thedatashownh figure1for2024-T3al.uminum-hlloypanelswerefoundtocorrelatedwithin+lo-pacmtl~ts witheqution(1).Thevalueof j3c= 1.26forZ-stiffenedpanelsisingoodagreementwiththevalueof1.30establishedinreference1 frcmtestdataonmulticornerelementsof2024-T3alumtiunalloyformedto R/t= 3 atthecorners.Theslightdifferenceinthetwocoefficientsmaybeattributedtothefactthat,incountingthenum-berofcorners,noincreaseinyieldstrengthoccursattherivetline

. asdoesoccurataid.oftheformedcornersofthemulticornerelements.

Thedataoffigure1 representwe firstisetoftable1 andcoveronematerial,2024-~aluminunalhy,witha widevariationinthetJts psrsmeter.Thesecondsetofdatacoversninedifferentmaterialswitha widevariationin E and Ucy for ~/ts = 1. Thissecondsetofdataispresentedinfigure2.

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Toaccount fori+e ~/ts

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theparsmeterct2/Afortheformedelement isreplaced by c~ts/A .

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andonefortherivetline.Thismethodofdet~ c is arbitrsry.

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8 NACATN3785. .

Infigure2(a),thedataarepresakdintermsof (A/*2)(acy/$’/2andincludetestvaluesupto 7f/acy= 1. Ontherightside,theheavy .linecorrespondstoequation(1)with c = 3 and PC= 1.26.Itcanbeobservedthata considerableportionofthedatafailsbelowtheline.correspondingtoequation(1).’

CsrefulscrutdnyofthesedatasuggestedthatforsamepanelswrinKUngprobablyoccurred(seesectionentitled“StrengthofShortRivetedPanels”)and.therefarethesepanelscouldnotbeconsideredasmonolithicfromthestandpointofcripplingstrength.Itwasdecidedtousethetestdab forthosepanelsidentifiedas25-54)-XIand37.5-75-200- stice,accordXtothecriteriaofthesection“StrengthofShortRivetedPsnels,” thesepanelsa~earedtobeunaffectedbywrinkling. Thedataforthisgroupofpanelsfortheninematerialslistedintable1 areshowninfigure2(b).~tcanbeobservedthat,forthesepanels,thecripplingstrengthcsnbepredictedadequatelybyequa-.tion(l),utilizingc = 3 and PC= 1.26.

. Thefinalsetofdatalistedintable1 consistsofpotential-strengthestimatesof2024-T3and7075-T6aluminum-alloyZ-stiffenedpanels.Thepotentialormsximwnattainablestrengthwasdeftiedasthehighestaveragestressatmaximumloadthatcanbeobtainedfora givenpanelbyvaryingrivetdismeterandpitchtof~ theqtimun.Thepotentislstrengthcorrespondscloselytothecripplingstrengthofa .monolithicpanelofthesameconstruction.

Thesedataareshowninfigure3 in conjunctionwithequation(1) .. fore= 3andf3c = 1.26.Agati,itcanbeobservedthatthepotential- -

strengthdatacorrelatewellaccordingtothemethodsproposedherein.

ToSummarizetheavailabledataonthemonolithiccripplingstrengthoffarmedZ-stiffenedpsnels,thedatafranthethreesourceslistedintable1 arepresentedinfQgure4 groupedaccordingtothe ~/ts values.Satisfactorycorrelationisobtainedwitheqpation.(1)inallcases,usingc =3 a pc.=1.26. Thiscorrelationholdsuptoa vslueof Ff/acy= 1.

Iht-StiffenedPanels

Thecripplhg-stiengthanalysisofformedhat-stiffenedpanelsisessentiallythesameasthatusedfw theZ-stiffenedpanels.Thetest .dataofreference5 covera rangeof * values(bh iswidthoftopweb;~ isheightofsidewebs)betweenO.6and1.2anda rangeof

‘WPS valuesof1.25,1.00,0.63,and0.39.Fora typicalhat-stiffened--..

—-.

panelareaelement,thefacta c = 6 inequation(1),.consistingof4 cornersfcmthehatplus2 rivetlines.

—______ ----- -..—. ___

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theqtimun.The potentisl strength corresponds closely tothecrippling strength ofa . monolithic panelofthesameconstruction.

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Thiscorrelation holdsuptoa vslueof Ff/acy= 1.

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Thecripplhg-stiength analysis offormedhat-stiffened panelsis essentially thesameasthatusedfw theZ-stiffened panels.

WCA m 37/35 9

The test dataforeachvalueof ~/ts are, -- arebasedonthencmdnalvaluesofthegecmetric

showninfigure5 andparametersandthe

compressiveyieldstragthofU ksi.mfildatac-&rel.atewellwith-equation(1)althoughthereisa smallsystematicvariationofthe j3cvaluewiththeparsmeter~/ts,asshownintable2,thatmaybeduetotheraisedyieldeffectinthecorners.Theabsenceofa j3cvariationfortheZ-sectionsuggests,however,thatpossiblytheclosedformofthehatsectionhassaneinflu6nce.

Fortheparticularrivetingissomeevidenceofwr~ing atshowninfigure5. Furthermore,

usedforthehat-stiffenedpanelsthere~f/~cy-ues greaterthan0.8asananalysisofthepanelswith

%/% = 0.39 inreference6 indicatesdefinitepossibilitiesofwr~ing.This~ accountforthesaewhatanmilousbehaviorofthedatashowninfigure5(d) inwhichthe f3cvalueforthegroupwith bs/ts= 75 is

. scmwhathigherthanforthegroupsof bs/ts= 25,35,and50. Becauseofthesuspicionofwrinkling,itisrecommendedthata cutoffof7(7f/Cy=o;8 beplacedone~&tion(1)that&autionbeexercisedinusingthis

forhat-stiffenedpanelsandequationforpanelswith

%/% = 0.39.

C!RIEPLINGSTRENGTHOFPANELSWITHEXTRUDEDSTIFFENERS

.M attemptingtoextendthegeneralizecrippling-strengthanalysis

topanelswithextrudedstiffeners,inthemamnerdemonstratedinthesection“CripplingStrengthofPanelsWithFarmedStiffeners,” snessen-tialdifficultyIS encountered.Thisdtificul~centersaroundtheselectionofthenumberofcornersforanextrudedsectioninwhichseveralfI.angesorwebsmaymeetata ccmmmijuncttie.

Also,asshowninreference1,thebehaviorofthejunctionofadjacentweborflsngeelementshasa significantinfluenceonthecripplingstrength.Forexample,thejunctionoftheflangeelenentsofansngleissubjecttodistortionafterbuckling.Ontheo@erhand,theflangeelementsofa cruciformsectionarehorizontallyopposedsothatthejunctionoftheflangeelementsremainsessentiallystraight.Forthisreaaon,itwasfoundthatthecripplingstrengthperflangeofthecruciformwhichisessentiallyccmposedoftwoanglesisgreaterthanthecrippklngstrengthperflangeoftheanglealone.

h ordertocharacterizethisclifferenceinbehaviorthefollpwingnomenclaturehasbeenadupted:“Angle-type”isusedtorefertotwoadjacentelematswhichmeetata junction,whereas“T-type”refersto

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Fortheparticular riveting issomeevidence ofwr~ing at usedforthehat-stiffened panelsthere ~f/~cy-ues greater than0.8as

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ofwrinkling, itisrecommended thata cutoffof 7(7 f/Cy=o;8 beplacedone~&tion(1) that&aution beexercised inusingthis forhat-stiffened panelsand equation forpanelswith %/% = 0.39.

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hasbeenadupted:“Angle-type” isusedtorefertotwo adjacent elematswhichmeetata junction, whereas“T-type” refersto

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threetheseposed

NACATN3785“.

ormoreadjacentelementsmeetingata commonjuncture.withdefinitionsitcanbeobservedthatallformedsectionsarecom-ofangle-typeelements,whereasextrudedsectionsmsybecmposed

.

ofsngle-and/orT-me elem&nts.—

Thus,forextrudedsectionscomposedofonlysngle+ypeelements,thegen=elized-crippling-analysisprocedureoftheprecedingsectionmaybeused.Insuchcases,thereisnomajorclifferencebetweencom-parableextrudedandformedsections.Theminordifferencesincludefilletradiuseffectsfortheextrusionandraisedyieldcornereffectsfortheformedsection.Anydifferencesinyieldsti-h exeaccountedfordirectlyinthecripplhg-strmgthformula.

Forextrudedsectionscmposedwhollyor partiallyofT-typeelements,thecornerconceptinequation(1)isnowreplacedbya newconceptwhichinvolvescuttingthesectionintoa seriesofflanges.Ihorderto$urMfythis.methodofsnalysis,testdataonV-grooveplates,extrudedengles,.squaretubes,T-,H.,andcruciformsectionsarereviewed.Theanalysis oisthenextendedtostiffenedpanelswithextrudedY stiffeners.Finally,intheinterestofa singlemethodofanalysisforalltypesofmulti-cornersectionssmds,tiffen~,panels,thedataoftheprecedhgsectiononZ-andhat-stiffenedpsnelsarereviewedintermsoftheanaly’sisofthissection.

Angleand T+pe Elements

Ihref=ence1,equation(1)wasusedtocorrelatetestdataonsqyaresadrectsnguhrtubes.Itwasfouudthatavalueof Pc= 1.42for c = 4 gaveexcellentcorrelationwiththeavailabletestdataonfourdifferentaluninum~OyS .

I$ycuttingthetubeintoa seriesoffouranglesasshowninfig-ure6 andcorrelatingthetestdataaccordhgtotheparameterg whichisthetotalnmhr ofcutsplusflanges,thefollowingrelationfaangle-typeelementsisobtained:

. [011/20.85%=pg$#-=Cy Cy

Byuseofequation(1),itisevidentthat

~g = Pc(c/g)o”85

(2)

..

(3)

.

.— -— . — ___ _

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three ormoreadjacent elements meetingata commonjuncture.

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Forextruded sections cmposedwhollyor partially ofT-typelements, thecornerconceptinequation (1)isnowreplaced bya newconcept which involves cutting thesection intoa seriesofflanges.

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thetestdataaccordhgtotheparameterg which isthetotalnmhr ofcutsplusflanges,

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. [01 1/20.85 %=pg$#- =Cy Cy (2)

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Angleand T+pe Elements

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Pc= 1.42 for c = 4 gaveexcellent correlation

NACATN3785

Thus,forthe

—

11

extrudedtubes

Bg= 1.42(4/Q0”85= 0.558 (4)

Thecorrelationaccordingtoequations(2)and.(4)fortheextruded-tubetestdataofreference1 isshowninfigureT(a)bythelinedesignatedangletype.Alsoshownwiththislinearesometestdatafromrefer-ence1 onextrudedaug~esfm whichg = 2 andonV-grouveplatesforwhichg = 3. Goodcorrelationisobtainedwiththesedataalthoughtheextruded-angledataaretoofewinnumbertop-t definiteconclusiaustobedrawn.

TheanalysisforT-typeextrusionsisbasedonthefollowingrela-tionestablishedinreference1 frcmtestdataoncruciformextrusions:

af [()]@2 ~ 1/20.40—=Pg~~acy

(5)

ForthecrucifomnPg= 0.670and-g=4 asshowninfigure6. TMRrelationshipalsocorrelateswell.withsanelimitedtestdataonT-extrusionsasshowninfigurey(a).

RatherextensivetestdataonH-extrusionsoffouralminumalloysandonemagnesiumalloyareavailabletotestfurthertheg-correlationscheme.h reference1,theH-adzrusionwastreatedasa’specialtype.oftwo-cornerelementandthegeneralizedcripplinganalysiswasnotappliedtothissection.

ASshowninfigure6, g = 7 foranH-extrusion.ThetestdatacorrelatedaccordtigtotheparsmeterA/gt2axeillustratedinfig-urey(b).Itcanbeobservedthatsatisfactorycorrelationwitheqya-tion(5)isobtainedbyutilizingthe ~g valueforthecruciformfor5tJ < 3/4.Asdiscussedinref~~ce1,beyondthiscutoffflCy=

‘f= ‘cr I

for Zf/acy> 3/4.

(6)

.- —..- ... . . .. . .._ —— —— -—— . _____ -.—. —

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Theanalysis forT-typextrusions

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af [()] @2 ~ 1/20.40 —=Pg~~ acy

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ForthecrucifomnPg= 0.670and-g= 4

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thatsatisfactory correlation witheqyation( 5)isobtained byutilizing the ~g valueforthecruciform for 5tJ < 3/4.Asdiscussed inref~~ flCy=

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20.40

.. — . .-

12 NACATN3785..

FYomtheresultspresentedinfigure7,itappearsthattheg-correlationschemeforangle-sndT-typeextrusionspermitsaninte-gratedapprosch“tothecrippling-strengthanalysisofextmudedelements.

--

Y-stiffenedPsnels

InanslyzingthecripplingstrengthofmonolithicstiffenedpanelsutilizingextrudedY-stringers,certainadditionalconsiderationsareencounteredwhichhavenotarismpreviously.Theseinclude:.

(1)Themethodofdeterminhgg fora stiffenedpanel.

(2) Thethicknessesofthevariousflangesoftheextrusionmaynotbeconstant.

(3)Thecompressiveyieldstrengthoftheextrudedstiffenermaybesignificautilydiff~entfromthatofthesheet.

Themethodofdeterminingg fm a Y-stiffenedpanelisillustratedinfigure8. Sincethetestdataareforpanelstestedwithsixstiff-eners,itisdesirabletodetemnheanaveragevalueof g fora typicalareaelementeqpaltothestiffenerspacing.Itcanbenotedfrcmfig-ure8 thatthecutsmidwaybetweenstiffenersarecreditedtotheelementtotheleftofthecut.Thusthelastelementontherighthasa value .

of g ofoneunitlessthantheotherelements.Thus,theaveragevalueof g = 18.83fortheY-sttifenedpanelaccouutsforthisfact. ..

FortheparticularY-extrusimusedinreference7,thethicknessofthehorizontallyopposedflsngesatthetopofthesectionisgreaterthanthatof‘theotherelementsinthecrosssection,asshowninfig-ure8. Con~equently,indeterminingtheeffectivethicknessofthe ●

stiffenert+ foruseinthegeneraliz~cripplingrelation,thefollowlngmethodofweightingwasused:

(7)

b equation(7),bi and ti refertothelengthendthickness,respec-tively,ofthecross-sectimalelements.

Similarly,forthe7075-T6alunhum-alloypanels,thecompressiveyieldstrengthofthestiffener(Ucyw= 78ki) was Signific=tl.yhigher ‘.

thanthatofthesheet(ucys= 67ksi). Thefollowingweightingprocedurewasused:

,

. — . -.——— .—— .—— -.—— . . .

