CA

NATIONALADVISORYCOMMITTEEFORAERONAUTICS

TECHNICAL NOTE 4137

FATIGUEBEHAVIOROFAIRCRAFT

STRUCTURALBEAMS

ByW. S. Hyler, H. G. Popp,D. N. Gideon,S. A. Gordon,andH. J. Grover

BattelleMemorialInstitute

WashingtonJanuary 1958

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TECHLIBRARYKAFB,NM

.Bb

NATIONALADVISORYCOFMITTEE

TECHNICALNOTE

FATIGUEBEHAVIOROF

I:lllllllllllll[lfllllll-FORAERONAUTICS ciobbi5i

4137

AIRCRAFT

STRUCTURALBEM&

ByW..S. Hyler,H. G.Popp,D.N. Gideon,S.A. Gordon,andH. J.

SUMMARY

Thisinvestigationinvolveda studyof

Grover

thecorrelationof compositestructuralfatiguebehavior,basicmat&ial,andshple-elementbe-~vior.Fatigueandrelatedstatictestsweremadeonaluminum-alloyboxbeamsandI-beamsandalsoonelementssimulatingkeyfailurelocationsinthetwobeams.Thestudyindicatestlutthesimulationapproachwillbe usefulforthosecaseswhereit ispossibleto assessreasonablyfactorscontributingto stress-raisersinthestructure.Themorecom-plexthesecondarystresspicturebecomes,themoreexactingwill.&therequirementsofthestressanalysis.

\ Fatiguenotch-factorsK+ muchhigherthanmightbe expectedfromdataon simplynotchedcouponswerefoundinbothbeams.Thestudyoftheshmlationelementssuggestedthatsuchhighfatiguenotchfactors

d maybe expectedincompositestructuresinvolvingstressgradientsandbiaxialstressdistributionsat ornearrivets.Thisobservationservesto emphasizethatconsiderablecautionshouldbe exercisedindesigninusingKf valuesobtainedfrcmsimplynotchedcoupons.

Thesimulationapproachthusappearstoprovidea technique,insomecases,forevaluatingthefatiguestrengthof compositestructures.Useofsuchsimulationelementsembodyingcomplexstressinfluencesalsoappearstobe a helpfulresearchtoolindeterminingvaluesof ~whichmaybe morerealisticfordesigningbuilt-upstructurestkn thosewhichcanbe obtainedby simplynotchedcoupons.

INTRODUCTION

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Aircraftstructuresareoftenso complexthatpredictionoftheir% resistanceto fatiguecrackingis impossible.Avaihblefatiguedata

onlaboratory-testpiecesdonotreproducethedetailedstressconcen-trationsinthestructuresandareofMmitedhelpindesign.At present,

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2 NACATN 4137

the”laboratorydataservechieflyas guideswhichthedesignermustusewithdiscretionand,sometimes,withconsiderable~certaintY. e ‘-

Severalstudiesofthefatigueperfornmnceofactualstructureshavebeenreported(see,forexample,refs.1 to6). Inmanyofthese,thereisinsufficientinformationonthedetailsoflocalizedstressesinthesti?ucturetopermitcompleteanalysiswithrespecttolaboratorydataonthebasicmaterialsinvolved.In someinstances,suchanalysisas feasiblehasindicatedthefatiguestrer@hofthestructuretobesignificantlylessthanthatestimatedfromdataonsimplematerialcoupons..Values,ofthefatiguenotchfactorKf reportedforstruc-tureshavebeenhighincomparisonwithvaluesforsimplecouponshavi.~sharpnotches.Suchobservationsimplythatdesign,basedonlaboratorydataon simplespecimens,maybe unconserntive.

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Accordingly,itseemedinterestingtoattackthisproblemfromadifferentpointofview. Thiswasto testa compositestructureinfatigueandthentoattempttodevisesimplecouponswhich,underappro-

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priateloading,wouldduplicatethemodeoffailureandthefatiguelifetimeofthestructure.In otherwords,“theapproachwasto find

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whatkindof simplecouponswouldeffectivelyduplicatethestresscon-centrationsinthecompositestructure.

Itwasbelieved’thatthisapproachmightclar~ theapparentgaP.betweenobservedbehaviorof structuresandlaboratory-testdataonsimplynotchedspecimens.Moreover,ifit_gouldbe shownthatsimplespecimenscanbe devisedforreasonableduplication,ofbehaviorofacompositestructure,thisshouldbe a useffiprocedureinsomedesignproblems.An aircraftengineermightmakea detailedstressanalysisofoneprototypeand/ora fatiguetestofonesampleofa newstructureto determineregionscriticalinfatigue.Then,simplespecimensdupli-catingthefatiguebehavioroftheseregionscouldbe usedfora fatigue-testingprogramadequateto obtainGoodmanQiagamsto coverallstressrangesofdesigninterest. —

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Thestructureschosenfortheinvestigationwerebuilt-upbeamsofaluminumalloy.Onewasa boxbeam,theother,an I-be~. AS willbe notedsubsequently,fatiguefailuresin.theboxbeamwereinthewebsection.TheI-beamstructurewasdesignedtoproducefailureinthe

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Itwasbelievedthatstudyofthetwotries,withdifferent—

chord.modesoffailure,wouldprovidea reasonablefivestigationofthe‘simulationelementtlapproach.

Duringthecourseofthisinvesti$ationj~l~ble suggestionswerereceivedfroma numberofpeople.Theauthorswould-liketo express_ *,theirappreciationforhelpandsuggestionsparticularlyto thefol-lowing:Messrs.M.RoscheandP.K,phn,NationalAdvisoryCommitteeforAeronautics,Mr.R. L.Templin,AluminumCompanyofAmerica,and Y

NACATN 4137 3k

Mr.S.Levy,GeneralElectricCompany.CreditalsoisduetheMcDonnell* AircraftCorporation,andtheColunibusDivisionofNorthAmerican

Aviation,Inc.,fortheconstructionofthebeamstested.

Thisinvestigationconductedat theBattelleMemorialsponsoredby andcarriedoutwiththefinancialassistance

INVESTIGATIONOFBOXBEAM

DesignofBoxBeam

A numberof factorsgovernedthechoiceandstructures.Itwasbelievedthatthestructures

designofshouldbe

InstitutewasoftheNACA.

suitablefabricated

withmaterialforwhichconsiderablebasicfatiguedataareavailable.To simulatetypicalaircraftconstruction,thestructureswerebuiltup ofetirudedanglesandsheetmaterials.Sinceitwasconsiderednecessarytoknowtheactualstressesinthestructure,eachstructurewassimpleindesign.Forfurthersimplicity,itwasdecidedtomakethestructuressymmetrical.

Forthefirststructure,theseconsiderationssuggesteda box-beamspecimensubjectedto four-pointloading.Thiswouldprovidea constant-

+ stressmidspanandwouldeliminatesheardeformationinthetestarea.Thedesi~ wassuchastomaketheskinnonbucklingthroughouttherangeoffatigueloading.

dFactorschieflyrelatedtoaccuratestressanalysesandto consist-

encyinthelocationandmodeoffailureofthebeamwereconsideredinthedetaileddesignoftheboxbesm. Thefollowingfactorswereregardedtobe ofmajorimportance:

(1)A reasonablelengthofmidspansectionto insurepurebending(nosheardeformation)

(2)Sibility

(3)buckling

(4)

Carefuldesignof supportandoffailureat supportsandin

Rivetspacingandunsupportedthroughtheexpectedrangeof

loadpointsto precludethepos-theoverhang

skinproportionedtopreventfatigueloading

Useofbs3e2024-!L’3alminum-alloysheetand2024-T4aluinum-alloyextrusionsto takead%ntageofthe;olumeof fatiguedataavail-

% able. Brazier-headedrivetswereusedthroughoutforthesamereason.#

Figure1 isa schemticdrawingoftheboxbesm. As noted,the< beamwas60 inchesbetweentheendsupportsandthemidspanlengthwas

4 NACATN4137*

24 inches.Beamdepthwas6.128inches,andthetopandbottomskin -.widthwas22 inches.Twodiametersofbrazier-headedrivetswereused:8

i-forthe2017-T3 alwninumalloy,~/32-inchdiameter;forthe2024-’lY3aluminumalloy,3/16-inchdiameter.Webstiffenerswereof2024-T4alloy,5/8inchwideand1 inchdeepincrosssection;theywerespaced3 inchesbetweencenters.,Mechanicalpropertiesofsheetandchord-amglematerialsusedexelistedintableI.