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(2) Thethicknesses ofthevariousflangesoftheextrusion may notbeconstant.

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Themethodofdetermining g fm a Y-stiffened panelisillustrated infigure8.

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Y-stiff enedPsnels

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equently, indetermining theeffective thickness ofthe l stiffenert+ foruseinthegeneraliz~ crippling relation, thefollowlng methodofweighting wasused:

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panels,thecompressive yieldstrength ofthestiffener (Ucyw= 78ki) was Signif ic=tl.

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esta relacion no es para nada "clara" a la hora de determinar la estabilidad local del nervio

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la resistencia de proporcionalidad del 7075 extruido es mas que sorprendente. las aleaciones de litio presentan una resistencia de proporcionalidad aun mayor, o a igual magnitud de esta, mayor estabilidad de placa. esto es tanto por el mayor modulo de rigidez, como por los fenomenos de anisotropia (excesivos en la serie 8xxx).

NACATN3785

where~ istheeffectivethiclmessofthestiffened

Asa consequenceoftheseweight”&procedures,cripplingrelationfortheY-stiffenedpanelhasthe

u

(8)

panel.

thegeneralizedform

(9)

Thetestdataofreference7 for2024+3and7075-%aluminum-alloypanelswerecorrelatedaccordingtotheparametersofequation(9)forthreedifferent~/ts ratios.Ihallcasesncminaldimensionswereused.SincetheY~extrusionisccmposedofbothsngle-andT-typeelements,thevalueof m ineqyation(9)isnotevidenta priori.Asshowninfigure9,satisfactorycorrelationisobtainedbyconsideringtheY-extrusiontobeanangle-meelementsothatm = 0.85.The ~gvaluesvarysomewhatwiththeparameter‘~/tsasgivenintable3.!Ihisvariationwaspreviouslyobservedforthehat-stiffenedpsnels.

PanelsWithFormedStiffeners

Inviewofthedestiabili@ofhavingonemethalofanalysisforbothformedandextrudedsections,ifpossible,theresultsofthesection“CripplingStrengthofPanelsWithFormedStiffeaers”onpanelswithfomed Z andhatstiffenersarereviewed.Thesepqnelswere-z~ accOI’dingtoequation(1)fOr multicornerelementsasdemon-stratedinreference1.

~ useofeqyation(3),thec-correlationmethodcanbeconvertedtotheg-correlationmethod.Theresultsarelistedintable4.Similarly,byuseoffigure8,thevaluesof g canbeobtainedforthestiffenedpanelsandthe PC valuesconvertedto ~g valuesbyuseofequation(3).Suchresultsaregivm intable4.

All pg valuesaresmmarizedasa functionof %Jts infigure10.Itcanbeobservedthatat ~/ts = 1,all Pg valuesareh gocdagree-ment.Furthermore,thevariationof ~g with~/ts forthehat-andY-s”tiffenedpanelsissubstantiallythesame.

.. .. —-. — ——-.. ..— .z— —. .

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crippling relation fortheY-stiffened panelhasthe thegeneralized form (9)

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satisfactory correlation isobtained byconsidering theY-extrusion tobeanangle-meelement sothatm = 0.85.The ~g valuesvarysomewhat withtheparameter‘~/

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PanelsWithFormedStiffeners

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Hay que notar que el canal e y, aumentan el modulo de torsión de la placa en su conjunto. Mientras que el Z no posee rigidez torsional apreciable.

14 MAOATM3785

STRENGTHOFSHORTRIVETEDP-

. .

‘-

Illtheprecedingsections,thecripplingstrengthofmonolithicpanelswasconsidered.Suchpanelsincludeintegralformsofconstruc-tionsuchasmachined,extruded,fygedorrolled,andgenerallybondedorsesmwel,dedp=els. lhrivet~orspotweldedpanels,thediscretelocationsoftheattachmentscanpermittheoccurrenceofadditionalbucklingandfailuremodeswhichreducethecripplingorcolumnstrengthofthepanelbelowthatofthecorrespondingmonolithicpanel.

.SpotWeldsgenerallycanbeplacedsufficientlyclosetogetherso

thatthemonolithicstrengthcanbereadilyachievedinspotweldedpenels.Forpanelswithrivetedattachments,however,carefuldesignisoftenreqxlredtoachievemonolithicstrengthlevels,particularlyinshortpanelsofheavy-sheetandlight-str~erconstruction.Insuchcases,closelyspacedlarge-diemet~rivetsareoftenreq.ed.

Theadditionalbucldingorfailuremodesthatcamdestroythemono-lithicbehaviorofrivetedpanelsaxetiterrivetbuckling,wrinklhgorforcedcrippling,andrivetfailure.Inthepresentsection,thebehaviorofstiffenedpanelssubjettedtotheseadditionalbucklingandfailmemodesisreviewedandavailabletheoriesarepresented.Designcriteriaaregiventhatpresenta rationalapproachtotheachievementofmono-lithicstrengthlevelsforrivetedpanels.

AdditimalFailureModes

.

.

Theinterrivetmodehml.vesbuckl@ oftheskinofthesttffenedpanelasa widecolwnnuponessentiddyundistort$istringerssothatseparationoccursbetweentheskinendstringers.Thewidthofthewidecolumnisgenerallyequaltothatofthepanelendthelengthcorrespondstotherivetspacing.DifferentrivetQpes suchasftit-headorcounter-sunkrivetsprovidedifferingendrestraints,th~ebyreducingtheeffec-tivelengthofthecolmn. Sincefailureendbucklingofa widecolumnsreessentiallycoticident,interrivetbucklingt~tes theability -oftheskintocarryadditionalloadsbeyondbuckling.

FailureinthewrinklingmodeMS thesanegemmala~earsmceastheinitialinstabili~andoccursata somewhathigherstresslevel.Ithasbeentemned“wrhlCldng”becauseofcertainshuileritieswithwrinklingofthefacesinsandwichconstruction.Atfailure,thebuckleshavegrownsothatthesldnactsasa widecolmnonenelasticfounda-tion.However,incontrastwiththeinterrivetmode,thestrhgerdis-tortsappreciablyastheattachmentflmgefollowsthebuckledskincon- .tour.Sincetherivetsareactiveincausingtheflangetoconfomto

.

thesldn,rivet-strengthconsid=ationsareofimportancehere.The

—. . —.—. .. . . . . . . ---- — .—. . . .. ___ ..—. -.-. —

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STRENGTH OFSHORTRIVETEDP-

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However, incontrast withtheinterrivet mode,thestrhgerdistortsappreciably astheattachment flmgefollows thebuckledskincon- . tour. .

B NACATN3785

distortedattachment-, stringersectionand

~>

flmgecausesdistmtionofotherelementsinthehencethetezm“forcedcrippling”isalsousedfor

thisphenomenon.Thebucklewavelengthisgreaterthantherivetspacinganddependsupontheeffectivefouudationcharacteristicsofthestring=.

h figure11,thevariousfailuremodesofa short,riveted,stiffenedpanelareshownschematically.Itisassum~herethatonlytherivetspacingisvaried.Forsmallrivetspacings,themonolithicstrengthlevelofthepanelisatttiedandcanbepredictedbythemethodsofthesections“CripplingStrengthofPanelsWithFormedstiffeners”and “CripplingStrengthofPanelsWithExtrudedStiffeners.”, Formoderaterivetspacings,wrinklingoccursata wavelengthgreaterthantherivetspdcing.Atlargespacings,interrivetbucklingoccurs

“

atanoverallwave

Historically,

lengtheqpaltotherivetpitch.

WterrivetBuckling

interrivetbucklingwasobservedshortlyafter-the-.introductionofall-metalconstructionintheairframe.Howland(ref.8)analyzedthisproblemforpauelswithflatheadrivetsbyassumingthat .theskinactsasa tidecolwnnwhichisclampedattheendswheretherivetsarelocat~.Thus,theinterrivetbucklingstressisgivenw

eJc2qm()ts 2

“i = 12(1 - V2)~(lo)

Inequation(10),q and ~ aretheplastici@-reductionfactorandcladdingreductionfactor,respectively,forplatecolumnsasdiscussedinPartI ofthisHandbook(?%f.9).

A surveyofscmeMmitedtestdataontiterrivetbuclClingindicatesthatthevalueofend-fixitycoefficiente inequation(10)isgenerallyclosetothatforclampingexceptformachtnecountersunkrivets.Fromthesedata,thevaluesofend-fixitycoeffickntgivenintable5 fromreferences8,10,and11aretentativelysuggestedforusewithegpa-tion(10).~Althoughnopublisheddataareavailableonrivetsind~ledjoints,itmaybetentativelyassmwdthatthevalueof e = 1 forcounter-sunkrivetsmaybeusedinthiscaseintheabsenceofsubstantiatingdata.

Afterinterrivetbucklingoccurs,itisreasonabletoexpectthat9 undercontinueddeformationtheskinwillcontinuetocarrytheloadat

buckl!hgbutnosdditimalloadsincethebehavioroftheskinisthatofa widecolmn. !l?hus,thefailingstressoftherivetedpauelinthis

c caseis ..

.

.— .—. . .. . . — ——. — — ——...

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Thus,theinterrivet buckling stressisgivenw

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itisreasonable toexpecthat 9 undercontinued deformation theskinwillcontinue tocarrytheloadat buckl!

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hus, thefailingstressoftheriveted pauelinthis c caseis

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distorted attachment -, stringer section and flmgecausesdistmtionofotherelements inthe hencethetezm“forced crippling” isalsousedfor thisphenomenon. Thebucklewavelengthisgreater thantherivet spacing anddepends upontheeffective fouudation characteristics of thestring=. .

.—

16

.. .— — —-

NACATN3785..

(m .

where2bei isthetotaleffectivewidthofskincorrespondingtotheinterrivetbucldiingstressUi givenbyequation(10).Thecripplingstressofthestring=alone~fst canbedetermined~ themethods

ofPartIVofthisHandbook(ref.1).

RivetGeometryandStrength

Withtheuseofheavierskingageswhichapproachor”exceedthestringerthiclmess,i.nterrivetbuc~ingisrarelya factortidecreasingthestrengthofshortpanels.However,ithas.beenobservedthattherivetdiameterandpitchandrivetstrengtharefactorsofconsiderableimportanceinachievingmonolithic-panelstrengthlevels.

TheNACAhasconductedanextensiveexpertientalprogramtoestablishtheeffectsoftherivetvariablesuponthestrengthofshortpanelsthatfailinthelocslinstabilityandwrinklingmodes.Theresultsofaprogrsmforshort2024-Uand70~-T6ahminum-alluyZ-stiffenedpanelswith2117-T4flatheadrivetsinwhichtherivetdiameterandpitchwere .varied(ref.4)aresummarizedinfigure1.2(a).Theordinateoffig- .ureU(a)representstheratioofthestrengthoftherivetedpanelFf tothatofa correspondingmonolithicpanel.Thelattercanbe

..

obr~inedbythemethodsofthesection“CripplingStre&thofPanelsWithFormedStiffeners”asdiscussedthereinforZ-stiffenedpanels.

Testdataofreference12indicatethatthestren@hofpanelsofmoderateslendernessratio(L’/p= 35)isaffectedconsiderablylessthauthatofshortpanelsbyrivetpitchanddiametervariations.Thestrengthoflongpanels(Lt/p= 60)wasnegligiblyaffectedbyrivetconfigurationinthersngetested.

Anotherexperimentaltiestigationofreference13wasconcernedwiththeinfluenceofrivettensilestrengthuponthestrengthofshort7075-T6alumimm-alluyZ-stiffenedpanels.Theresultsfareightrivettypesaresummariz~infigure12(b)intermsofsubstantiallythessmequantitiesusedinfigure12(a).Thesoledtiferenceistheuseofan&fectiverivetdiemeter~ -ss~ 2n7-@ dUUiINZU-SUOY

definedintermsofa standardrivettakenrivetwiththefolluwingtensileproperties: ..

---- . ..__ .._ _ —- .—— —-.

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(m

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Testdataofreference 12indicate thatthestren@hofpanelsof moderate slenderness ratio(L’/p= 35)isaffected considerably less thauthatofshortpanelsbyrivetpitchanddiameter variations. The strength oflongpanels(Lt/p= 60)wasnegligibly affected byrivet configuration inthersngetested.

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&fectiverivetdiemeter~ - ss~ 2n7-@ dUUiINZU-SUOY definedintermsofa standard rivettaken rivetwiththefolluwing tensile properties:

NACATN3785

.—.

17

s = 57ksi

I

<1.67dejtav=(12)

S=”&-~ de/tav>l*67

wheretav istheaverage-ofskinand

Theeffectivediameterofa rivet

string=thicknessinfiches.

ofanothamaterialis

(13)

wheresr isthetensilestrengthoftherivetdefinedasmaximumtensileloaddividedbyshankareainksiunits.

FailureinWrinklingMale

Thedatapresentedinfigure12relatethe“strengthofshortrivetedpanelstothecripplingstrengthofthecorrespondingmonolithicpanel.However,thesedataareoflittlevaluefranthedesignstaulpointofprovidingcriteriatoachievemonolithicstrengthlevels.Furthermore,recentanalysesofthewrinklingphemnenonhaveprovidedamoredetailedunderstandingoftheinfluenceoftherivetvariablesuponthecompressivestrengthofpanels.

.

AWWiS andDunne(ref.14)appeartohavebeenthefirsttoconsidertheoccurrenceofthewrinklingphenamnoninrivetedpanelsinthepub-lishedliterature.Theydiscusseditqualitativelyintermsoftherivetoffsetdistsncefra theplaneofthestiffenerweb.

BijlaardandJohnston(ref.15)havepresentedanextensiveanalysisoftheforced-cripplhgphenomenon.Bucklingcoefficientsforthiscasearepresentedfora limitedrangeofriveted-panel-configurationvariables~andeffective-widthdataaregivenfromwhichthefailureloadofthepanelinthewrinklingmodecan& estimated.Theresultsoftheanalysisareinreasonableagreementwithtestdataonseveralstiffenedpanelsusedtocheckthetheory.

A morerecentanalysisofwrinklhglzySemonisnsndPet=son(ref.6)utilizesa structuralparameterwhichccmbinestherivetpitch$diameter~@ offsetdistancefrcmthewebplaueofthestiffenerintoa singleparameter,theeffectiverivetoffset.Thelatterisevaluatedbyuseofa relativelyrigorousinstabilityanalysisinconjunctionwith~=imentaldataonrivetedpanels.A semiempiricalfailing-strengthanalysisofthe

. . . . . .—. ——. — —— . ..-— -.—- .-.