Thedesignofthestiffenersrepresentedthegreatestdeparturefromnormalaircraftconstructionofanyoftheelementsintheboxbeam. Thiscompromisewasmadetokeepconstructioncostswithinrea-sonablelimits;itwasconsideredjustifiablesincethecenterofthebesmcontainedno shear.Theappendixofthisreportcontainsa summaryofcomputationsofmomentsofinertia,ofinterrivetbucklingloadsandstresses,andofdeflections.

Notillustratedinfigure1 istheconstructionneartheloadandsupportpoints;however,thisconstructioncanbe inferredfromfigure8whichisdi.cussedlaterinthereport.At thesepoints,solidrectangu-larblocksofaluminumalloywereused,drilledtopermitpress-fitassemblyofhardenedsteelbushings.Insidethewebs(betweenwebandsolidblock),0.051-inchsheetsweresodesignedthattheshearload

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wasgraduallydissipatedintheconstant-momentsection.Thiswasaccom-plishedwithin6 inchesofthecenterlineofeachsupport.Itwasbelievedthatsuchconstructionwouldprecl_udefailuresnearloadand

e

supportpoints.P

LoadingandStressAnalysisofBoxBeam

Figure2 showsthebeamInpositiononthefatigue-testingmachine(usedforstaticloadingforstressanalysisaswellasforrepeatedloadinginfatigue..testing).Figure3 illustratessomedetailsofthefixtureforapplicationofload.Thisfixturewasdesignedtopermitfreerotationat supportandloadpoints.Supportsconsistedofpinsthroughhardened-steelbushingsintheboxbeams.Ballbearingswerepressedonthepinstoproviderollingsupportonhardenedandgroundblocks. Fourloadingscrewsjoinedthebearingplatetothebaseplate(attachedtothemovableheadofthefatigue-testingmachine).Thesescrewswereusedforthemeanloadad~ustment.Onthereducedsectionofeachloadingarm,eightSR-4straingageswereattached,fouroneachsideofthearm. Thisarrangement,withcalibration,wasusedformeas-urementandadjustmentoftheload. —

Tl@fatiguemachineusedinthisinvestigationhasa capacityof *50,000pounds.Theplatenmovementrangesupto2 inches,adjustable

F’

NACATN4137 5b

withthelargecamatthefrontofthemachine(fig.2). Speedis

4 adjustableup toabout250cpm;thesetestswererunat 220cpm.

Itwasbelievedthatsomeofthemostimportantdataforcomparisonr of structureandelementbehaviorwouldbe providedby rathercompletestrain-gagesurveys.Furthermore,a detailedstrain-~gesurveywouldprovide(1)possibleevidenceofunexpectedstressirregulzu?ities,(2)possibleregionsofbucklingforloadscontemplatedinthefatigue-testingprogrsm(3)stressdistributiononvariouscrosssectionsinthemidspan,and(h~stressvariationalongtheextremefibersofthemidspan.

Accordingly,thefirstbesmwasinvestigatedunderstaticloadingpriortothefatiguetest. Insideandoutsidethebesm,78SR-4straingageswereattachedat criticallocations.Loadwasappliedto theloatingarmsinincrementsofabout18,cQ0inch-peundsofbendingmomentuptoa maximummomentof90,~ inch-pounds.Strainmeasurementsweremadeat eachloadlevel.Theresultswereexaminedcarefullyforstressdistributionandstressirregularities.

Subsequenttestson otherbeamscontributedadditionalinformationon stressesandstaticbehavior.Theresultsofthisadditionalworkandoftheinitialstressanalysisareas follows:

(1)At eachsectioninvestigated,thestressdistributionwask essentiallylinear.Figure4 showsresultsofa representativesection.

(2) At manygagelocations,thestressvariedlinearlywithbending* momenttoa momentof90,000inch-pounds.Figure5 showsthisvariation

fora numberofgageslocatedona sectionatthemidspan.A numberofothergagesshowedsomedeparturefromlinearityinthestressversusbending-momentplot. Thecurvesinfigure6 sretypicalof curvespre-paredfromdataobtainedwiththesegages.

(3) Themiddle12 inchesofthemidspanwereessentiallyat con-stantstress.Therewasno detectabledropoffinouterfiberstrainupto 3 inchesfromthecenterlineanda decreaseofonly3 percentat6 incheseithersideofthecenterline.Therewasa gradualdeclineinstresstowardtheloadpoints.

(4)st~inm=smementsbetweentheverticalrowofrivetscon-nectingthewebandstiffenerindicatedsecondarytensilestressestrans-versetothebeam. Figure6 showstypicalresults.

(5) NO localizedbuc~~ W= observedUP to a compressionflange-skinstressof45.0ksi(117,000inch-poundsofbendingmoment).This

* compareswitha calculatedbucklingstressof40.0ksi. Finalcollapseoccurred6 inchesfromtheinnerloadpointandintheconstant-momentsectionatabout130,000inch-poundsofbendingmoment.

u

6 NACATN4137

(6) Beamdeflectionwaslinearwithappliedloaduptoabout99,000inch-poundsofbendingmoment.

FatigueTestsofBoxBeams

Twofactorsgovernedthechoiceoffatigue-testconditions:(1)Theloadfactorwastoapproximatethatusedincommercialaircraft “-design,and(2)thealternatingloadsweretoapproximateloadsthatmightbe experiencedby commercialaircraft.A meanstressof14.0ksiontheextremefiberwasselected.Thiscorrespondstoa l.Ogloadingfora loadfactorof4.6. AlternatingloadsrangedfromabouttO.30gtoabouttO.93g. .

Eachboxbeamtestedhada-numberofstraingagesattached.Thesewereusedto load.eachbeamto itspredeterminedmaximumstressand ..

minimumstress.The straingagesonthecalibratedloadingarmswere—

usedto determinetheactualappliedbendingmoments.—

Duringeachtest,thestrainbehaviorwasobservedat selectedintervals.

Afterthefirstfewfatiguetests,smallcopperwireswerecementedto subsequentbeamsintheregionofexpectedfailures.Whena fatiguecrackoccurredunderthewire,thewirebroke.Thewirewasenergizedsothatfailureofthewirestoppedthemachine.This techniqueper-mittedtheobservationoftheearlystagesof crackdevelopment.For

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halfofthebeams,thetestwasterminatedwhenthecrackor cracksfirst*

wereobserved.Inthesecases,theboxbesmiiwereturnedoverandretestedunderotherstressconditions.Withthistechnique,additional Edatapointswereobtainedfromthelimitedbox-beamspecimensavailableforthiswork.