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panels.A semiempirical failing-strength analysis ofthe

18 NACATN3785. .

wrinklingtie basedonthisparameterispresent~therein.compari-sonsoftheresultsoftheanalysiswitha largegroupoftestdataon2024-T3and70~-T6almdnnn-alloyZ-andhat-stiff=ed panelsfiicate ‘ -goodagreementalthoughitwasfoundthatthesmilysisreqtiessanemodificationforpanelsofothermaterials.

EffectiveRivetOffset

Thegoverningparameterinthisanalysisoftheeffectiverivetoffsetwasevsluatedbyrelatingtheexperimentallyobservedbucklingstressh thewrinklingmodetothetheoreticalvalue.Thetheoreticalvaluesarepresentedh figure13(a)andtheexperimental,infigure13(b)intermsoftheeffectiverivetoffsetdistancef,andthereforef canbedeterminedfrcmeachpsneltested.Thebestfittothesedatawasdeterminedfromsuccessivecrossplottingandtheresultsareshowninfigure14. Sincethischartisbasedonexperimentaldata,certainlimi-tationsasgivenbelowareimpliedinitsuse.

Thedataoffigure14wereobtatiedprimsrilyfra 2024-T3and7073-T6aluminun-slloy”-paneltestsutilizing2117-@kalumimm-alloyNACAcountersunkrivets.Apparentlytheinfluenceofotheraluminun-alloyrivettypessuchasuniversal-headorflatheatrivetsonthewrinklingstressissmallandthereforefigure14maybeused.However,figure14wasestablishedfrcmtestsonpanelswithrivetshavingadismetergreaterthen90percentoftheskinthickness.Therefore,fig-

.

ure14shouldnotbeusedfor d ts<0.9 withoutconfirmation.I.

Sincetherivetstiffnessisa contributingfactorintheeffective-rivet-offsetpsrsmeter,changesh rivetmaterialfrcmtheal~um alloyscanresultinf-valuesclifferentfrcmthosegiveninfigure14. Testdataindicate,however,thatrivetmaterialswitha hi~erelasticmodulusandstrengththan2117-T4alminunalloydonotsignificantlyincreasethestrengthofthepanel.Ontheotherbend,al.minun-alloypanelswith.FS~lmagnesiumrivetsorCherryBlindrivetsfailedatloadslessthanthoseofcorrespondingpanelswith2117-T4rivets.Therefore,figure14shouldbeusedwithcautionforaluminun-alloypanelsutilizingrivetmat=ialsoflowerstrengthsandstiffnessesthan211.7-T4rivets.

Thedatausedtoconstructfigure14arebasedonpaneltestsusingfmmedstiffen=s.Theuseofextrudedstringerswithsharpexteriorc-ers usuallyeliminatesthewrinklingmodebecausetherivetoffsetdistancecanbereducedandthestiffnessofthefilletedattachmentflangeisgreaterthanfortheformedstiffeqer.Theavailabletestsonpanelswithextrudedstiffenersindicatethatfigure14providesaconservativeestimateof f althoughthedataaretoofewtopermittheconstructicmofa chartsuchasfigure14forthiscase.

..

. . —.—— . . .. —.-——_ .._ . . -—-——— - .—— ---, .---

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wrinkling tie basedonthisparameter ispresent~therein.

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byrelating theexperimentally observed buckling stressh thewrinkling modetothetheoretical value.

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thatrivetmaterials witha hi~erelastic modulusand strength than2117-T4 alminunalloydonotsignificantly increase the strength ofthepanel.Ontheotherbend,al.minun-alloy panelswith .FS~lmagnesium rivetsorCherryBlindrivetsfailedatloadslessthan thoseofcorresponding panelswith2117-T4 rivets.

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s.Theuseofextruded stringers withsharpexterior c-ers usuallyeliminates thewrinkling modebecause therivetoffset distance canbereducedandthestiffness ofthefilleted attachment flangeisgreater thanfortheformedstiffeqer.

-—— ..-—..

19NACATN3785 “

WrinklingInstabilityofPauel.-. Intheanalysisofa shortrivetedpanelwithaprescribedconfig-

uration,threebucklingties arepossible:LocalbucklingwhichistreatedinpartIIofthisHandbook(ref.16),titerrivetbucklingwhichwasconsideredpreviouslyinthepresentsection,andbucklingin,.thewrinklingmode.inconjunctionwith

Thelatter cm bedeteminedtheusualrelation:

()lQr2q7jEtfJ2‘cr=

12(1-Y)2F

byuseoffigure13[a)

. (14)

Ineqpation(14),theappropriatevaluesoftheplastici~-reductionfactorq andcladdingreductionfactor~ areforlongshplysupportedcompressedplatesasgiveninref~ence9.

WrinlilingFailureofSkin

Thefailurestrengthofamonolithicstiffenedpanelisgivenbythecri~linganalysisofthesections“CripplingStrengthofPanelsWithFormedStiffenms”snd.“CripplingStrengthofPanelsWithExtrudedstiffeners.“ Forrivetedpanels,failurecsmoccurinthewrinklingmodeandlessfrequentlyasa resultofrivetfailureorthegrowthof

.’, interrivetbuckling.b suchcases,thecompressivestrengthislowerthanthemonolithiccrippl@strengthandcsnbedeterminedbythemethrxlsgivenbelow.

Ihthewrinklingmode,theaveragestressatfailureexceedsthebucklingstressgivenbyeqyation(14)bya relativelysmallsmount.Atfailure,thelateralforcesonthestrqersgenerallybecmelargead forcecripplingofthestringers,therebydestr@ngtheircapaci~toC&I’I’yadditionallosds.

~ useofa semiempiricalanalysis,SemonisnsndPeterson(ref.6)havedeterminedthewrinkling-failurecoefficientspresentedinfig-ure13(b)whicharetobeusedinconjunctionwith

~= A!+%212(1- ()V)2bs

(15)

.

—- —— . . —. —- ..-.

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Wrinkling Instability ofPauel

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(14)

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valuesoftheplastici~-reduction factorq andcladding reduction factor~ areforlongshplysupported compressed platesasgiveninref~ence9.

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Atfailure, thelateral forcesonthestrqersgenerally becmelarge ad forcecrippling ofthestringers,

. .. . .. .. ..—.—.

al NACATN3785-.

todeterminefailureoftheskininthewrinklingmcde.Forhat-stiffenedpanelsorthosewithunegpalstfifenersprings,anaveragevalueofb~/t~maybeusedh equation(15). ~.

Testshaveindicatedthattheredistributionofstressafterbucklinginthewrinklingmodeisrelativelymoderate.Infact,theaveragestressend-shorteningrelationforpanelsthatwrinklenearlycoticideswiththestress-straincurveofthematerialuntiljustpriortofailure.There-fore,ithasbeenrecommendedthatthevaluesof q and ~ correspondingtoa longsimplysupportedplateat ‘~ beusedineqpation(15).Testsappeartobeinreasonably‘god~eementwiththisassumption.

lMnlClingFailureofAlwnin~-AllqPanels

Equation(15)canbeusedtodeterminethewrinklingstrengthoftheskin.b estimatingthewr~ing strengthofa shortpanel,however,itisnecessarytodeterminethecripplingstragthofthestr~er alonetoascertatiifitisstableorunstableatwrinldingfailureoftheskin.1%suchananalysis,thefollowingquantitiesareofimportance:

~fst cripplingstrengthofstringeralonewhichcanbedeterminedbymethodsofPartIVofthisHandbook(ref.1)

ZW wrhEMngstrengthofskinwhichcanbeestimatedfrcm .eqmtion(15)

Gf monolithiccripplingstrengthofpanelwhichcanbedetermined .bymethodsof.thesections“CripplingStrengthofPanelswithFormedstiffeners”and“CripplhgStrengthofPanels.WithExtrudedStiffeners”

strengthofrivetedpanelwhichcanbebelow

Afterafat and ‘~ havebeendetermined,

stringerisstablew notinthefollowingway:

(1)~ ~fat> ~, thesti@er isstable.failscmpletelyinthewrinklhgretieand

determinedasgiven

itwill.beWown ifthe

Therefore,thepanel

(16)..

.— .——. .—.

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moderate.Infact,theaveragestress end-shortening relation forpanelsthatwrinkle nearlycoticides withthe stress-strain curveofthematerial untiljustpriortofailure.

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lMnlCling FailureofAlwnin~-AllqPanels

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se sugiere que los nervios cumplan con esta condicion; siguiendose aproximadamente la regla del 10%; esto es, cada modo de falla esta un 10% por sobre el otro, a fin de atenuar los fenomenos de acoplamiento. Se puede probar que una estructura asi construida es mas eficiente que una "equilibrada".

NACATN3785

. .

21

.

(2) ~ =f~t <=& thestringerisunstable.

suggestedinreference6 whichyieldspredictions

Anapproximation

whichareslightlyhighwhenthestringersareunstablebutgivessatisfactmyresultsovertheentirepracticalrangeofpopnelproportionsisthatthestringerscarrythesamestressastheskinupto Vfst.Beyondthisthestringerscarrynoadditionallosd.!llms,thefailingstressoftheshortpanelis

kbsts + ~&f%tafr=bsts+ &t (17)

(3) ~ either c==, the fail- stre@h oftheriveted panelcannotexceedthecri~lingstrengthofthecorrespondingmonolithicpanel.Therefore,thelowerofthetwovaluesI?Pror Gf istobetakemasthefailingstrengthoftheshortpanel.

RivetCriteria

Themaxhnzn-strengthanalysisofcompressionpanelsgivenh theprecedingsectionregpirescertainlimitationsonthepitchandstrengthofrive’tsinorderthatthepanelwi~ carrythepredictedload.Therivetsmustbespacedcloselyenoughandhaveadequatestrengthtomakethestringerflangefollowtheplatecontour.Iftiespacingistoolarge,thepanel&y failbytiterrivetbuckling.H thestrengthisinsuffi-cient,thepanelmayfailprematurelybecauseofrivetfailure.

.

A criterionfortherivetpitchfoundfrainfailuretnthewrinklingmcileratherthanasbucklingiS

1/2.p/bs< 1.27/~

testdatawhichresultsa resultofinterrivet

(18)

where~ isgiveninfigure13(b).

lhelateralforcereqtiedtomakethestr@y3rattachmentflangeconformtothewrinkled-skincontourloadstherivetintension.Anapproximatecriterionforrivetstrengthderivedfrm thatgiveninreference6 is

2

()Sr>0”7bsP ‘wEstddq (19)

------ .—— .. —..- ——. — — —.—.——.——. — -

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se sigue la filosofia de naca tn-455

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kbsts + ~&f%t afr= bsts+ &t

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RivetCriteria

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1/ p/bs< 1.27/~

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2 () Sr>0”7 bsP ‘w Estddq

.. .——

22 NAOATN3785-“

Thetensilestrengthoftherivet~ isdefinedintermsoftheshankarea.Itmaybeassociatedwitheithershankfailureorpullingofthe “.coumk%unkheadoftherivetthroughtheskin.ValuesOf Sr for2U7-T4alminuu-alluyrivetsaregivenbyegpations(12)..

Wi-iIIMh&FailureofPanelsofOtherMaterials.

ThewrinlWng-failurecoefficient~ h eqpation(15)wase.yaluatedbySesmnianendpeterson(ref.6)frcmtestdataonthefailurestrengthofshort2024-Dand~~ -T6alminun-alluypanels.Whenthismethdof_sif3 wasusedtocheckthetestdataofreference3 onshortpanelsofotheraltium alloys,magnesiumslloy,steel,c~er, endtitanium,itwasfoundthatthetheorywasopttiistic~ asmuchas230percentwhenccmparedwiththetestdatainscmecases.I%rther,itwasdeter-minedthatthefailurestrengthinthewrinlilingmodeisapparentlyrelatciitothe ucy/Eratioofthematerial.Therefore,inthissectionanattemptismadebasedontheavailabletestdatatoextendtheanalysisofrefer-=ce6 tomaterials.

Analternateforthewrinkling

includetheeffectsofthephysicalpropertiesofthe

formofequation(15)givenbySemonianendPetersonfailureofshortalminum-alloypanelsis .

Thiseqpationcanbeverywellapproximatedbythefollowing,for v = O.3:

~ =o.k8qi,($+4’3(#’(~)’2 (a)

Egpation(21)isequivalenttoequation(20)andeqpation(15)andisina convenientformforcorrelationpurposessinceitdoesnotrequireuseoffigureU(b)todetermine~. .

.-,Testdataonshortalminum-allqyhat-endZ-stiffendpanelsare

showninfigure15in~tams oftheparametersofequation(21).Itcanbeobservedthatthedatacorrelatereasonablywellwithin*lO-percentMUits. Itistobenotedthattheagreementofthetestdataoffig-ure15withequations(20)or (15)isrelativelythesameasthat

.

. —___ . . . ___ .——. — ——- ..— — — —

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Wi-iIIMh& Failure ofPanelsofOtherMaterials

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Egpation (21)isequivalent toequation (20)andeqpation (15)andisin a convenient formforcorrelation purposes sinceitdoesnotrequireuse offigureU(b)todetermine~.

B lulcllml3785“ 23

,,

obtainedforequation(21).Therefore,itappeaxsthatequation(21)isinreasonableagreementwithwrinklingtestdataonshorthat-end

. Z-stiffenedpsnelsof2024-T3and7075-!!?6aluminumalloys.

Equation(21)wasusedtocorrelatetestdataofreference3 onwrinklingfailureofpanelsofothermaterialsthatfirstbuckledinthewrinklingmodeintheelasticrange.Forthesedataa systematicvariationwiththe E/ucyratioisobservedasshowninfigure16.Thetestdatashownhereareforpanelsoftheseinegeanetry,withidenticalrivetoffset,relativelytheseinerivetstrengths,andrela-tivelystiilarcaressiveyieldprc@rtiesintheearnersoftheformedz stiffener.!l!herefore,onlythephysicalpropertiesofthepanelmaterialswerevariedh thisseriesoftests.

FYamfigure16,:twasfoundthatforspecifictiuesof

(bs/ts)(bw/Q@(f/q $/3

Consequently,equation“(21)canphysical-propertyvariationsintheoryapparentlyappliesfora

bemodifiedtoincludetheeffectsofthefollowingformbynotingthatthevalueof E/ucyequalto125:

(22)

(23)

Itcanbenotedthatequation(23)isina formsimilartothatobtainedinthegeneralizalcri~lingstudypresentedinthesection“&ipplingStrengthofPanelsWithFormedStiffeners”“and“Crippling.StrengthofPanelsWithExtrudedStiffeners.” b factbothwrinklingandcripplingtestdatacanbecorrelatedoncmechartbynotingthat

Ap#6 ~a—.=

%/%

Thus,thegeneralizedcrippling&mla forformedZ-stiffenedp,anels.becanes,fromequation(1), .

(24)

.. . .. . ..- .. --— -.--—- .- .... .. —— ______—. ---- — ----- ..—. —

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obtained forequation (21).Therefore, itappeaxs thatequation (21) isinreasonable agreement withwrinkling testdataonshorthat-end . Z-stiffened

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Consequently, equation “(21)can physical-property variations bemodified toinclude theeffects of

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Thus,thegeneralized crippling &mla forformedZ-stiffened p,anels. becanes, fromequation (1),

24 NACATN3785

%= ’*2’[i=E-r’70”8--

(25).

Kid.ofthetestdataofreference3 havebeenplottedinfigure17.Ontherightside,monolithiccripplingbehavioraccordingtoeqpa-tion(25)isindicatedfor u = 1.3and1.8,whichcoverstherangeofpanelstested.Ontheleftandupperportions,theapensymbolsareforthealuminunandmagnesiumalloyswhichdo-notcantraisedyieldeffectsintheformedcornersofbythe ~Cy/UCYratiosgiveninfigure17. Theseagreem~twithequation(23).

Thesolidsymbolsareforthematerislswhich

e@zriencesignifi-theZ asindicateddataareingood

havevaluesof7cy/a&J@eat=- m 1.4.Titaniumisincludedinthisgroup,sinceitwasseverelyanisotropicandmoreoverhadconsid~ablescatterinyieldstrength.Thesedataarereasonablywellcorrelatedaccordingtoequation(23)usinga coefficientof20.5inplaceof17.9inthisfOrmula.

Onthebasisofavailabletestdata,equation(23)witha suitablecoefficientthatdependsuponGcy/ccymaybeusedtodeterminethestrengthofshortrivetedpanelswhichfailbywrinklhg.~ conjunc-tionwithequation(23),f/~ valuesaretobedeterminedfrcmfig-ure14,andequation(17)istobeusedifthestrhgerisunstable.BecauseoftheempiricalnatureofSemonianandPetersontsanalysis(ref.6)audthatcontainedinthissection,theaboveconclusionsmustberegardedastentative,subjecttofurthersubstantiationbypaneltests.

COLUINSTRENGTHOF STIFFENED

latheprecedz sections,‘thecompressive

PANELS

strengthofshortmono-lithicandrivetedstiffenedp&nelshas-beenconsid&3. Sincethecolmnstrm ofthepaneldecreasesasthelen@hincreases,thestrengthofshortpanelsisessentiallythemaxtiumstrengthwhichcanbeachievedfortheparticularcross-sectionalconfigurationandsheet-Stiffmer fasteningarrangement.Havhgestablishedmethmlsforesti-matingthecrippl~strength,itisnowpertinenttoccmsidertheColwnnstrengthOfpanelsOfval?iOUSkn@hs.

Wior toabout1945,itwascustmarytopresentchartsofthecolumnstrengthofstiffenedpsnelsintermsoftheeffactiveslendernessratioofthepanel.Methodsofconstructingsuchchartsarewellknown

..- .? .

.*.. -. ..—. .-

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%= ’*2’[i=

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Onthebasisofavailable testdata,equation (23)witha suitable coefficient thatdepends uponGcy/ccymaybeusedtodetermine the strength ofshortriveted panelswhichfailbywrinklhg.~ conjunctionwithequation (23),f/~ valuesaretobedetermined frcmfigure14, andequation (17)

..

NACATN3785

intheaircraftindustryandDunn(ref.17)andotherson

25

aresummarizedinthebooksofSechlerandaircraftstructures.

Since1~5,therehasbeena growingtendencytousedirect-readingdesignchartsforstiffenedpanelsinwhichthecoluunstrengthispre-sentedasa functionofthestructuralindexI?/L~. TheindexcontainsthelosdingperinchN andtheeffectivecolwnnlengthLt andisha convenientformforminimum-weightstudiesofstiffenedpanels.

h figure18,thetwotypesofstiffen~-pauelcolumnchartsarepresented.Figure18(a)representstheEuler-andtangent-modulusbehaviorofa stiffenedpanelwithsturdystiffenersandnotsubjecttobucklingoftheskin.b figures18(b)and18(c)cripplingofthestiffeneroccursgenerallyprecededbylocalbucklingoftheskinorstiffenerelements.Thisistheusual@pe ofbehaviwofstiffenedpanelsandisdiscussedinscmedetailasfollows.

Column-StrengthRanges

(1) Belowthelocalbucklingstressofthepanel,thecolumnstrengthisusuallyinthelong-columnraugeandcangenerallyberepresentedbytheEulerrelation

(26)

for aes Ucr.Thiseqpationisgenerallyvalidwiththeexceptionofpanelswithstiffenersofverypoortorsionalrigidity.

Fordirect-readingdesigncharts,suchasfigure18(c),theEulerrelationis

(27)

for Ue~ Ucr.Here,pfi isa d~ensionlessshapeperamet~ofthepaneland N/L’ isthestructuralindex.

(2)Thelocalbucklingstmmgthofthepanelwhichrepresentsthelimitofapplicationofequations(26)end(27)csmbeobtaix.iedfrcmPartIIofthisHandbook(r&.16).Figures13and14thereinpresentcompressive-local-bucklingcoefficientsforvarioustypesofintegralpanels.Figures3,5,end6 ofreference16givecoefficientsforindividualstiffenersorstiffenerelementsandfigure19(a)ofthesamereferencecanbeusedtoestimatethebucklingstressoftheskin.

.-.r.

-—. . . _ _ .: - ——. — .. .—

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26 NACATM3785

. (3)Thecriwlingstrengthofmonolithicpanelsandwrinklingstrengthofrivetedpsnelswhichpertaintotheshort-panelrangemqrbeobtainedbythemethodspresentedinthesection“CripplingStrengthofPanelsWithFormedStiffeners”tothesection“StrengthofShortRivetedPanels”herein. .

Thus,theoryisavailablefordeterminingthecolunnstrengthintheEulerrsmgeaswellasforthectioffatthelocal-buckling-strengthlwel. Semiemptiicalmethodsareavailablefortheshort-panelstrength.Theremainingcolmn-strengthrangeisthetransitionfrcmtheEulerramgetotheshort-panelrange.b thistransitionrange,thereisaconsiderablerelianceontheuseofpaneltests.~ fact,themajorportionoftheextensiveMACAprogrsmondirect-readingdesignchartswasconcernedwithtestdatainthistransitionregion.

TransitionRange

Toreturntothe@pe ofcolumnchartshowninfigure18(b)fm themoment,a veryusefula~roximationinthistransitionrangewhichhasbeenusedquiteextensivelyisthepsraboliccolumncurve.Forstiffenedpanelssubjecttolocalbucklingandcrippling,theparabolicapproxima-tionhasthefollowlngform:

for ~co> Ucr”where

Ue = #E/(L’/p)2

(28)

(29)

M egyation(28),acr and ~f areknownfarthepanelcross-sectionalconfiguration,and ue istheEulerstressfortheparticularpanellen@h. Thisrelationisessentiallyaninteraction-typeequationforthetransitionrange.mom equation(28),Gc#5f= 1 f~ L’/p= Oand Gco= acr for ue= Ucr.

Forthedirect-readingdesigncharts,itisalsopossibletoemployequation(28)inthetransitionregion.Ihthiscase,howwer,equa-,tion(28)istobeusedinconjunctionwith

cre= [#E(p/%)2(I?/L1)~l/3 (30)

.

.

.

NACATN3785 27

.

.

Asindicatedpreviously,~co=~f for L~/p= O. However,inmostcrip@ingtests,thevalueof T7fisobtatiedat L~/p= 20. infact,thecripplingmethodofthesections“CripplingStrengthofPanelsWithFormedStiffeners”and“CripplingStrengthofPanelsWithEx&udedStiffen-s”isbasedonsuchtests.Consequently,itisdesirablethatequation(28)bemodifiedsothat~co=Gf at L’/p= 20. Thisisreadilyaccomplishedbytheadditionofa correctiontermtoequation(28):

(31)

Ineqution(31),am representsthestressobtainedfranequation(29)for Lt/p=20. Aspreviously,equation(31)appliesfor Gco> ucr.ticaseswhereUcr> %1 ~pl is~eprop-i- limitstress)~1replacesUcr inequations(28)snd(31).

Todemonstratebrieflytheuseoftheparabolicapproximationfordirect-readingdesigncharts,figure19hasbeenpreparedbasedonZ-stiffened-psneltestdataofSchuette(ref.18). Inthisfigure,Uewasobtainedfromequation(30),~f frcmequation(1)usingc =3 andPc= 1.26,and ~cr byuseoffigure14ofPartIIofthisHandbook(ref.16).Thetrsmsitionregionisrepresentedbyequation(31).Itcanbeobservedthatthemethodisiusatisfactoryoverallagreementwithtestdatainthiscase.

Direct-ReadingColunnCharts

TheNACAhasengagedinanextensive~erimentalprogamfcwthepurposeofconstructingdirect-readingcolumnchartsofseveralclifferenttypesforhat-,Y-,andZ-stiffenedpanels(refs.7 and18to25).Theuseofthesechartsindesigndependsuponwhetheraxialcompressiveconsiderationsgovernortheminimumskh thiclmessisanoverridingcondition.Becauseoftheextensivenumberofthesecharts,theperti-nentreferenceislistedintable6 andnoattemptismadetoreproducetheseriesofchartsherein.

Thepanelstestedinthisprogramutilizedstronglyrivetedconnec-tionsbetweentheskinandthestiffener.W spiteofthisprecaution,however,wrinklingorforcedcripplingprobablyoccurredinmanyofthepanels.Conseguentl.y,theseresultswillbeconservativewhenappliedtocorrespondingpanelsofmonolithicconstruction.

..——-- .-. — -— ——— — _____ -— —--. — — - -

NACATN3785.

Itistobenotedthatminimum-weightpaneldesignsobtainedbyuseofthesechartsgenerallyresultinhighbuckl~ stressesoftheskinasa resultofverycloselyspacedstiffeners.Forlargerstiffener .spacings,withouta resultingsignificantdecreaseh structuraleffi-ciency,theuseofmagnesium-all~skinsinconjunctionwithalumimm-alloystringersoffersantit=estingpossibili~indesign(ref.19).

OPTIMWISTIFFENEDPANELS

Althoughitisnotpracticaltoreproducehereinofdirect-readingcolmncurvesobtatiedbytheNACA,tosummarizetheresultsofthisinvestigationinthe

theentireseriesitisconvenientformofoptimwn-

columncurves.Thesecurvescanbeofconsiderablevalueinpreliminarydesignstudiessndrepresenttheenvelopeofall.minimum-weightstiffened-paneldesignsforspecifiedstructural-loadingpsmmeters.

b thissecticm,opthmm-columncurvesforhat-,Y-,andZ-stiffenedpanelssrepresentedintwoforms:Plotsof Fco againstN/Li andplotsof GCo againstN/ts forspecifiedvaluesof N/Li.Thelatterformofpresentationisusefulwhendesignconditionsreqtietieuseofaminimwnskinthickness.

Inordertoextendtherestitsoftheoptimum-stiffened-panelstudytomaterialswithphysicalpropertiesotherthanthoseinvestigated,methodsofgeneralizingtheoptinnmresultsareccmsidered.Thesemethcds .arebasedonavailabletheoriesforthedesignandanalysisofstiffenedpanelsofmhimunweight.

Optimum-l?snelTheoriesandResults

Theoryandtestdataintheavailableliteraturep-elshavebeenreviewedsndconsider~indetail~

.

onopthmmstiffenedward (ref.26).

ThetheoryofthedesignofmonolithicstiffenedpanelsofminimumweighthasbeenconsideredbyZahorski(ref.~) andFarrar(ref.28),andtheresultsoftheseanalysescanbesummarizedinthefollowingformula:

Emu thethemy,thepanelefficiencycoefficient~ andtheplasticity-reductionfactorfortheoptimumpenelF axe

(32)

“

.

-—_ _

NMM m 3785

.

. %?=

29

(33)

(%)

Fromequation(33),itcanbeobservedthatincreasesinstructuralefficiencyareobtainedwhentheradiusofgyrationp islarge,thestiffenerspacm bs issmall,and tO/% a~roachesuni@,whichimpliesrelativelythickskins.l?arrsr(ref.28)hasactusllychrriedtheanalysisuptothepointwhere~ hasbeenevaluatedformono-lithichat-,Y-,andZ-stiffenedpsnels.Hisresults,infact,arewithin8 percentofthevaluesobtain~frcmtheNACAexperimentalpro-grsmonminhnum-weightrivetedpanels.

TheresultsoftheNACAinvestigationareshowninfigure20,foroptimumz-,hat-,andY-stiffenedpanels.Thedatausedtoconstructthesechartswereobtainedfra thereferenceslistedintable7.

Ihfigure20,thestraight-lineportionsofthedatawereextra-polatedtorepresenta hypotheticalelasticmaterial.Itissignificantthattheslopeofthislineonthelogarithmicplotinallcasesisalmostexactlyone-halfofthatpredictedbythetheoryofequation(32).Thisisremarkableinviewofthefactthatthislinerepresenlmtheenvelopeofa largesetofempiricalcurvesobtainedbyvaryingthestiffened-panelgecmetry.

~ appropriatelyaccountingforthemodulusofelasticityofthepanelmaterials,theexperimentalvaluesoftheriveted-panelefficiencycoefficientsgivenintable8 weredetermined.Alsoshownarethetheo-reticalvaluesofFarrar(r&.28)formonolithicpanels.

Recently,Catchpole(ref.29)investigatedtheoptinnzndesignofstiffend panelshavingunflangedintegral.stiffeners.Thetheoreticalpanelefficiencycoeffickntforthis$asewasfoundtobe ~ = 0.81.Thecross-sectionalproportionsoftheoptimunconfigurationarebps = 0.65 - t#O = 2.25.Thereisnopublishedqertientalsubstantiationoftheseresults.

Specified SkinThickness

Ihcertaindesigncases,itisnecessarythatthestiffe.nedpanelsatisfya skin-thicknessrequirementh additiontocarryinga canpressive

. .. . . —. —-—— .. —-—.—..—— —. — - --

30 NACATN3785

.

10SJ3. Thissituationcommonlyariseswhentorsional-stiffnessrequire-mentsgovern.b suchcases,theminimum-weightchartspresentedinfigure21forZ-,hat-,andY-stiffen&ipanelsareuseful.Thesecharts .weretakenfranthereferenceslistedintable7.

Towardtheright-handsidesofthesechsrtsthevalueof ?&correspondingtospecifiedvaluesof N/Lt a~roachestheoptimumindicatedinfigure~. Asthevalueof N/tsdecreases,however,thestressleveldecreasessmdsaneweightpenaltyisincurred.