Sixboxbeamsweretestedinfatigue.Threeofthesewereturned .overandretestedunderdifferentstressconditionsafterthefirst

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crackwasdetected.Somebeamtestswerecarriedto completedestruc-tion(completedestructionas definedhereinoccurredwhenthecrackor

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cracksprogressedat leasthalfthedepthofthebeam);load-carryingabilityofthebeamwasreducedessentiallyto zero.Forthesecases,thenumberofcyclesof stressfrom‘initialcrackdetectionto completefailurewasnevergreaterthan15percentof_~hetotallifetime.

TableIIpresentsa summaryofspecific-testinformationandresultsforeachbeamtested.Theseincludebendingmoments,fatiguelife,webstressesdeducedfromstrainmeasurements,andcalculatedwebstresses(basedongrossareaandonnetarea).ThemeasuredandcalctiatedstresseswereatthelineofrivetsJoiningthewebandchordanglewherefailureswereinitiated. & ::

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NACATN4137 7

Stress-lifetimedata(stressvaluesbasedonstrainmeasurements)areplottedonS, logN coordinatesinfigure7. An S-Ncurveisdrawthroughtheplottedpoints.

TableIIIsummarizesfailuredataonthesixboxbeams.Inthistable,thelocationsofthefatiguecracksaregivenby componentandby numberedrivethole.Figure8 shouldbe usedin conjunctionwiththistableforidentificationoftherivethole. Ofthe29 fatiguecracksobserved,25 occurredinthemiddle12 inchesofthemidspan~theconstant-stressarea(fig.8). Theremainingfourcrackswerenearertobutnotattheloadpoints.Infact,itwillbe notedgen-erallythatfatiguecracksoutsidethemiddle12-inchregionwereaccom-paniedalsoby fatiguecrackswithintheregion.Withbuttwoexcep-tions,fatiguecrackswereassociatedwiththerivetholeinthewebandchordangleat therivetrowconmonto thechordangle,webJandstiffener.Typicalfailuresin someoftheboxbesmsareshowninfigures9 and10.

SimulationElementsforBoxBean

Possiblecorrelationoftheresultsofthefatiguetestsoftheboxbeamswithpreviouslymeportedresultsoffatiguestudiesof simpleelements(refs.7, 8,and9)wasinvestigated.Thesesimpleelements

* (includingspecimenswitha hole,havingKt = 2,andspecimenswithanedgenotch,havingKt = 5)didnotresemblethegeometryof criticalregionsofthebeamsbutwereofthesamematerial,2024-T3aluminum& alloy.ItwasnotedthattheshapeoftheS-NcurveforthebeamisdifferentfromshapesofS-Ncurvesfortheseelements.

Thislackof correlationisnottoosurprising,sincetheses@legeometricnotchesareconsiderablydifferentstress-raisersfromthoseoccurringina complexstructure.Theydonotcontainthesecondarystiffnessesofa structure,theredundanciesof severalstress-raisers}orresidualstressesandotherfactorsassociatedwiththebeam: Accord-ingly,itwasconsidereddesirableto isolateelementsfromtheboxbean,to testtheseinfatigue,andto comparetheirperformancewiththatoftheboxbeam.

Firsteletient.-Thefirststructuralelementwaschosento duplicatetherivetedjointbetweenthewebandchordangle.,Thiswastheregionincludingallfatiguefailures.Figure11 showstheelementdetails.Thisspecimenwasdesiguedto haveitsgrossareacentroidcoincidentwiththeloadingaxis. Thus,extraneousbendingstresseswereminimized.

Eachspecimenhada numberofl/4-inchSR-4straingagesattachedinthelongitudinaldirection.Theelementwasloadedto duplicate

8 NACATN4137 .—

*

essentiallythemeasuredstrainsintheboxbeam. Themeanstresswasabout12.5ksi(basedonstrainmeasurements).Thedataaresummmrized ?intableIVandareplottedinfigure12. . —-

Itisobservedfromthetablethatallfailuresoftheelementwereoneortworivetsremovedfromtheminimumtestsection.Allthesefailureswereinthechordangle.Thisrepresentsa differentmodeoffailurethanwasobservedin~heboxfatiguebehaviorofthiselementsmdreflectsthisdifferenceinthemodeworkwasdoneonthiselement.

Secondelement.-Itwasthoughtencingfailureoftheboxbeams.In

beam- Thedifferencebetween—

oftheboxbeam(fig.12)probablyoffailirre.Therefore,no further —

thatotherfactorsmightbe influ-reexaminingthebeamfailures,it

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.——wasnotedthatmostofthefailureswereat therivetholescommontothechordangle,web,andstiffener.Itwasbelievedthatseconmstressimposedinthewebby thestiffenerm“ightcontributetofailure.Onesuchsecondarystresswasthoughttobea transversetensilestressbetweenthetworivetswhichextendedthroughthestiffener.Iftheserivetsfilledtheholes,thenormaltransverseshorteningoftheweb(Poisson’seffect) duetothelongitudinalbendingstresswouldberesistedby thebulkystiffener.Thistransversetensilestresswasapparentina statictestofa box-besmspecimen(seefig.6). Inthisstudy,l/4-inchSR.4gageswerecementedon~hewebas closetothe ._ ~ ~chordangleaspossible. u.-

Thesecondstructuralelementwasdesignedto incorporatesuchasecondarystress.Figure13 showsa diagrazz_oftheelement.It con- b:sistsoftwostiffenerblocksrivetedtoa sheetofwebmaterial.Two3/16-inch-diameterrivetscompletetheassembly.It isnotedthattheserivetsareona lineperpendiculartotheloadingdirection.Thus,iftheyfill.thehole,transversedeformationmightbe inhibited.

Groovesweremachinedinthestiffenerblocksoftwospecimensformountingthel/4”-inchstraingagesonthesheetbetweenrivetholesunderthestiffenerblocks.Thesestraingagesweremountedtransverselyandlongitudinallytotheloadingdirection.Twospecimenswerecali-bratedstatically.As indicatedinfigurel+,theratioofthelongi-tudinalstresstothetransversestressoftheelementwasnearlythesameasthatfortheboxbeam(fromfig.6). —

.A numberoftheseelementsweretestedinrepeatedaxialloading.

Straingageswerenotusedonallspecimensbecauseofthecloseapproxi-mationinmeasuredstressandcalculatedstress(grossarea).It is ~believedthatthenominalmeanstressrangedfromaboutI-.2.5ksitoabout13.0ksiinthesetests.Thesevaluescomparecloselywiththemean &

stressvaluesforthebox-bes.mtests(12.1k$ito 12.9ksi).r “-

:B NACATN4137 9k

ThetestresultsaresummarizedintableV andsreplottedh fig-4 ure15. Inthefigure,thedashedlineistheS-Ncurvefortheele-

ments;stressesarecalculatedfromstrain-gagereadingsorsrecalcu-latedonthebasisofgrossarea. ThesolidlinerepresentstheS-Ncurveoftheboxbeam. Itappearsthatthetwocurvescoincidewiththeprobableprecisionof eithertest.

INVESTIGATIONOF I-BEAM

Designof I-Beam

Afterexperienceinthebox-beaminvestigation,itwas decidedtostudya fabricatedI-beamof somewhatgreaterlengthanddepththanthoseoftheboxbeam.

Itwasthoughtthatthistypeofbeamwouldafforda goodchanceofa fatiguefailureinthechordwhichwouldbe a differentmodeoffailurethanthatobtainedintheboxbe&m. Simplicityofdesignsug-gestedthattheI-beambeloadedina mannersimilarto thatusedhtheboxbeams.

To insure,asmuchas possible,thatfatiguefailureswouldoccur\ inthechordsection,thefollowingprecautionsweretaken:

(1)●

(2)

(3)

(4)

Chordcross-sectionalareawasreducedinthebeamatthemidspancentersection.

Rivetholesinthewebsectionaroundthe8 inches)werereamedanddeburred.

theouterflangeof

criticalspan(center

Outeredgesofthewebwerebrokenwithfipe-gritpaper.

Theedgedistancefortherivetrowwasmadegreaterinthewebthaninthechord.

SchematicdrawingsoftheI-besmareshowninfigures16and17.TheprincipaldimensionsfortheI-beamareshowninthesedrawings.Asnoted,inthecenter8 inchesofthemidspanthedepthofthebeamwasreducedto Z inchesforreasonsdiscussedpreviously.

4

Thematerialsusedforthevariouspartsofthestructureswereasfollows:Forweb,spacers,andshearplates,0.072-inch2024-T3al-~-

+ alloybaresheet;forchordsandstiffeners,2024-T4aluminum-alloyextrusions;forbushinghousings,2024-T4aluminwn-alloyplate;andfor

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theThe

NACATN4137d

3/16-inch-diameterBrazierheadedrivet=,2024-T3aluminumaldoy.mechanicalpropertiesofthesematerialsareshownintableVI. P

As indicatedinfigure17,themomentofinertiaofthecentersec-tionofthebeambasedonnet-areacalculationswas I= = 40.88inches4.Themomentof inertiabasedongrossareas Igg was41.55inches4.Typicalcomputationsofmomentof inertiaandofdeflectionareshown —intheappendix.

Theconstructionofthebeamnearthesupportandloadpointsisillustratedinfigure18. At thesepoints,constructionis similartothatusedontheboxbeam. However,thesolidrectangularblocksofaluminumareontheoutsideofthebeam. Oneachsideoftheweband - ““-extendingoverthechordsareshearplates,whichgraduallydissipatetheshearloadintotheconstant-momentsection.

>

LadingandStressAnalysisofI-Beams

TheloadingfixturefortestingtheI-beamswasessentiallythe—

sameas theoneusedintestingtheboxbetis.ThemaindifferencewasthatthefixturewaslargeYto acconmmdatethelargerbeam. Loadwasappliedthroughcalibratedloadingarmsequippedwithstraingages.Thefatigue-testingmachineandthemachinespeedwerethesameasthose e ““usedforthebox-beamtests.

As inthebox-beamtests,a thoroughstatic-stresscalibrationof ~–theI-beamwasconsiderednecessarypriortothefatiguetest. —

Accordingly,thefirstofthebeamstobe testedinfatiguewasstaticallycalibrated.A numberofstraingageswerecementedtothebeam. Theloadwasappliedinincrementsof45,000inch-poundsofbendingmomentinthemidspantoa maximummomentof270)000inch-pounds.A bendingmomentof270,000inch-poundscorrespondstoa stressof30ksiintheouterfibersat a sectionthroughthemidspancenterlineofthebeam. Strainmeasurementsweretakenat eachloadlevel.Theresultswereexaminedcarefullyforstressdistributionandstressirregularities.

Duringthecourseofthefatiguetests,additionalexperimentalstressstudiesweremadetoprovideotherinformationas itappeared

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necessary.Forexample,aftercompletingfatiguetestsonthefirstbeam,itwasdecidedto removethecenterstiffeners(markedA infig.”18) onthesecondbeampriorinselectedregionsofthesecondwereremoved.Theresultsofall

totesting.A stressstudywasmadebeambeforeandstressanalyses

afterthestiffenersareas follow: *

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NACATN4137 l-l

(1)Inthereducedsectionofthebeam,thestressdistribution3 withdepthwasalmostlinear.Figure19 showsa representativesection.

An exceptiontothiswasobservedona sectionattheedgeofthefilletmachinedonthechord.

(2)At sectionsoutsidethereducedsectionofthebeam,thestressdistributionswerenotlinear.Forexample,at sectionB-B(about6 inchesfromthemidspancenter)therewasalmosta constantstressacrossthechord,whereaswebstressdistributionwaslinear.A non-lineardistributionwasalsofoundona sectionthroughthefirstrivetintheshearplate(seefig.203notetheslight~iations in stressdistributiononthissectionfortheindividualbeams).

(3) At allgagelocations,theprincipalstressvariedlinearlywithappliedbendingmoment.Foranyonevalueofappliedbendingmoment,therewasa gradualreductioninstresswithdistancefromthemidspancenterlineofthebeam.

(4)An exceptionto item(3)wasnotedontheouterfibersofthetensionandcompressionflanges.At theseregions,a peakstressoccurred4 inchesfromthemidspancenterline. Thispositionis coincidentwiththefillet.Thepeakstressatthesepointswasabout20percenthigherthanwasthestressatthemidspancenterlineofthebeamonthesesurfaces.

*(5)Secondarystressesperpendiculartothemidspandirectionwere

greatestinthewebinanareaaroundthestiffenersandthefirstrivet* intheshearplate.Thesestresseswere,withthestiffenersinplace,

lessthan1 ksioftensilestressand,withthestiffenersremoved,lessthan2 ksiof compressivestress.Themeasuredprincipalstresseswerenotaffectedappreciablyby theremovalofthecenterstiffeners.

(6) Withthestiffenersinplace,nobucklingwasobservedthroughthestressrangeinvestigated.A smallamountofbucklingwasobservedinthewebwhenthestiffenerswereremoved.However,thiswasnotcon-sideredsufficienttoaffectthefatigueresults.

(7) BeamdeflectionW= line= with applied load upto 27’0,000inch-poundsofbendingmoment.Themagnitudeofthemeasureddeflectioncom-paredcloselywiththemagnitudeofthecalculatedvaluesfordeflection(seecalculationsinappendix).

Comparisonoftheresultsoftheexperimentalstresssnalysiswiththeresultsofthetheoreticalanalysisshowedthebeamtobe behavingaboutas hadbeenanticipated.

12 NACATN 4137

Thefatiguetestsanalogous_tothoseforincommercialaircraft

D

FatigueTestsofI-BeamsPontheI-beamswererununderloadingconditions

theboxbeam. Theldadsapproximatedthoseuseddesign.Allbeamsweretestedata meanstress

of 14ksioftheextremefiberofthemidspancentersection.Thisstressisequivalentto l.Ogloadingbasedona loadfactorof4.5.AlternatingloadvariedfromtO.&9gto*0.9~g.

Thestraingagesattachedto eachbem.served(inloadingthebeb,m)to determinemaximumandminimumstresses.Thestraingagesontheloadingarmswere.usedtobalancetheloadandto~easuretheapplied

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bendingmoment.Tbro~houtthetest,.——

a numberofloadandstrainreadingsweretskento correctforloadchangesduringthetest.

—Crack-

detectionwiresalsowereusedto determineoccurrenceofthefirstcrack,thuspreventingcatastrophicfailure.ofthebeams.Whenthefirstcrackwasdetected,thetestwasconsideredcomplete.Thebeamthenwasturnedoverfora secondtest.

TwoI-beamsweretestedinfatigue.By usingthetechniquedescribedabove,foursidesofthebeamsweretestedandfourpointsontheS-N

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curvewereobtained.

TableVIIsummarizesthefatigue-testresults.Thetableindicateswhichmemberofthestructurefailedandthecracklocationby theuse *ofnumberedrivets.Thesenumberscorrelatewithnumberedrivetsinfigure18.