Itisinterestingtonoteinfigure21thatsincetheordinaterepresents??Co= N/% andtheabscissais N/*s,secantsdrawnfromtheoriginrepresentlinesofconstantvaluesof ts/%.Micks(ref.30)hasconsideredthisproblemb somewhatgreaterdetailbycross-plottingchartssuchasfigure21intheformoffigure20fen?specifiedvaluesof tsfi.Fromthis,heisabletoestimatetheweightpenaltyassoci-atedwithdesignsbasedonspecifiedv&luesof ts/~.

GecmetricProportions

Forpanelsofoptimundesign,itisassuredthatlocalbucklingofallthecross-sectionalelementsoccurssimultaneouslywithfailureofthepanelintheEulermde. Consequently,itispossibletoestimatevariousgeometricparametersofthepsnel.

The”effectivethiclmessofthepanelcanequation(32):

The b/tsratiooftheskinfollowsfrm theequationfor k=4 and v=O.3

beobtaineddirectlyfrom .

(35)

fsmiliarplate-buckling

(bs/ts)o= 3.6~~/Tco

Fromequation(34),for k = 4 and v =0.3,

(36)

(37) .

------ .._.

B

.

NACATN3785

Bysubstituting

31

equation(36)intoequation(37),

(Pmo=o.605u@ GCo (38)

Mickshaspresentedformulasfordeterminingthecross-sectionalpropertiesofpanelsrequiredtosatisfyspecifiedvaluesof (pfi)n(ref.m).

InelasticBuckling

. A ccmp~isonofthevaluesof ~ obtain~frantestson2024-II?3al.&ninwn-allqyhat-,Y-,andZ-stiffenedpanelswiththetheo-

reticalvaluesof T = (Es/E)(Et-/Es)1/2 asgiveninequation(34)isshownirifigure22,whichistakenfrcmreference26. A typicalstress-straincurvefor2024-Ualmimzualloyhavhga ccmrpressiveyieldstrengthof~ ksiwasusedtofindthevaluesof Et/E,Es/E,andthetheoreticalvalueof ~. Sincetheproportional-limitstressofthetypicalstress-straincurveappesredtobesamihathigherthanthestressatwhichthecurvesof Gco againstN/Lt departed&cm alinearrelationshipinfigure20,a nondimensionalrepresentationwasusedinfigure22. Theabscissarepresentsvaluesof ~ %. where~plristhestressatwhichthecurvesdepartfruna straight-l-tierelatio~hipontheplotof ~co againstN/Li.

Withinthelimitationsimposedbythelackofprecisestmess-stratidataforthestiffenedpanels,itappearsthatsatisfactorycorrelationisobtainedbetweentestdatasndthetheoreticalvalueof ~. However,itisofinteresttoconsiderpossiblereasonsforthea~srentlowvalueof 6P1 oftherivetedpanels.

Onecausepaybeassociatedwiththestressconcentrationsattherivetholesina built-upstructureresultinginanapparentlow~ingoftheproportionallimit.Thisphenomenonhaabe= observedinotherbuilt-upstructuressuchasstiffenedcylinders.A secondcausemaybeattributedtowrinklingorforced-cripplingfailuresofthepanels.TheZ-stiffened.psnelsareparticularlysuspectinthisregardandthereissaneadditionalevidencetobepresentedinthefolluwingdiscussionwhichSllppOrtSthisContention.

Itistobenotedthatbothofthesereasonsareassociatedwithrivetedstructures.Therefcme,itmaybeexpectedthatthevalueofT givenbyequation(*)wouldapplydirectlytoamonolithicstructurewithoutanyuncertaintiesconcerningtheeffectiveproportionallimit.

.

.-—.— _______ - —-—-- _ .— ——— ————..—— ____ . . . . .

-.—.

32 IWCAm 3785.

GeneralizationsforOtherMaterials

Sticemostoftheavailabledataareforrivetedstiffenedpanels, .however,itispertinenttoconsidermethcdsofgeneralizingtheresultsonopttiumpanelsofonematerialtopanelsofothermaterials.Suchmethodshavebeenconsid~edbyYounger(ref.31),Micks(ref.30),andSchnitt,RruU,a wolko(ref.32). Thefollowingprocedureisbasedontheresultsofopttium-psneltheoryasgivenbyequation(32).

AccordingtotheprinciplesofbucklingsimilitudediscussedbySteinbacherandGerard(r&.33),thebuckling-stressequationcanbewrittensothatthephysical-propertyparameterscanbeeqmtedtothegeometricandloadingparametersoftheproblem.Thus,fromequation(32)fortheoptimumstiffenedpsnel: .

Toccmparepanelsefficiencycoefficient

IGco(a)l/2=a@/L’)1/2ofthessmetypeofconstruction,thepanelisconstantandtherefore

(39)

(40).

Further,sinceitisdesiredtocmpsreoptimunstiffenedpauelsatthesamevalueof N/L’,set (N/L’)1= (N/L’)2 h equation(40)withthe ,result

(41)

Itisconvaienttosolvethisproblemonplotssuchasthoseoffigure23where (?lZ)l/2isplottedasa functionof =Co. Here,

Isecants,drawnfromtheoriginrepresentconstantvaluesof (TE)l/2~co

andhence [~(N/L’)1/~-1,accordingtoegyation(39).

tifigure23(a),theoreticalsmdtestresultsonqptimumZ-stiffenedpanelsof2024-T3ml 70~-T6aluminumalloysareccmpsred.Thelinesmarkedtheoryarefrcm7 valuesccmputedfrcmtypicalstress-straincurvesaccord=toequation(34).Thepointsrepresentdataas

..

.

..

NACATN3785 33

●

✎

.

computedfrcmlfrcunthetest

figure20(a).Thecurveforthe‘7075-T6panelsderiveddataon202k-T3 panelswasobtainedbyratioingstress

levelsalonga.secantasfollaws: -

T-75 = ( )6=24 “5/”~4 (42)

Thesubscriptsg amd th refertoexperimentsndtheory,respectively,andthesubscripts75and24arederivedfrauthealloydesignations.

Itcanbeobservedthattheagreemmtbetweenthederivedcurvefor7075-T6aluminumalloyandthecorrespondingtestdataisnotgod. How-ever,whenthismethodwasappliedtotheoptimumY-stiffenedpanelsshowninfigure23(b),relativelygoodagreementwasobtained.ThisdifferenceinthedegreeofcorrelatimbetweentheZ-andY-stiff=edpanelsisattributedtowrinklingorforcedcripplingoftheZ-stiffenedpanels.Thisfailuremodewasnotaccouutedforinderivingequation(32)andconsequentlythediscrepancymsybeattributedtothisfactor.

Itistobenotedthatinderivingthethecrreticalvalueof ?forthe7075-T6al.uminum-allqyY-stiffenedpanels,itwasnecessarytoaccountfora fairlylargedifferenceinpropertiesoftheAlcladsheetad extrudedstiffeners.Thiswasaccomplishedbyusingtherootmeansquareofthe T valuesccmputedindividuallyforthesheetandstiffener.

STIFFENED-PANELI!OXCONSTEUETION

Thematerialpresentedintheprecedingsectionshasbeenconcernedwiththecompressivestrengthofisolatedstiffenedpanels.~ aircraftconstruction,ofcourse,suchpauelsareanintegralportionofwingamdtailstructuresandareformedbytheuseofsparsaudribstostidividethecompressioncover.Consequently,itisofimportancetoinvestigatetheinfluenceoftheboundaryrestraintsprovidedbythesparaudribsupportingstructureaswelld lateralpressureloadsonthestrengthofstiffenedpanelsasusedh boxstructures.Thesefactorsareconsideredinthissection.

Thecolumn-strengthrelationshipsforstiffenedpanelspresentedinthesections“ColumnStrengthofStiffenedPanels”and“OptimumStiffenedPanels”indicatethatthestrengthisinverselyrelatedtotheeffectivecolumnlength.Thus,theuseofa lateralsuppm?timgstructureconsistingofribsorfozmersprovidesaneffectivemeansofobtaininghigherpanelstrengthwithanacccunpanyingincreaseinstructuralefficiency.

—-. . — ..— — —— A--- —.. — . .

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Para el dimensionado de los paneles con restricciones de fatiga, se determina primero la carga maxima equivalente tolerada según el historial estimado de cargas, junto a la carga mas desfavorable de la envolvente de vuelo. Esta se toma como punto de partida en la optimizacion global, variando luego el distanciamiento de las cuadernas.

lkm thes-point thatthepressionCOVW,itispossibletocertatisimplifyingassumptions.

NACATN3785

“Lribsactsolelytostabilizethecom-deriverib-stiffnesscriteriabasedonHowever,inanaircraftwingtherib

stiucturep-s anadditionalroleintransmittingtheatiloadstothespas. Thus,sincetheairloadingandcanpressiveloadingonthecuverarerelated,itisgenerallynecessarytoincludestrengthconsiderationsintheribdesigninadditiontothestiffnessrequirementsforgeneralstabili@.

~ testsofaircraftwlmgstructures,effectivecolumnlengthsdifferentfrcmtheribspacinghavebeenobserved.Saneofthemostl~elycausesforthisbehavioraxethefollowlng:

(1)

(2)

(3)

(4)

(5)

(6)

The

The

Generalinstabili@ofthecompressionsurface

Torsionalrestiatitprovidedbytheribstructure

Continuityofthestiffeneruvertheribstructure

Lateralairloadeffectsonthepanel

Presenceofsparsattheunldadedpaneledgesresultinginorthotropicplatebehavior

Membraneeffectscausedbyintenx!parcurvatureofthepanel

abovefactorsarec@sideredinthepresentsection.

StabilizationofCompressionCover

ribstructureofa wingw tailprovidestheprimarymeansofstabilizingthecompressionsurface.Inordertoavoidgeneralinstab-ilityofthissurface,certainflexural-stiffhessrequirementsmustbesatisfiedbytheribstructure.E thesereqtiementsaremet,theeffectivelengthofthestdf’fenedpanelcorrespondstotheribspacing.Continui@ofthepanelovertheribstructureaswellasthetorsionalrigidi~oftheribscanproviderestraidmwhichfuz?therdecreasetheeffectivepanellength.

Thusthedesignoftheribstructuretoachievea desiredvalueofend-fixitycoefficientattheloadededgesofa stiffenedpanelentailscertatiflexural-andtorsional-stiffnessrequirements.Thesereqpiremntshavebeenconsideredh certainidealizedcases:13uaiansky,Seide,andWeinberger(ref.%) treatedthebucklingofa singlecolumnsupportedby1,2,3,andaninfinitenumberofeqyallyspacedreflec-tionalandrtiationalsprings;Zahorski(ref.35)analyzedthebucklingofa gridofcolmnssupportedby1,2,3,andaninfinitenumberof

.

.

— — —.. . .—. ___ ___ _

lisandro

las costillas o cuadernas alares transmiten CORTE a los largueros, y estan sometidas a un esfuerzo usualmente menor de flexion; que segun el tipo de estructura puede ser absorbido por el revestimiento.

NACATN3785

eqyallyspacedflexural-typelateralstiffenersofrigidities.Forplates,BudianskyandSeide(ref.ofa simplysupportedplaterestingonaninfinitespacedflexural-@pelateralstiffenersofvarious

35

varioustorsional36)COIlSide3?edbuclCUngnumberofequallytorsianalrigidities.

Ananalysisoftheserefermcesindicatedthattheresultsfm?asinglecolumn,gridofcolumns,orsimplysupportedplateofaspectratiolessthan0.20canbereducedtoa uniquefunctionalrelationshipforthecaseofaninf@itenmub=oflateralstiffeners(practically,threeormore)ofzerotorsionalrigidity(ref.26).Thisrelationshipisshowninfigure24(a)whichshowstheend-fixi@coefficiente interms

. of&e stiffnesspsrameterK@/B.

Thedefinitionofthetermsinthestiffnessparameterforvariouscasesisasfollows:Thegridofcolumns(ref.35):

B = (rEI)stlbst (43)

me plate(ref.36):

B = @#/1.2(1-V2) (44)

!Cheflexural-typelateralstiffenerwithhingedends(refs.35and37):

K = fi4(EI)r/w4 (45)

Theflexural-typelateralstiffenerwithclampedends(ref.37):

K = 5m (EI)r/W4 (46)

.Theshear-typelateralstiffener(ref.37):.

K = fi2~/w . (47)

TheeffectivespringconstantsK ofthevarious@pes ofribstructureshavebeenconsideredbyLsm@aarinreference37. Thevaluesgivenbyequations(45)to (47)arefrm thispaper●,.

.— . . ..- .— —-— — - —.—— —- .—

.— -..—

36 NACATN3785

“.me a~licationoftheseresultstostiffmed-panel-ribconstruc-

tionrequiresconsiderationofthebehaviorofthepanel.Gridactionisapproachedasa limitingcaseforpanelscmposedofheavystiffenersandverythinskins;intheotherlimitofthicksldnswithlightstiffeners,platebdmntorisapproached.Sincetheresultsforthesetwocasescoincidewhengivenintermsoftheparametersoffigure24(a),itisassumedthatfigure24(a)canbeusedalsoforsttifenedpanels.Thevalue of B fora stiff&n&ipanelcanbeobtaintifrcunthe-followingcolmnrelationship:

/N = X%(L:)2b8t

Ey letting

IJMenccmbiningegpations(48) and (49) ‘

(48).

(49)

(n)

thata largenwnberofareused.InWPWW

Theresultsgiveninfigure24(a)assumelat=alstiffenersofzerotorsionalrigiditytheseresultstodevelapa rib-stiffnesscriterion,itisassmmlthatthetensionsurfaceofthewingdoesnotcontributetotheeffectivespringconstantoftherib.Forformers(partial-depthribs)thisassumptionisvalid,althoughforribsattachedtothetensionsurfacethisassumptionwillbeconservative.

General~tability

suitabledesigntherequirement.

Forthepurposeofavoidinggeneralinstability,acriterionfortheribgiveninreference26isbasedonthattheribsofzerotorsionalrigidi~possesssufficientflexuralrigidi~toachieveanend-fixi@ooefficientofuni~. lhxmfigure24(a)itcanbeobservedthateffectivdyrigidribsareobtatiedwhen

Ihfact,anyincreaseinthevalueof KL3/Bbeyondthatgivenbyeqm-tion(51)doesnotresultinanyincreaseh end-fixitycoefficientforribsofZ=O torsionalrigidim.

..

.

.

— . ..__ ______ ------ .. .

NACATN

wminhmm

.