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rInall,thereweresevenfatiguecracksdetected.Allbutoneof

thesewereinthechords.TheonecrackinthewebwaslocatedatarivetatwhichfailureinthechordalsoW=”detected.Thisfailurewasinthefourthbeamside(specimen2-1)tested.Ofthesixfailuresremaining,fivewerelocatedinthechordata commonrivetholeasso-ciatedwiththefirstrivetintheshearplate,@ inchesfromthecenter

4ofthebeam. Ofthethreebeamsidesfailingat thislocation,twohadfailuresinbothchordsat thisrivethole.Theremainingfailure,thatinthefirstbeam(specimen1),wasinthereducedsectionofthechord.However,itwasassociatedwitha metallographicflawinthe

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surfaceoftheextrusion.Therefore,thistestwasnotconsideredchar-acteristicofthebeam. A typicalI-beemfailuremaybe seenin ..figure21.

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!TableVIIIpresentsthestressdataforI-beams.Inthetableareindicatedthebendingmomentappliedtothemidspan,thestressesat thepointoffailureas determinedfromthestaticcalibrations,thelife- *timein cyclesto crackdetection,andthecalculatedstresses(basedonbothneteffectiveareaandgrosqarea).

?

NAMTN4137 13

Stress-lifetimedataforthethreebeamsidesforwhichfailureoccurredat theedgeoftherivetholeinthechordareplottedonS, logN coordinatesinfigure22; Stressesarebasedon strainmeas-urementsobtainedinthevicinityoffailure,extrapolatedto thefail-urelocation(seesectionentitled“ElementsConstructedFromBeamMaterial”).

SimulationElementsforI-Beam

TheI-beauhadbeenplannedto failinfatigueinthechordat asectionwherethestressescouldbe analyzedrelativelyeasily.Whilethebeamsfailedinthechordangle,failuresinitiatedata regionofconsiderablecomplexityfordetailedstressanalysis.However,itwasdecidedtoproceed,withthesomewhatlimitedinformationavailablecon-cerninglocalstressesintheI-beamsat thislocation,in constructionof simpleelementswhichmightduplicatethefatiguebehaviorobserved.

ComparisonoftheS-NcurvefortheI-beamwithcurvesforsimplynotchedspecimens(refs.7, 8,and9)andwithcurvesforthetwotypesof elementforsimulationofbehavioroftheboxbeamshoweddissimilari-ties.Accordingly,considerationwasgiventodesi~ ofa differenttypeofelement.

Pretiinaryexperiments.-FailuresintheI-beamwereintheextrudedchordangleata rivetholewhichcontainedthelastrivetintheshearplate.At thislocation,a nmiberof factorscontributedtothelocalstressdistribution.Theseincluded(1)thediscontinuityinthestructureat theterminationoftheshearplate,(2)thesecondarystressesinthechordanglefromtheshearplate,(3)thestresscon-centrationofthefilledrivethole,and(4)theresidualstressfromfabrication.

Threetypesofelementsintendedto containsimilarfactorswerefabricatedfromavailable0.081-inch2024-T3sheetstock(toconservethesmallreminingsupplyofactualmaterialsusedfortheI-beans).Fig-ure23 showsthespecimendesigns.Inthesespecimensthemainsheetisconsideredto representthechordangleofthebesm;thesideplateorplateswhichendjustshortofthetransversecenterlineofthespeci-menareconsideredtheshearplates.As showninfigure23,eachendofthespecimenscontainedsixrivetsina line.

ThreespecimensoftypeA weretestedatnomtial(P/A)stressesof8.0f 6_Oksi. Thesefailedinlifetimesfrom300,000to 600,000cycles.However,failureinitiatedunderthe“shearplate”inthe“chordangle”atregionsof intensefretting.Thiswasascribedto localstressesresultingfromnonsyrmnetryinthethiclmessdirection.

14 lwx m 4137d

A specimenoftypeB (plannedtoreducethenonsymmetry)wasnexttested.Thislasted,underthesamenominalstressrangeinthechord Gsheet,morethan3,000,000cycles.However,eventualfailurewasagainneartheedgeoftheshearplateandfrettingwasagainpresent.

.

OneconditionintheregionoffailureoftheI-beam,notduplicated.

intheseelements,wasa stressgradient.Accordingly,twospecimensoftypeC wereconstructedandtested.Inthese,thelineofloadingwasslightly(about1/4inch)offsetfromthelineofrivets.Straingageeonthesespecimenswereus’edto (1)verifythata straingradientexisted

—

acrossthewidthand(2)obtain,by extrapolation,valuesofthestraininthechordsheetatthepositionofthelastrivetintheshearplate.Thefollowingresultswereobtained(seefootnoteoftableIXformethodof computingstresses):

Specimen Nominalstressesin sheetatrivet Lifetime,number Fromcomputations Fromstraingages cycles

1I

10.4* 7.7 7.0f 5.3 I 608,0002. 16.8* 10.7 8.3-* 6.1 146,OCX) IForbothspecimens,failureoccurredat theedgeoftherivetholecor- 3–respondingtothelastrivetintheshearplate.

—Thus,themodeof

failurewassimilartothatintheI-beam.Sincethelifetimeforthe-.

elements,forstressconditionsroughlysimil~tothoseintheI-beam, ●wereintherangeofthebeamlifetimes,itseemedreasonableto carryoutfurtherstudieswiththistypeof specimen.

Elementsconstructedfrombeammaterial.-Accordingly,sevenele-mentssimilarto thoseoft~e C (fig.23)weremachinedfrommaterialsusedfortheI-beams.Figure24 showsthedimensionsandconfigurationofthecentersectionofthis(typeD) specimen.Thesheetwasthe0.072-inchmaterialfromstockusedontheI-beams.Thechordsections -wereplanedto 0.072-inchthicknessfromtheetiruded-anglestockusedfortheI-beams.

Some32 straingageswereusedoneachspecimen.A numberoftheseservedmainlytoassistinloadingforreasonablesymmetry(forexample,tominimizebending)andtoassistinest”-tingtheoverallstrainpat-tern.Thelocationsoftheeightgagesgenerallyusedforloadingandevaluationsofstressesareshowninfigure24. —

Theloadingprocedurewasas follows(seefig.24). Stressesweree

extrapolatedlinearlyfromgages1 and2 topositionX at therivetwherefailurewasexpected.Similarextrapolationsweremadefrom R

IVLCATN4137 15

gages 3 and4 andfromgages5 and6 and7 and8 to thecorrespondingpositionY. Afterreasonableadjustment(byshims,etc.) toprovideminimumbendingandtwisting,theaver%eoftheseefirapo~ted~luesonthehigherstressendwasusedfora loadingstress.TableIX showsthesestressesandtheobservedlifetimesto failure.Figure25 showstheresultsonanS-Nplot(loadingstressesusedforplotting).

A dashedlineisdrawnthroughthepointsrepresentingdatafortheelements.Itwillbe notedthattwoofthedatapointsfallmuchbelowthisline. Evidencefromadditionalstraingagesindicatedthatthecorrespondingtwospecimenshadstraindistributions(particularlyacrossthechordsheetbetweentheshearplates)whichwasextremeincomparisonwiththoseoftheotherfivespecimens.It ispossiblethattheseunderwenttwistinginadjustmentofthegrips,buttheonlycertainconclusionisthattheyweredifferentin stressdistribution.Accord-ingly,thesepointsweredisregudedin~a~ thel~e.

ThesolidlinerepresentingtheI-beamisabout20percentlowerthanthedashedline.A nuniberoffactorswhichmightaccountforthiswereconsidered.Theratioof chordmaterialto shear-platematerialwasmuchhigherintheI-beamthanintheelements.IntheI-beam,bendingmomentsprovideda differentmeansoftransferofloadbetweenchordandshearplatethanwaspresentintheelementunderaxialloading.Consequently,thestressesobtainedbyextrapolationinbothcaseswerereallynotdirectlycomparable.A limitedstrain-gageexplo-rationofonespecimen(oftypeD) showedthatstraingagesontheshearplatehadsomewhatlowerreadingsthsmvaluesobtainedfromlinearextrapolationofgagesontheedgeofthechordoftheelement.Infact,ifthestressamplitudevaluesforthedashedlineinfigure25arereducedby aboutthevaluesuggestedby thisexperiment(15percent),thedashedlinecomes(withintheexperimentalerror)in coincidencewiththesolidlinerepresentingthebeam.

Justificationfortheassumptionthatstressesinthechordunder-neaththeshearplateareequaltothoseintheshearplateisquestion-able. Themeasurementsserveto emphasizethedifficultiesthatmightattendthesimulation-elementapproachforthosecomplexstructuresforwhichfatiguefailuremightoccurinregionswherestressescannotreadilybe determined.

ThetypeD elementsfailedinthechordat theedgeofthelastrivetholeintheshearplate.Thus,thefailuremodewasthesameast~t oftheI-beam.Withreasonableallowanceforthemannerinwhichvaluesfromstrain-gagereadingswereetirapol.ated,itappearsthattheelementshowedqualitativeagreementwiththeI-beam.However,unliketheboxbeamitisdoubtfulwhetherquantitativeagreementcouldbeexpectedwithoutadditionalevidencebothon simulationelementsandon

16 NACATN4137

theI-beanregardingthelocalstrainorstressdistributioninthewebat ornearthechordangle.

DISCUSSIONOFRESULTS

CorrelationofFatigueBehaviorofElementsWith

FatigueBehaviorofBoxBeamandI-Besm —

Thesimulationapproachto studyingthefatiguebehaviorofa com-plexstructureappe~rsto involve..~processOZduplicating.intheS.fmU-””-la.tingelementsthestressconcentrationsinthecomposibestructure.

—

Onceit isshownthatsimyleelementscanprovidea reasonableduplica- .4 ‘tionofthebehaviorofa compositestructure_itmaybepossibleto usesuchelementsto establishGoodmandiagramsfortherangeof stresses

.:.—ofdesigninterest.Thislatteridea,of cotise,alsowillneedveriff-cation. As indicatedsubsequently,theuseof suchelements,embodyingthesecondarystressesandstiffnessesfoundinactualstructures,as aresearchtaolinfatiguestudiesalsomayprovidemorerealisticvaluesof Kf pertinenttoaircraftstructurestharcanbe obtainedby simplynotchedcouponsorlap-jointspecimensthat@ve beenexaminedinthepast.

B NACATN 4137*

stressesintothe

4 chordangleunder

17

chordangle)andofthefrettingcorrosionofthetheshearplate.

Threeelementswerestudiedin investigatingsimulationoftheI-beamfatiguebehavior.OnlywhensecondarybendtigwasIntroducedintooneoftheelementswasitpossibleto duplicatethemodeoffail-ure(typeD). WiththiselementqualitativeagreementwiththeI-beamwasachievedwithinthelimitationsoftheapproximationsusedinextrap-olatingstraindatatothecriticalsection.QuantitativeduplicationwoulddependuponanaccuratedeterminationofthelocalstressesbothintheI-beamandinsimulatingelements.

StressConcentrationFactorsofBeams

It iscommonpractice,indesigningtopreventfatigue,to evaluatenominalstressesandtoapplyfactorstoallowfortheindeterminablestressconcentrationsthataresoimportantindeterminingtheinitia-tionofa fatiguecrack.Onefactoroftenusedin suchdesignisthefatiguenotchfactorKf. Thismaybe definedby

Kf = StresssmplitudeforunnotchedmaterialNominalstressamplitudeforpartat samenominalmeanstressandssmelifetime

I*It isinterestingto considerresultsofthebeamtestsintheseterms.

s Figure26 showsvaluesof Kf fortheboxbeauandfortheI-beamintermsof cyclesto failure.Theseweredeterminedlydividingvaluesofnominalstressamplitudel(fromtables11andVIII)intovaluesofstressamplitudeforunnotched2024-T3sheetata meanstressof10ksi(fromref.7). Since,overthislifetimerange,thefatiguestrengthgenerallyisnothighlysensitivetomeanstress,no allowancewasmadefortheactualvariationsinmeanstressforthetwobeams(boxbeam,I-2.ltow.9ksi, I-bean,7.8to 8.2ksi).Forcomparison,dashedlinesinfigure26show valuesof Kf forspecimenswithsimplegeometricalnotchesoftwoseverities(takenfromrefs.8 and9).

Intheregionofhigherstresseswhichproducecrackinginabout10,000cycles,theboxbesmshowsa valueof Kf lowerthanthatofaSha17Jl (Kt= 5.0)notchin sheetspecimens.Forlowerstressamplitudescorrespondingto failureinabout1,000,(XIOcycles,theboxbeamshowsa muchhighervalueof Kf (oftheorderof6.o).Thenotchedsheetshowsa decreasein Kf inthisrange.TheI-beamcurve(basedononlys

%&&mm stressminusmeanstress.u

3 points)indicatesa trendsimilartothatoftheboxbeamfor Kf.Thus, Kf continuesto increasewithdecreasingstressamplitude.The kvalueof Kf inthiscaseapproaches5.

Similarhighvaluesof Kf canbe computedfromresultsof othertestson compositestructures.Failuresat rivetedshearjointsinc-46wingtests(ref.5)providevaluesintherangeof3.7to 4.5atlifetimesoftheorderof200,000”cycles;inthesametests,failwesat cornerinspectioncutoutsindicateKf valuesfrom4.8to 5.3atlifetimesoftheorderof300,000cycles.

.—

Suchobservationsimplythat,indesign,itisnotsafetoapply,to conventionalnominalstressvalues,valuesof Kf as lowasthoseobservedinlaboratorytestsofevensharplynotchedcoupons.

FactorsInfluencingValuesofStressConcentrations

Thestudiesof simulationelementsforthetwotypesofbeamspro-videsomeindicationofthefactorsinfluencingKf valuesof structures.

Figure27 showsvaluesof Kf for(1)thefirstsimulationelement}ortheboxbeam,(2)a geometricnotch(Kt. 5.0)insheetmaterial,(3)theseconds~fiationelementfortheboxbeam,and”(4)theelement

@

fortheI-beam.It isobviousthatthe Kf valuesforallthesimula-tionelementsincreaseinmagnitu~eforlongervaluesofllfetjme(and ●

lowervaluesofnominalstress)thandovaluesof Kf forthegeometricnotch.It seemspossiblethattheserelativelyhighstressconcentra-tionsarerelatedtothecomplexflowof stressthrougha rivetaswellastheinteractionsimposedonthecomponentsby adjacentrivetgeometry.Frettingaroundtherivetevenat lownominalstressesalsoisa contrib-utingfactor.

—

.It isfurtherapparentthatthevaluesof Kf aremuchlargerfor

thesecondelementfortheboxbeamthanforthefirstelement.Itwillbe recalledthatonedifferencebetweenthestressdistributionsinthese

—

twoelementsisthepresenceofa significanttransversestressinthesecondelement.Itmayalsobe recalledthatonlywhentherewasastressgradientintroducedacrossthesimulationelementfortheI-beamwerefailuresobtainedattherivet.Theseobservationsimplythattheeffectivestressconcentrationata rivetcanbeparticularlyhighinthepresenceofa stressgradientandoftransversestress.

+–

r

NACATN 4137

SimulationApproach

19

Thisinvestigationhasdemonstratedthefeasibilityofusingsimpleelementsto studythefatiguebehaviorof complexstructures;however,thestudyalsohassuggestedcertainlimitationsto suchanapproach.