3785 37

ccmbtiingequations(51),(5o),(45),WI (46)jtiefohmrib-flexural-rigidi~criteriaareobtainedforanend-fixity

coefficiatof e = 1: Ribswithhingedends:

(EI)r ()=4:4: (52)

RibswithCISmped-S:

(EI)r=* ~ “(53)

Fl@xural-typeribswithelasticrestraintattheendswillhavestiffnessreqyirematsintermediatetothevaluegivenbyequations(52)and(53).Forshear-meribstructures,bycombiningegpations(51),(50),and(47),the~m

Theanalysisflexural-rigidity

shesrrigidi~isobtained:

Rotational-StiffnessConsiderations

(54

oftheprevioussectionindicatestheribminimun-requirementsnecessarytoavoidgeneralinstabili~

ofa compressioncov=-support~structureccuuposedof- ribsofzerotorsionalrigidity.Itisevidentfranfigure24(a)thatoncetheribshavesufficientflexuralrigiditytoachieveanmd-fixitycoef-ficientofuni~,nofurtherincreaseinfixi~canbeobtained~increasingtheflexuralrigidi~.Furtherincreasescanonlybeobtainedbytherotationalrestraintsprovidedbytheribstructureforthestiffenedpanelcontinuousoverthisribstructure.Therestraintisgenerallycharacterizedbya rotationalspringconstante.

Manyinvestigationshaveconsider~theinfluenceofrotationalrestraintsproviddbyintermediatelateral.s~orts ontheinstabilityofcontinuouscolumns,gridsofcolmns,andsimply-supportedplates(see,e.g.,refs.34-39).Thedetailsoftheindividualsnalysesaresummarizedintable9 andreferencetothesepapersissuggestedwheresuchdetailsmaybeofimportance.

lhgeneral,however,itispossibletorepresentthesignificantaspectsoftheseanalysesbyconsideringapanelwithmanyintermediate“.

—-. — —. —— . ——— .—. -—.———— --- .

..

38 ‘ XACJITTJ3785

supports(practically,threeormore)ofuverallaspectratioL/w< 0.20.Inthiscase,theresultsapplytocolumns,gridsofcollmlns,andplatesandcanbeassumedtoapplytostiffenedpanelsbyUSQ thestiffnessvaluedeftied~ equations(49)amd(50).

In figure24(b), theend-fixitycoefficiente ispresentedasafunctionofthereflectionalspringstiffnessparameterI@/B audtherotationalspringstiffhesspsmsmeterOL/B.Itcanbeobservedthatoncetheminimunvalueof K@/B neededtoavoidgeneralinstabilityisachieved,nofurtherincreasein e isobtainedwithincreasesinK@/B. Thisregionisdenotedasaneffectivelyrigidreflectionalspringsystem.

lhfigure25,thecharacteristicsoftheeffectivelyrigidreflec-tionalspringsystemarepresentedintermsoftherotational-restraintparameterQL/B.Fora givenvalueof (3L/B,theend-fixitycoefficientandtheminimumvalueof I@/B foraueffectivelyrigidsystem~ bedetermined.Alsoshownarethevaluesof K#/B neededtoachieveanend-fixi@coefficientof e = 1 inthepres&ceof

Lateral-PressureEffects

Stiffenedpanelsunderccmbinedcczupressiveandfreeunloadededgeswereinvestigatedexp=hmtallyti Zibritosky(ref.40)at a pressureupto16psi.

rotationalrestraints.

pressureloadswith ,byMcPherson,Levy, -Thisworkindicated

thata simplecorrectiontoaccountpanelduetopressureeffectscouldempiricaleqpation:

% (=i5co1

forthereductiminstrengthofthe .beevaluatedfrcmthefollowingsemi- -

-0 .39qL3/B) (55)

Ihequation(55),B isthebendingstiffnessofthepanelperchordwiseinchincludingthe“actuslareaofsheet(noteffectivearea)and ~co isthepanelstrengthundercompressiononlyasdetermined&cm thesection“ColumnStrengthofStiffenedPanels.”

Fortunately,therearenootherpublisheddataontheeffectsoflateralpressureonthestrengthofstiffenedpanels.Whileequation(55)doesprovidesaneinformation,itisoflittleuseforpanela~licationswheretheribendsparstructurescanhelptodevelopsignMicantmenhaneeffectsinthepsnelunderlateral-pressureloads.

. Inadditiontothereductionofpemelstren@h,theatiloadsimposecertainstrengthrequirementsontheribstructure.Theserequirementsareinadditiontothereflectionalandrotationalstiffnessconsiderations

—. -— . .. .. —-—.. _ .

NACATN3785

discussedpreviously.Forments,refertoreferences

Instiffened-panel

39

a briefpresentationofrib-stzmmgthrequire-26-41.

hrl?luenceofSpars

tests,theunloadededgesaregenerallyuusuP-Tortedandtheref&ethepanei actsasawideorthotr~iccol&n. fiawingortailstructure,sparssregenerallylocatedattheunloadededges.Consequently,theinfluenceoftheedgesupportprovidedbythesparsuponthepsnelstrengthmaybeofimportanceincertaincases.

E theoverallaspectratioofthepanelina boxstructureformedbytheribandsparstructureisscmewhatlessthanuni~,thenthepanelusuallyactsasa widecolmm. Ihsuchcases,theresultsofpaneltestscanbeapplieddirectlytothewingstructure.

Whenthepanelaspectratioapproachesorexceedsunity,particularlyforthick-skinpanels,thestiffenedpanelbehavesasanorthotropicplateintheboxstructure.Insuchcases,theresultsofpaneltestsmqybeconservativeanditisnecessarytouseorthotropicplatetheorytodeter-minetheincreasedcompressivestrengthofthepanelwithunloaded-edgesqpport.

Sandorff(ref.38)hastreatedthisproblembriefly.Morecanpleteresultscanbeobtainedbyutilizingfigure10ofPartIIofthisHandbook(ref.16).Thesechartsindicatethecompressive-bucklingcoef-ficientsofsimplys~ortedflatplateswitha largenumberofstiffeners.Ihestimatingtheflexuralstiffnessofthestiffenedpsnelrequiredforuseofthesecharts,eqyations(48) to (50)msybeused.

Ihadditiontotheunloaded-edgesupportpruvidedbythespars,furtherincreasestipanelstrengthina boxstructuremsyresultfrominterspsrcurvatureofthepanel.Suchstrengthincreasesareassociatedwiththemembraneeffectscontribut&ibythesparstructureandarenotfrm thecurvatureofthepanelitself.Thecmvaturesconsideredheregenerallydonotresultinanysignificantincreaseinstrengthofthepanelwhentestedwithfreeunloadededges.

Lan@aar(ref.42)hasconsideredthisproblembytreatingthecom-pressionsurfaceofa camberedwingbetweenribsasanorthotropiccurvedplatewithrotationalrestraintsattheloadededges.Theribswereassmnedtobeaneffectivelyrigidreflectionalsystem.

Thetheorydevelopedwascheckedsga-instseveralidealizedbeam‘testswithgoodagreement.ItiSsignificantthatend-fixitycoefficients~to3 wererealizedforcamberedbeamswhweas e = 1 wasobtainedforcorrespondingbeamswithflatcovers.

.

----- . —— —— ——- -— —-— ——--

40 NACATN3785-.

Opthmm Construction

Optimunfmns ofstiffened-panelconstructionareconsideredinsanedetailinreference26. 12dbrmetiononoptinnnnribspachgandtheefficiencyofst~ened-panelconst-”tionrelativetootherformsofconstructionispresented.

ReseerchDivision,CollegeofEu@neering,NewYork~VerSi~,

NewYork,N.Y.,April17,1956.

—.— —.. --

NACATN3785 41

.

APPENDIXA

APF?GICATIDNSIKITIIIN

TheresultsofthispartoftheHandbookofthatmsybeofimportancefrm thestandpointofaresummarizedinthissection

.

Structural%abili~-sis anddesign

*CripplingStren@h

Thegeneralizedcripplinganalysisofreference1 hasbeenextendedtomonolithicstiff=edpanelsinthesectionsentitled“CripplingStrengthofPanelsWithFormedStiffeners”aud“CripplingStrengthofPanelsWithExtrudedStiffeners.” Ihdoingso,theresultsobtainedinreferace1 onindividualelementshavebeenccmbinedwiththestiffened-panelanalysis.

luuzle-type elements.-Thecripplingstren@ ofsectionscmposedofa seriesoftwoadjacentelementswhichmeetata junctionisgivenby

0.85(Al)

whereg isthenumberofcutsplusflangesasdiscussedinthesec-tion~’CripplingStrm@h ofpanelsWithExtrudedStiffeners”andillus-tratedinfigures6 and8. Theappropriatevaluesof Pg me givenintable4 andfigure10.

Forstiffenedpanels,thequauti~A/t2 inequation(Al)istobereplacedby.A/~t8● I& cmplexstiffenershapessuchasY-sections,aweightedvalueof ~ shouldbeusedasdefinedbyequation(7).Incaseswherethesheetpropertiesaredifferentfrcmthoseofthestiffener,a weightedvalueof ticydefinedbyeqyation(8)shouldbeused.

.

T-tIYPe elements.-Extrudedsectionsccmposedofa seriesofthreeormoreelementswhichmeetata ccammnjuncture(e.g.,T-orH-sections)arerefmredtoasT-typeelements.Thecri~lingstrengthofsuchsectionsisgivenby

,s. . (A2)

. .

.

. ---- .- —— — —. .—— —- —— --- ——...——. .. . . .

k2 NACATN3785.

Equation(A2)iSvalidfor ~ a < 3/4.lleyondthisvalueeqpation(6)f/Cy=holdstrue~

af= Crcr (6)

Shortrivetedpanels.- Shortrivetedpanelscanhavestrengthslowerthanthemonolithiccripplingstrengthsasa resultofinterrivetbucklingandwrinlClingorforcedcrippling.Thestrengthofpanelswithtiterrivetbuc~ing~ bedeterminedfrcmegpations(10)end(U.)andtable5..

Thestrengthofpanelswithforcedcri~lingisgivenbyequa-tions(16)to (19)and(23).

ColumnStrengthofPanels

Thecolumnstrengthofstiffaedpanelsistreatedinthesectionbythatname.ForcolumnsintheEulerrange,equations(26)and(27)apply.InthelengthrangeintermediatetotheNer andcri~lingranges,equations(28)or (31)q besatisfactory.

ThepertinentNACAreportscontainingdirect-readingcolumnchartsforhat,Y-,andZ-sttifenedpsnelsarelistedintable6.

Panelsof optimwn designformtiimurnweightareconsideredinthesection“OptimumStiffenedPanels.” Theefficiencyofvariousstiffenershapesisgivenintable8 andfigure20. Panelswitha specifiedskin

.

thi&ness&e presentedinfigure-21.Methodsresultstopanelsofothermaterialsareshown

BoxConstruction

Rib-stfifnesscriterianecesssrytoavoid

ofgeneralizingtestinfigure23.

0

generalWtabili@ of,

.

transverselystiffen~panelsaregivenbyequtions(52)to (*). Theendfixitycontributedbythecontinuityofthepanelaverribspos-sessingrotationalrestraintsispresent~infigures24-and25. Lateral-pressureeffectsandthesidesupportcontributedbythesparstructurearealsoconsideredinthesection“StiffenedPanelBoxConstruction.”

___ —___

NACATN3783 43

1.Gerard,George:Handbook●

ofPlatesandComposite

lwFERENcEs

ofStructuralStabili~.PartIV.FailureElements.“NACAm 3784,1957?

2. Gallaher,GeorgeL.,andBoughan,RollsB.: A MethodofcalculatingtheCompressiveStren@hofZ-StiffenedPanelsThatDevelopLocalInstability.NACATN1482,1947.

3. Dow,NorrisF.,Hickman,WilliamA.,andRosen,B.Walter:DataontheCompressiveStrengthofSkin-StringerPanelsofVariouslkterials.NACATN3064,1954.

4. Dow,NorrisF.,andHickman,WilliamA.: EffectofVsriationinRivetDiameterandPitchontheAverageStressatMaximumLoadfor24S-T3w 75s-T6Aluminum-Alloy,Flat,z-Stiff=ed PanelsThatl?ailbyLOC~ Instability.NACATN2139,1950.

5.~C_, Willi~A.,ad DOW,NorrisF.: C_&ssive Stre@h of24S-TAluminum-AllqFlatPanelsWithLongitudinalFormedHat-SectionStiffenersBhvingFourRatiosofStiffenerThicknesstoSld.nThick-mSS. NACATN1553,1948.

6. Semonian,JosephW.,~d Peterson,JamesP.: ~ -sis offieStabilityandUltimateCompressiveStrengthofShortSheet-StringerPanelsWithSpecialReferencetotheInfluenceofRivetedConnectionl%weenSheetandStringer.NACATN3431,1955.

7. Dow,NorrisF.,and~CbUl, WilliamA.: DesignChsrtsforFlatCom-pressionPanelsHavingLongitudinalExtrudedY-SectionStiffenersandComparisonWithPanelsHavingFormedZ-SectionStiffeners.NACATN1389,1947.

8. Howland,W.Lavern:EffectofRivetSpacingonStiffenedThinSheetinCompression.Jour.Aero.Sci.,vol.3,no.12,Oct.1936,~. 434-439.

9. Gerard,George,andBecker,Herbert:HandbookofStructuralStability.Put I - BucklingofFlatPlates.NACATN3781,1957.

10.Levy,Samuel,McPherson,AlbertE.,andRaniberg,Walter:EffectofRivetandSpot-WeldSpacingontheStrengthofAxiallyLoadedSheet-StringerPanelsof24-S-TAluminumuoy. NACATN856,1942.

11. Brook,E.A.: BehaviorinCompression02AltinumAlloyPanelsHavinga FlatSkinWithCorrugatedReinforcement.R.&M. No.2598,BritishA.R.C.,1945.

.

—. —. —-.—— ——.. — ___ .

44 NACATN3785

l-z!.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

Dow,NorrisF.,andHickman,WilliamA.: EffectofVariationinDiameterandPitchofRivetsonC~ressiveStrengthofPanelsWithZ-SectionStiffeners-Panels’ofVariousLengthsWithCloseStiffenerSpacing.NACATN1421,1947..

.

.

Dow,NorI’iSF.,IZLckman,WilliamA.,andRosen,B.Walter:EffectofVariationinRivetStrengthontheAverageStressatMsximumLoadforAluminum-Alloy,Flat,Z-StiffenedCompressionPanelsThatFailbyLocallhC~. NACATN2963,1953.

Argyris,J. H.,andDunne,P. C.: StructuralPrinciplesandData,Pert2,StructuralAnalysis.HandbookofAero.,no.1,fourthed;sirIsaacl%.tman&Sons,Ltd.(London),1952,~. 179-185.