Themainthesisappearstobe thatsimulationcanbeachievedifitispossibletoanalyzethestructuresowellthatthestressdiscontinui-tiesofthestructurecanbereasonablywellduplicatedinthesimulatingelements.Forthosecaseswhereitmaybe impossibleto characterizetheentirenatureofthestressirregularities(ortheircontributory ‘causes)itappearsthatthesimulatingelementwillbe lessuseful.

Itwouldappearthattheuseof simulationelementscanbe con-sideredfroma somewhatdifferentapproach.Forexample,considerabledatahavebeenassembledon simplynotchedbarsandonsimpleelements,suchas rivetedlapjoints.Suchdatamaybe of interestin character-izingthefatiguestrengthofmaterialsbutmay%e lessusefulinpro-vidingdataofgeneralsignificanceindesigningcomplexstructures.Thespecificreasonforthisisthatsuchnotchedcouponsandsimpleelementsdonotcontain,ingeneral,thesecondarystressesandrestraintsfoundina complexstructureand,hence,fatiguenotchfactorsobtainedfromsuchspecimensmaynotapproachthehighvaluesof Kf foundin structures.Ontheotherhand,theuseof simulating

4 elementswhichcontainprovidemorerealisticandusefulinterestin.

stressfeaturesfoundin complexstructuresshouldestimatesof Kf,whichdesigningstructuresto

wouldbe ofmoreinmediaferesistfailureby fatigue.

COI’?CLUDINGREMARKS

Thisinvestigationwasinitiatedto exploretheproblemof corre-latingcomposite-~tructurefatiguebehavior-andbasic-mat&rialor simple-elementbehavior.To thisend,fatigueandrelatedstatictestswerecarriedoutonboxbeamsandonI-beamsandalsoon elementssimulatingkeylocationsinthetwotypesofbeams.Loadandstressconditionsforthefatiguetestswereselectedintherangeexperiencedbycommercialaircraft.

Thefollowingconclusionsappearwarrantedonthebasisoftheinvestigation:

Fortheboxbeam,thefatiguebehaviorat thecriticallocationof+ failurewasapparentlycorrelatedwiththebehaviorofa simplesimula-

tionelement.Correlationwasobtainedwhenthemodeoffailureandthesecondarystresseswereduplicated.FortheI-beamthereappearedtobe

4

-—

20

qtilita~ive@eernentwith&......,.....detailedstressdistributionude @electionof& element

NACATN4137.

siiiilat’fbnerement.Uncei’taintiesinthein.{he,,region’offailure 01theI-beam Ec~n~ain~~t&s@ess irregularitiesdif-

ficult. Itthusappearsthatthesi.uiulationapproachfillbe useful - ‘“forthosecaseswh&~e,by e~erfien~alstiidy,~~willbe possibleto_assessreasotiblyfactorscontributi~to stress-raisersinthestructure.

High.fati@e,notchfactors(intermsoftheconventior~ldefinitionof stress)werefoundinboth~e~. Thisobservationsuggeststhatindesigntheuseof Kf ValuesobtainedfromSimplynotchedcouponsmaybe anunconservativepractice.

Thestudyof sim~atfonelementssugjjestedthatsuchhighfatiguenotchfactoi?s&~ be e~ectedincomposite.structureswherebiaxialstressdistributionsandmarkedstressgradientsoccuraroundrivets.Thetijjoriaticeofriv=tedcmstructioninaircfiftdesi~ suggeststhat..-.

fu&herabse$srn~iitof~fiee?i%~tof co~l~~Io&dingson~hefatiguenotchfactorsofrivetedcomponents,shouldbemade. If simulationele-mentsareiesi&edto containt~icalHecb-pdarystressandloadinflu-ences.asobservedinstructures,theresul@ntdatamayyieldmoreus&-ful K~ tiluesthanthosectientlyobta~nedonsimplynotchedcoupons.

—

h. . . —.

30, 1956. P

.

NACATN4137

APPENDIX

21

A

a

1)

c

d

E

10

K

z

P

s

t

v

x

TYPICALCALCULATIONSOFWMENTSOT INERTIA,BUCKLING

STRISSES, BENDINGMOMENTS,ANDDEFLECTIONS

symbols

Thefollowingsymbolsareemployedinthisappendix:

cross-sectionalareaofeachcomponentofbeam,in.2

distancebetweenloadandsupportpoints,in. ●

distancebetweenrivetrows,in.

distanceto outerfibers,in.

distancefromcentroidof componenttorespectiveaxisofinertia,in.

Yew’s modilus

momentof inertiaof eachcomponentofbeamaboutitsowncentroidalaxis,in.4

momentof inertiaaboutneutralaxisofbeamsection(grossarea),in.4

momentofinertiaaboutneutralaxisofbeamsection(netarea),in.4

endrestraintconstant

distancebetweenloadpoints,in.

appliedloadineachloadingarm,lb

bucklingstress,ksi

weborflangethiclmess,in.

Poisson’sratio

centroidaldistanceofnet-areasectionfromaxisA-A (axiscoincidentwithcompressionsurface),in.

22 N4CATN4137u

mtdspandeflection,in.

overhangdeflection,in.

SummaryofMomentsofInertia,BucklingStresses,

BendingMoments,andDeflectionsofBoxBe~

Themomentsofinertia,bucklingstresses)bendingmomentsjanddeflectionsofthe

Momentofinertia:,

Neteffective

boxbeam”areas

area,inches4

follow:

1==’sAd2’Y‘0-&=7.7~L-J uGross area, inches4

— —

l==L‘d2+P0=8“727Flange-skininterrivetbucklingstress,

s=fi2~t2

12(1-+’)b

Flange-skininterrivetbucklingbending

Neteffectivearea,inch-pound

ksi:

= ko.o

moment:

Pa . %= 93,500c

Grossarea,inch-pound -.

SImPa=Y= 113,200

b

.—

——

—

—

.

-.

F

—

—

+

u

NACATN4137 23

Deflection:

Neteffectivearea,inch

PaZ2Yl=— = 0.00000088Pa

m%

Pa2(3Z+ 2a)Y2 = = 0.000~39Pa

6EIm

Grossarea,inch .

PaZ2Yl=~ = 0.00000078pagg

y2 = Pa2(3Z+ 2a)= o.m35 Pa6EIgg

Momentof inertiaat centerofbeam:

Neteffectivearea,inches4

%J= xAd2+ 10 -&S = 40.88Grossarea,Inchesh

‘=‘I “2‘z10=41”55Momentof inertiaat sectionthroughthefirstrivet=d shearplate:

Neteffectivesrea,inches4

In= 57.8

Grossarea,inches4

%3= 58.67

24

Deflection:

Neteffectivesrea,inch

‘1 =

Y2 =

Grossarea,inch

Y1 =

y2 =

fQ&=0.000000333Pa

~a2(3~+ 2a) s o ooooo156pa6EI= “

.

Pa12 _8EIa

o.000000328Pa

Pa2(3Z+ 2a)= 0.00000154Pa6EIgg

NK!JJTN4137

—

.—

—

NACATN 4137

REFERENCB

1.Brueggeman,W. C.,Krupen,P.,andRoop,F.of10AirplaneWing-BeamSpectiensby theTN 959,1944.

c.: AxialFatigueResonanceMethod.

TestsNACA

2.Anon.: FlexuralFatigueTestsofSomeAluminumAlloyWingBeamsofSeveralDesigns.Prog.Rep.No.1,Bur.Aero.,Aug.1947.

3.Howard,DarnleyM.: FlexwalFatigueTestsofWingBeams.NBSRep.1350,Bur.Aero.,Dec.1951.

4.Johnstone,W. W.,Patching,C.A.,andPayne,A. O.: Anl&qerimentalDeterminationoftheFatigueStrengthofCA-12“Boomerang”Wings.Rep.SM 160,Aero.Res.Labs.(Melbourne),Sept.1950.