Bijlaard,P.P.,andJohnston,G.S.: CompressiveBucklingofPls.tesDuetoForcedCripplingofStiffeners.PreprintNo.408,S.M.F.FundPaper,Inst.Aero.Sci.,Jan.1953.

Becker,H~bert:HandbookofStructuralStability.PartII-BuclQingofCompositeElements.NACATN37&, 1957.

Sechler,ErnestE.,andDunn,LouisG.: AirplaneStructuralAnalysisandDesign.JohnWiley& Sons,Inc.,1942.

Schuette,EvanH.: ChsrtsfortheMinimum-WeightDesignof242.-TAluminum-All~FlatCompressionPanelsWithLongitudinalZ-Section

.

Stiffeners.NACARep.827,1945. ..Dow,NorrisF.,IHckmam,WilliamA.-,”andMcCracken,HowardL.:Compressive-StrengthComparisonsofPanelsHavingAluminum-All~SheetandStiffenersWithPanelsHavingMagnesium-All~SheetandAluminum-AlloyStiffeners.NACATN1274,1947.

Dow,NorrisF.,andKkevil,AlbertS.,Jr.: Direct-ReadingDesignChartsfor24S-TAluminum-AllwFlatCompressionPanelsHavingLongitudinalFormedZ-SectionStiffeners.NACATN1778,1949.

Hickman,WilliamA.,andDow,NorrisF.: Direct-ReadingDesignCWrrtsfor75S-T6Aluminum-AllwFlatCompressionPanelsHavingLongitudinalExtrudedZ-SectionStiffeners.NACATN2435,1952.

Hickman,WiU.ismA.,and”Dow,NorrisF.: Direct-ReadingDesignChartsfor24S-T3Aluminum-AllwFlatCompressionPanelsHavingLongitudinalFormedHat-SectionStiffenersad ComparisonsWithPanelsHavingZ-SectionStiffeners.NACATN2792,1953.

.

NACATN3785 45

23.

24.

25.

26.

27.

28.

29.

30.

31.

32.

33●

Dow,NorrisF.,Hubka,RalphE.,andRoberts,WilliamM.: Direct-ReadingDesignChartsfor24S-TAluminum-ld.lwFlatCompressionPanelsHavingLongitudinalStraight-WebY-SectionStiffeners.NACATN1777,1949.

Dow,NorrisF.,andHickman,WilliamA.: Direct-ReadingDesignChartsfor75S-TAluminum-All~FlatCompressionPanelsHavingLongitudinalStraight-WebY-SectionStiffeners.NACATNl@l.0,1948.

Dow,NorrisF.,and~CklUaIl,WilliamA.: CompsxisonoftheStructuralEfficiencyofPanelsHavingStraight-WebandCurved-WebY-SectionStiffeners.NACATN1787,1949●

Gerard,George:NewYorkUniv.

Zahorski,Adam:Panels.Jour.

MinimumWeightAnalysisofCompressionStructures.Press(NewYork),1956.

EffectsofMaterialDistributiononStrengthofAero.Sci.,vol.~, no.3,July1*, pp.247-253.

Farrar,D. J.: TheDesignofCompressionStructuresforMinimumWeight.Jour.R.A.S.,VO1.53,NOV.1949,pp.l@LL-1052.

Catchpole,E.J.: TheOptimumDesignofCompressionSurfacesHavingUnflangedIntegralStiffeners.Jour.R.A.S.,vol.58, m . 527,Nov. 1954, PP. 765-768.

Micks,W.R.: A MethodofEstimatingtheCompressiveStren@hofOptimumSheet-StiffenerPanelsforArbitraryMaterialProperties,SkinThickness,andStiffenerShapes.Jour.Aero.Sci.,vol.20,no.10,OCt.1953j Pp. 705-715.

Youuger,DemyG.: TheDevelopmentofOptimumDesignEnvelopeCurvesforSheet-StiffenerCompressionPanelsHavingHat,Z,orY-SectionStiffenersforVariousMaterialsandTemperatureEnvironments.Proc.FirstMidwesternConf.onSolidMech.,CollegeofEng.,univ.ofIll.,Apr.1953,PP.5-10.

Schnitt,Arthur,Brull,MauriceA.,andWOIJSO,HowardS.: OptinmStressesofStructuralElementsatElevatedTemperatures.Paper56-Av-u,SymposiumonStructuresforThermalFlight(l&r. 14-16, 1956; Los Angeles), Aviation1956.

Stetibacher,IkanzR.,andGerard,George:Mechanics. PitmanPub.Corp.(NewYork),

.

. . .

Div.Conf.,A.S.M.E.,

Airckftstructural. -1952,.PP. 302-30k.

. —— -.-——— —- .—— — .—.— .-— —.. ——. — -—

k6

3k.

35●

36.

37●

38.

39●

40.

41.

42.

43.

44.

NACATN3785

Budians~,Bernard,Seide,Paul,andWeinberger,RobertA.: TheBuclddngofa ColumnonEquallySpacedReflectionalandRotationalSprings.NACATN1519,L948.

Zahorski,Adsm:EfficiencyofLateralStiffenersh Panels.Jour.Aero.Sci.,vol.U, no.4,Oct.1944,pp.299-3o6.

Budiansky,Bernard,andSeide,-Paul:CompressiveBucklingofSimplySupportedPlatesWithTransverseStiffeners.NACATN1557,1948.

Lan@aar,H.L.: ParallelColumnsWithCommonLateralSupports.Jour.Appl.Mech.,vol.I-2,no.4,Dec.1945,pp.A-253-A-256.

Sandorff,PaulE.: NotesonColumus.Jour.Aero.Sci.,vol.11,no.1,Jan.1*, pp.1-12.

Tu,Shou-Ngo: ColumnWithEqual-SpacedElasticSupports.Jour.Aero.Sci.,vol.U, no.1,Jan.1$$+4,pp.67-72,75.

McPherson,A.E.,Levy,Samuel,sndZibritos@,George:EffectofNormalPressureonStrengthofAxialJyLoadedSheet-StringerPanels.TN1041,1946.

Shanley,FkncisReynolds:Weight-StrengthAnalysisofAircraftStructures.Firsted.,McGraw-HillBookCo.,Inc.,1952,~ ● 159-173.

L=@s=, mm L.:Jour. Aero. Sci.,

Dow,NorrisF.,and

StabilityofSemimonocoqueWingStructures.vol.13,no.3,k. 1946,pp.u9-E5.

Hickman.WilliamA.: EffectofVsriationinDiameterand-PitchofRivetsonCompressiveStrengthofPanelswithZ-SectionStiffeners.PanelsofVariousStiffenerSpacingsThatFailbyLocalBuclding.NACATN1467,1947.

Dow,NorrisF.,ahdllLckman,WilliamA.: EffectofVariationinDiameterandPitchofRivetsonCompressiveStrengthofPanelswithZ-SectionStiffeners.PanelsthatFailbyLocalBucldingandHaveVariousValuesofWidth-to-ThicknessRatiofortheWebsoftheStiffeners.NACATN1737,1948.

.:

.

.

3

.

.

.

NACATN3785

TABLE1

NACACRIPPLINGSTRENGTETESTDATAON Z-SITI?’FENEDPANELS

47

ReferenceMaterialtv/t~ variationFigure Remarks

TN1482 2024-T3 1.00,0.79,(ref.2) 1 Stronglyriveted

0.63,0.51 panels

TN3064 7075-T6 1.00 2 Dataforpanels(ref.3) 6061-T6 identifiedas

n52-1/kH 25-50-207075-0 and37.5-75-20SAX1010 usedsinceCopper atherpanelsFS-lh indicated18-8-3/4H evidenceofTi-1/4H wrinkling

TN23.39 2024-T3 LOO,0.63 3 Potential-(ref.4) 7075-T6 strength

estimates

.

..

+. .

. .. . . . ._ _ . —— -.—— — -—.. —

NACATM3785

.

‘lM131E2

Pc VALUESFORHNI!—STIKFENEDPANEIS

%’#s Pc

1.5 1.42

1.00 1.35

.63 1.2Q

.39 al.16

TABIx3

J3gVALUESFORY-STIFFENEDPANELS;

g = 18.83

t’#. w% 13g

1.00 1.16 0.562

.63 .732 ●5W

.40 .464 .478

.

.

--—-— .

49

mlimlz4

SUMMARYOFm?lmIMENTALVALUESOF ~ FORANGIE-AND

T-TYPEl?J@@NISANDSKII?I?IINXIIPANELS

Element c %/% Pc g twl% $g

Angle-typeelement;m = 0.85

V-groweplates ------------------ 3 ------ 80.558Extrudedangles ----------.------- 2 ------ a.558Extrudedtubes 4 ----- al.42 12 --.--- a.558Formedmulticornersections 3t08 ----- al.30b3c-1------ “c955

FormedZ-stiffenedpanels 3 ----- 1.26 7.83 ------ .558

dla4216.83 1025Formedhstpanels 6 1.25 %5911.00 ‘1.36 1.00 d.561.63 %*ZQ .63 %499.39 ‘~el.16 .39 %e.l@3

ExtrudedY-stiffenedpanels ------------------18.83f1.16 .562

f.732 .505f.464 .478

T-typeeiement;m = 0.40

ExtrudedT-section------------------ 3 ------ a.670Extrudedcruciform------------------ 4 ------ a.670ExtrudedH-section------------------ 7 ------ a.670

%’or 5f/Ucy5 3/4.b c isnumberofcorners.cAveragevalue..%or ~flacys 0.8.

?Forbs/ts$50.

f ~/ts value.

..— _ .—— —.——- --- ——-— ————- . .

50 NACATN 3785

TABLII5

END-FIXITYCOEFFICIENTSFORINTERRIVETBUCKLING

Fastenertype e Reference

Flatheadrivet 4 8Spulnrelds 3.5 10Brazier-headrivet 3 10Countersunkrivet 1 11

NACADIRECT-READING

TABIX6

COLUMNCHARTSFORAUMINLM-ALIOY

sTIl?FmEDPANELS

Stiffener Material W of Referencecolumnchart(a)

.Z-formed m24-T3 A Re~ort827(ref.18)B,C TN1~ (ref.20)

Z-extruded 7075-T6 . B,C TN2435(ref.21)Hat-formed 2024-T3 B,C

1

TN2792ref.22)Y-extruded 2024-T3 A TN1389ref.7)

B,C TTJ1777ref.23)Y-extruded 7075-T6 A

[TN1389ref.7)

B,C TN1640ref.24)CurvedY-extruded ~n-T6 A,B,C TN1787(ref.25)

a A,presentationof Uco againstN/L’;B,presentationof N/t*

.

againstN/L’;C,presentationof—

5C0 againstN/ts.

NACATM3785 51

TABm7

NACAOPTIMUM-~lWD-PANELDJYI?A

Stiffener

Z-formedZ-extrudedHat-formedY-extrudedY-extrudedCurvedY-extruded

Aluminum-alloymaterial

202k-T37075-T62024-T32024-T37075-T6

7075-T6

Reference

TN1389 (ref. 7)TN2435(ref. 21)TN2792(ref. 22)TN1389 (ref. 7)TN1389 (ref. 7)

TN1787 (ref. 25)

TABm8

13Xl?lRlMlZNMLV.&lX13SOFPANELEFFICIENCYCOEFFICIENT

Panelefficiency Farrar‘SStiffener theoretical~coefficient,~ (ref.28)

Z-extruded 1.02 O.%Hat-formed ●99 .96Y-extruded 1.15 1.=CurvedY-extruded 1.22 ----

.

.--— . . — .-.—.--.—— ----—- -— —-—. — . _

52 NACATN3785

TABLE9

CONTINUOUSCOLUMNSANDPLATESSUPPORTEDINVESTIGATIONSOF

BY DEFLECTIONALANDROTATIONALSPRINGS

Reference Structure SupportandBoundaryConditions(a)

38 Columnon 2,3,4,~ nuuiberofsupportsofrotational K SW, oses~; e ofneighboringspringsupports supportscanbeunequal

39 Columuon 1>2>3)m numberofintermediatedeflectional supportsof O~ K$ W, e = O;sup-springsu~orts portsatendsofcolumnof K = w,

e =0 ore=~

35 Gridofcolumns 1,2,~ nudberofcolumnson1 or2onsimply lateralstiffenersof OS K~ mj

supportedlateral OS e % ~;supportsatendsofcol-flexuralstiffenerumnsof K=w, o~e~~

~ nuniberofcolumnson w lateralstiffenersof O~ K~ W, (3= O

34 Columnon 1,2,3,w nuuiberofintermediatedeflectionaland supportsof OsK~w,O~egw;rotationalspring supports”atendsofcolumnofsupports K=w, O~e~~

36 Plateonsim@ly Platesof L/w= 0.50,0.35,0.20,<0.20supportedlateral oninfinitelymanysupportsofflexuralstiffener()~K~m, ()~e~ce

37 Effective Flexural types of ribs with supportsatdeflectional ends of ribsof K=~, O~e~Wspringstiffnessofvariuustypes Sheartypeofribofribs

-.

.

.

%, defl.ectionalspringstiffnessofSupportsj 0, rotationalspringstiffnessofsupports.

.

.

.

.

I!mrre l.-

.

Crippling

2 3 4 5

dataforE024-T3aluminum-alloyZ-6tiffemed

6

panels cm

78910

reference 2.

9+ NACATN 3785

.9

.8❑

.6.

.5

.4,2 3 < 56 78910

+++7(a)Testdataforallpanels.

ID●

.910%

.8●

.7 ~=0.85,~=L26: \\

.

(b)Datafor25-x-~ and37.5-75-20panelsonly(seeref.3).

Figure2.- CripplingdataforZ-stiffenedpanelsofvariousmaterialsofreference3. ~.t8 =1.

NACATN3785 55

.

.9— —

.6

.7 4/~ Ml MA7ERIAL40% –

.6 — o 20 /.00 2024- T3

b 20 .63 2024-73 FORC=3.5— A

● 30-40 /.00 2024- T3Q

A 30-40# — .63 E024-T3 ,

Q 20 /.00 ~75-T6

❑ 20 .63 70~- T6.3—

v 30-40 1.00 7075-7’6

v 30-40 .63 7075-T6

.2~I 2 3 4 5678 9 10

()A ~yt~ “

~t. E.

Figure3.- Potential-strength data for aluminum-alloyZ-stiffened panelsof references 4, 43, and44.

. ..

“

. ..— —.-... -.-—. — .. -—- .—- —. —------ --

56 NACATN3785

\.\\

+0%

&=L26~

REE \

o 2024-T3— 2 I IA 2024-T3 4, 43,44 POTENTIAL-STRENGTHESTIMATES● 7076- t6 4 8 u u

@ 7075-76 3 25- 6 3Z5-75 DATA ONLYq 6061- T6 3

— P 5052- I.ff 3b FS-t h 3w 7075-o 3Q SAEIO1O 3a COPPER 3b 18-8~4H 3

A Tk3/4H 3I -— ---

8 9

(a) %.p==1.00.

Figure4.-CripplingdataforZ-stiffenedpanels.

NACATN3785

.

(b) ~/t~ = 0.63.

ID

.9

B ‘

qy 45

0 Q51 2W#-T3 REE2.

● .79 2024-T3 REE24“/ .2 3 4 66 78910

(c) %.@ = 0.51 and0.79.

Figure4.-Concluded.

.

..-. . .. ——._ ...__ ___ ______ -———.——— —-—

--

/0

.9

.8

.7

6 4 /bwo 1.2

5 ‘0.8 w

IJ .6

4.-I 2 3 4 567 89/0

/’m’6??,T

(a) %p. = 1.25.

3-=Cy

m I.9 \

49

.7

6-/0%

5bh/~

o 124 —● .8 .❑ .6

2 3 4 56 78910

.

6&@)’”

(b) t@, = 1

.

.00.

Figure5.- Cripplingdataforhat-stiffenedpanelsofreference5.Compressiveyieldstrength,~ ksi. .

.

.— . . ..

.

..

10

9 \ \ \ -&l.20-*B

.7

-6L=Cy

5~/& -lo%

d— o 1.2● B❑ .6

\~1 2 3 4 567 8 91

(c) ~/t. = 0.63.

ID.8 \

/t$=lf6

.8~/~ 1$/&25=5075

7 10%06 n P

B \q .8 ● dqpq -lo%> \~y

5

.4

/ 2“ 3 456 789Jo

A (%)/..6~ E

(d) %/ts = 0.39.

Figure~.- Concluded.

. ..-. .. ..—. —____ . ——.. — — -— —. — ———

60 NACATN 3785“.

BASICSECTION J cur

g=2 2 FLANGESr= g

4 curs8 FLANGES

zg

BASICSECTION o CUTSg=3 4 FLANGES

4= g

/ CUT6 FLANGES

zg

Figure6.- Methodofcuttingsimpleelementstodetermineg (g isnumberofctisplusflsmges).

..

r.

.

NACATN3785

.

/..

.9

.8

.7— — — —

Zfq’

.5AU6LETYPE

3ANGLETY= g SECTIONS❑ TUES 12

4 o AIWES 3● PLATES :T- TYPE 3

T

.3:+ :

.253.4 .5 .6.7 .89D 2.0 30

(a)Correlationaccordingtoequations(2)and(4).

I.JI@— —

-9 — ‘E FORH-SECTION9=7O&?@—0 1

2014-T6❑ 2024-?3 LINEFORCRUCIFORM

7 —~ 7075-T6 — —Q R3a3-T

B —m O-IHTAEACWPOINTRERf?E~NTSiOR3 TESTS

.6 1 I

.- 3 4 6 .6 .789/0

*t$%)”(b)

(b)Correlationaccordingtoequation(5).twoorthreetests.

Figure7.-CripplingdataforangleandT-type

61

4?.0 3.0

kh pointrepresents

elementsofreference1.

-- .——. - —. — .—— —— —— .—. —— —... ._ _

62 NACATN3785

FFF

AV6WASF g*/8c836 curs

14 FLAN6ES/szg

(a) Y-stiffenedpanel.

8 curs6 FLANGES8%9

.

(%) Z-stiffenedpanel.

ga7 I - g*/7 I gJr/7 ‘ g~/6

AVERA6E 9=/6.83

/7= g

lkt-stiffenedpanel.(c)

Figure8.- Methodof cutting stiffened panels to determine g.

IB NACATN3785 63

..

10.9— — — J

I10%-—

B 02024-73,4~f ● ~-76 -10%

7Y 7 I 1

Js m=O.65~gxo532

?1 .2 .3 .5 .6 .7 .8 .9 1P

,+(%9-;’

(d ~/t~ = 1.00; ~/t~ = 1.16.

0

9

-B9 -lo%

ZJ I

.6

?1 .2 .3 .5 .6 .7 .8 .9 LO

,+32Wr

(b) %/t. =0.63; %/tB =0.73.

t+. =0.kO; ~/t~ = 0.46.

.1

(c)

Figure9.- CripplingdataforY-stiffenedpanelsofreference

.. ——. . ._ _ —. .—. .——. — . --- -—— ._. .—- ._. _

-Z-PANELS

)

u

HAT~ Y-PANELS

1

@ v-+c:: PLA7..ExmuDw ANGLES,WBES,WLTIGORNER;ORMED

o FORMEDZ - PANELS❑ FORMEDHATPANELSA EXTWOEOY- P~ELS

._ —““3 .4 -56 .7 B.9L0 /5 2!0 ao

lVgure 10.- Crippling

7/1’#.

coefficientsforangle-typeelements.

.

-t.

NACATN3785

.

‘MOIVOUZYIC+

\

~WRIMK#N@ ~

FORCED CRIPPLING

RIVET SPACING

FigureI-1.-Variousfailuremodesofshortrivetedpanels.

._ -.._ .. —-— —— —— ———. —-————. — —-—- -- --

lisandro

Una cuestion de costos; en los que entran los elementos primarios y el costo de remachado; puede mostrar que el punto economicamente optimo se halla en la interseccion entre la curva teorica de buckling de la chapa y la de resistencia "monoltica" del panel. Claro que la resistencia real estará por debajo de esta ultima. Ver Bijlaard.

66 NACATN3785.

,

‘1 I IFol I

.—-

40

-m

*0 100 200

+

.

t

.●

✎

e“Cl.

PANELS. 20E4-T3● 7076-76

F

300 400

(a) 2117-Tkrivets.Datafroqreference4.

Figure12.-Effectofrivettensilestrength,pitch,anddiameteruponcompressivestrengthofshort,riveted,aluminum-alloyZ-panels.

—. — ..— ..- _

NACATN3785 67

I “111111111111111111111111111Illllllillllllll[lu

, , , 1 I I 1 II .\ & * b“ I 1 I I

L I I I 1 1 1 I 1 1 -1

PP

(J.—de ~+t

(b)Variousrivet materials. Datafromreference 13.

Figure I-2.- Concluded.

. . . ...-. .-— .. —.. — —. --— —— “ .-. —-. —.. .-

68 NACATN3785.

k

6

5 \\ L\ 1

4 \ \7

3 \

2

/

O 2 .4 .6 .8 10 12 /94 46 /l?2.0 Z2 2.4 26

Wbb#8

(a)Theoreticalcoefficientsforbuckling.

Figure13.- Theoretical andexperimentallydeterminedcoefficientsfor buckling andwrinklingfailure of short riveted panels (datafromreference 6). .

.

. . -

NACATN3785 69

(b)Experimentallydetermined.coefficientsforfailureinwrinklingmode.

Figure13.- Concluded.

.—.—.- .—. —.— —. ———- .-. —.. -- .-—— —..-. ..-.

70 NACATN3785--

P-7

Figure14. - Eqerimentaldy determinedvaluesofeffectiverivetoffset(datafromref.6).

—.

NACATN37$5 71

/o-5

a.

7

6

5

4

2

.

.

o #?4.6o 395

—0 /?645

U

E&(#)‘SLOPE=l/2!

\

\

-lo%

REE6635

567 8910

7076-r6Z-PANELSu a aune -

SOS4-TSHAT PAhEL6

20

Figure15.-Wrinklingdataonshort

\

\s.

I

rivetedpanels.

. . .. . ---—- . . ..— .—— . . . — -.—— —. —.

72

“.

/cs

&

7

6

5

4

\

THEVRY

70?6-T8

6061-r6

FS-lh

/

606E-1/4H

/00 200 300 400 ~0 6~ 700 8tW 900E/@w

●

Figure16.- Influenceof E/uq & onwrinklingstrengthofshortrivetedpanels.Elastic-bucklingdataonlyofreference3.

.

-.

73

d r 1 . .,.

.6 \ \ -- ,\

k.5 .

.&.

MA7ER1AL~jdcw MONOLITHIC I. 0 7076-T6 L18 “ BE#W; , /

A 6061-T6 1,08 . a!3❑ 606E-lm 1.10

7076-0ad

● 1.82.3 B SAE1010 1.84

& COPPER 1.48V FS-lh f.26Q 18-8#’M‘1.49 .v T1-3/4H 1.00

21 2 3 4 56 789

Figure17.- Cripplingandwrhisling

ofreference3. f~

dataonZ-stiffenedrivetedpanels

= 5.4;%— = =.5.%

. . ..- -.- ——-- —— — .—.—.. — —— .— - -—

EULER; @E(L’/#e

=Co

(a)

L’/p

No crippling of stttfener; no bucklingof skin. Conventional chart.

I v EULER , EQ 126)

\ CR1PPLIN6

~oo

(b) Crippling of stiffener;buckling ofor stiffener. Conventional chart.

EULER EGli27)

Go

N/L’

(c) Crippliw of stiffener;buckling ofor etringer. Direct-reading chart.

Figure 18. - SMffened-pand column MB.

skin

skin

.“

.

-,, ,

-o ,2 .4 .6.N/L;ksi

q.,

ksi

bf /bwo 0,3● .4❑ .s

Fm ,kd

i8f -

All;,

Figure19.- Ccmrparisona? derived COIUMU cwrveB and test data d reference 18.

‘4 m

I

/

7

—

Lf .02 .04 .06 .08 .10 20 .40 .60 .80 LO

N/t, &s/

(a) Z-stiffened pmel.s. E = 10.5x 106psi.

)[email protected] Optimum-column charts for stiffenedpanels.

1. .

ma

80

60

40

3COB FORMED HAT

hi

m

I1 1 I I 1 1 106 .08JO 20 40 .m .&w

AM!,ksi

(b) Hat-stiffened panels. E = 10.5

Figure20.- Continued.

6)(10 psi.

o-

60

60 7075- T6 YCURED

40 — — — — —

Fm,kd

20

/O., I I t I 1 I I 1 I I

.= .04 .06 ,06 ./0 ,20 .40 m .60 Lo

/v/L’, ksi

(c) Y-stiffened panelI3. E = 10.0 X 106 pSi.

Figure 20.- Concluded.

1.

.m

~~=LO 450

.6 .s .4I

40

w

8k~ “

20

.

10

I:/

Izill I I I 1 I I I I I 1I I I Ill I I11 I II I I 11I 111I I I I 1 I 11I 1111-0 J?o ; 40 m m Joo Ieo MO

.

(a) Z-stMfenad panels of 202kT5 aluminum alloy.

Figurezl..- Minimum-weightchartB for Btifi’enedpanels with qecifled akin thickness.

80 NJLCATN3785.,

ZO,ksi

o m 40 @ m mm f40mmsm

..

(b) Z-stiffenedpanelsof7075-T6aluminumalloy.


.

.

.

.—. . .— .._—._-._ . . . . .-— —— -..

NACATM3785 81

t~=[O .8 .6 .5 450 * .- . .

, , , 1, , , , , 1 ‘sl’ /’” ,,, ,,

/

{’” , ,

1 /’-”/ JI 1 I I 1 I 1 ! I 1 / 1

I I I P v I /1 1/ v ——40 m I~~ , IA A / — A/

1- 1 I ,

10

d-kki

ILtEIIlI

I

-/’1tI t I I I 1 11t I 1111 t I I I 1*I I 1I I , t11! t1I I 1I t1 11I I , t I 1 I , 1, t , I 10 20 40 60 m m m /40

+, his

(c)Hat-stiffenedpanelsof2024-~aluminumalloy.


—--- . — .— ..- -—. .

50

40

30

10

L/F=Lo 8 6 ,6 ,4

P'''l'' ''l'' ''l'' ''l'' ''l'' ''v'' 'l''' 'v''' l'''xl' ''l'' ''v'' l''''i.

f

W2%-1---=l

f- ,/ /,/ I

< f- -,10

b. r‘,067

“/1

I

!i~

/

/

A ;

t~~

/’

-1I 1I I I I I II I I I II I 1I I t I 1I I I I I 1 1I I I

Q“ 20 * 60 80 100 MO MO

+, his

“(d) Y-stMfened panels of 202k-T3&hmlnumaUoy.

CnN

, hi

m 23---Continued.a

,.

%0,ksl

$w so

m

m

m

m

10

0 w 40 so m m w ao m MO m

#-#w

(e) Y-stiffened panels of 707>T6 aluminum alloy.

.hd

lUgure Z?I..- Concluded.

.s

.5

4 \

o Z- PANELSA Y - PANELS

2 ● HA r PANELS

o .5 15 2.0 25

.

Figure22.- Plaatlci-@reduction factor for optimum stiffened panels of 202Q13aluminumalloy.D8tataken from reference 2S.

3

,.,

, ,

E

i

Add

/

2024-r3DArA

7om-T6

o /0 20 30 40 m

F, hi

(a) Z-stiffened panelt3.

optiIulIul-panel

60 70 80

data for stlffetid panels.

i

4x/04

3

m+,

(pso g

4?

o

// --

/

DATA THEORY

.

=, ksi

(b) Y-stiffened panels.

_ 23.- Concl-.

Ks-E:WV:D

l?o#?4”r3am

●l&A THEORY

mZ5- T6.

7V 80

,. ,-

1

. ..

..’

. .

E

I

1I

i“ /.6

.6

.6

o

. .

(a) e

Figure 24. - End

i

-EFFECTIVELY —

,“

A1

/0 20 30

KLa/B

as a functic& of Id’/B. supports of

fixity of continuous panels over mzny

40 50 ‘@

zero rotational restraint.

reflectional.supports. L/n< 0.2.

.

I

mm

I

I

I

I

4

3

e2

/

o

, /0_TlvEiY RIGID DEfiECrlONAk

x r , SPRING S Y<TEAt

-k-2

0= @LfB

I a I I20 40 60 80 /00

KLs/B

(b) e as a function

Figure 24. -

of ld’/B

Concluded.

!7

.

‘-,. . d

,, -

e

4

3

2

/

o

END-FIXI TY GOEFFICIEtU~P, I

AS A FUNCTION OF @ UB ~—

11

I

_(KL%3&N FOR EkFE’C TWELYRIGIODEFLEC TIONAL SYSTEM

~4T= I IrKL#/B REWIRED ~oR e d I I

QLL- -— I —.. 1 I

/0 20 30 40 50 60

?00 .!4

w

9

RO?21710NAL - RESTRAINT PARAMETER @L/B

mgum 25.- lthlmumdeflectimal stiffness for effectively rigid deflectimd. system. Continuouspand over many supports; L/w <0.2.

I

1

Documents

TN-3785