5.McGuigan,M. James,Jr.: InterimReportona FatigueInvestigationofa Full-ScaleTransportAircraftWingStructure.ma ~ 2920,1953.

6.Howard,DarnleyM.,andKatz,Silas:RepeatedLoadTestsofAircraftWingBesmSpecimensUnderBendingandBending-TorsionLoads.Nat.Bur.StandardsRep.4720,Bur.Aero.,June1956..

7.Grover,H. J.,Bishop,S.M.,andJackson,L.R.: FatigueStrengths ,ofAircraftMaterials.Axial-LoadFatigueTestsonUnnotchedSheet-. Specimensof2kS-T3and75s-T6AluminumAlloysandofSAE4130Steel.NACATN 2324,1951.

8.Grover,H.J.,Bishop,S.M.,andJackson,L.R.: FatigueStrengthsofAircraftMaterials.Axial-LoadFatigueTestsonNotchedSheetSpecimensof2hS-T3and7x-T6AluminumAlloysandofME 4130SteelWithStress-ConcentrationFactorsof2.0and4.0. NACATN 2389,1951.

9.Grover,H. J.,Bishop,S.M.,andJackson,L. R.: FatigueStre@hsofAticraftMaterials.Axial-LoadFatigueTestsonNotchedSheetSpecimensof2&-T3 and75S-T6AluminumAlloysandofSAE4130SteelWithStress-ConcentrationFactorof 5.0. NACATN 2390,1951.

.

TimLEI

MECHANICAL PRolmTIEsa cm’MMcmIMs USED~BOXBl?AM

Tensile Yield strength ElongationMcdulusofMaterial. strength, (O.2 percentoffset),in2 in., elasticity,

ksi kai percent psi

O.@-inch 2@+-T3 72.3 53.4 18.2 10.6X 106aluminum-alloysheet

O.0~1-inch2024-T5 m.1 32.4 19.2 10.6aluminum-alloysheet

(3/4- X 3 4- X O.@l-inch 67.1 53.2 17.2 10.62024-T EihIOlhUItl~Oyextruded angle

aAv=e st~e~h VELIWS from f’o~Wec*ns.

4=G-1

1 t

Specimen

BendingmcdnentPa,1,000in-n

Maximum I Mean

TABLE II

S!rmi%msm EoxBEluS

Calculatedweb stress, ksi

Fat iguelife,cycles

(a)

Measured webstress, ksi

Maxmml

64.869.882.162.2$.257.082.751.26’7.1

41.844.842.842.543.744.443.641.941.0

Pm,m193,76036,670265,3ecl624,7(x)

1,137)12030,540

5,294,630108,m

20.220.624.217.715.816.724.215.620.3

Mean

12.712.912.512.112.41.2.212.312.712.7

Eased on grossarea

YMaximum-

19.4 I-2.620.9 13.424.6 IJ2.918.7 I-2.816.8 13.217.1 13.424.8 13.115.4 12.420.1 12.3

Based on ne%area

Maximum

23.925.’j’30.322.920.721.031.118.924.7

Mean

15.416.215.815.616.116.416.415.515.1

!24=

G-a

%ee tableIIIandfigure8 forlocationoff’ailme.

mm

$pecimen

1

2

3

4

k-l

5

5-1

6

6-1

TABLB III

SUIMARYOF EOX-REAMFATIGUEFAILUREDATA

Data cm firstobservedfatiguecracks

Member

WebFlangeWebChordangle

WebCh6rdangleW&bChordangleWebCbrd angleWeb

WebChordangle

WebFlmge

aseefigore8.

F@re.l.lust.ratiq

crack

9

10

r +

I

Rivethole

~

2; 59

2; 5; 5; 52; 5; 5; 8

2; 5; 5; 75; 8

2; 5; 5; 85552

55

22

Fatiguelife,cyclee

289,00289,@193,T60193,-@.3

36,67036,670265,3i?0265,3E!0624,700656,8&l

1,137,120

w>%

108,ooo

Final failm

Fatiguelife,cycle6

289,850

193,930

43,Ym

685,530

32,$L0

Renwks

Fatigue-crackdetectionwirewas not used

Fatigue-crackdeteetionwirewas cementedto flmgeteosionskin only;webapy=ed to failat rivet:

Web failedfirstat rivet7

Test stopped;b= turnedoverfor test 4-1

Webfailedfiret

Teststopped;beenturnedoverfortest5-1

Did mt fail;beam turnedoverfar test 6-1

Testwasmt continuedtoultimatef%ilore

f ? .

E3

Specimen

1

2

3

4

5

6

86-1

TAmLEIv

SUMWSRY OF FATIGUE-TESTDATA ON FIRST SIMULATION ELEMENT FOR BOX BEAM

Fatiguelife,cycleB

533,000

767,01x)428,ooo

165,000

791,000

16,625,m

$),634,0MI

Measuredstress, kai

19.5

19.021.3

25.4

17.9

l~.k----

Mean

12.6

12.211.2

1.2.8

12.o

14.0----

Calculated stress, ksi

Based ongross area

iaximm

21.1

20.3

=.8

25.1

18.8

16.2

17.9

Mean

14.1

14.511.7

=.8

12.8

12.8

u?.8

Based onnet axea

Maximum

24.9

23.9

25.6

29.5

22.1

19.0

21.0

Mean

16.6

15.413.8

15.0

15.1

15.0

15.0

Location of failure

Angle; l? in. off center

Angle; 7/8III.off centerAngle; ~ in. off center

Angle; 1$ h. off center

Angle; 1: in. off center

Did not fail

Angle; 7/8 in. off center

%etest of specimen 6.

30 NACATN 4137●

●

TABLEv

RESULTSOFFATIGUETESTSOFSECONDSIMULATIONELEMENTFORBOXBEAM

Calculated Calculated

SpecimenFatiguelife, stressbased stressbased Locationof

cycles ongrossarea, onnetarea, failureksi ksi(a (b)

7 35,700 25.0 33.5 Center8 92,900 21.0 28.1 Center9 278,400 18.0 24.3 Center10 432,000 17.0 22.8 Center11 2,787,000 16.0 21.4 Center12 47,000 23.0 30.8 Center13 1,244,ooo 16.5 22.1 Center14 289,000 19.0 25.2 Center15 +20,019,000 12*5 , 20.8 Didnotfail16 2,446,600 16.0 21.3 Center17 +25,165,000 15.8 21.0 Didnotfail18 121,900 20.0 26.9 Center

aEquivalenttomaximumstressesfromstrain-gagedataobtainedontwo~pecimenscalibratedoverthemaximumtest–ladrange.Meanstressrangedfrom12.5to 13.0ksi.

bMeanstressrtigedfromabout17.4to=.8 ksi.

+-G--4

TAELEVI

MECHANICAL PROPERTIES OF M4TERIALS USED IN I-13EAJSa

Tensile Yield strength Elongation Modulue OfMaterial strength, (0.2 percent offset), in2 in., elasticity,

ksi kai percent psi

0.0~2-inch 202k-~ 72.5 52.7 17.9 10.8x 106almimm-alloy sheet(sheet 1)

0.0T2-inch 202h-T3 72.8 55.7 18.4 lQ.7aluminum-alloysheet(sheet 2)

2024-T4 alminm-alloy 65.7 47.9 15.6 10.4extruded angle

aA_e stre@h VF&.ES forfOUZ Spechens.

32 NACATN4137

SUMMARYOFI-BEAMFATIGUEFAILUREDATA

Failing Locationof FatigueSpecimenmember failurelife, Remarks

(a) cycles

1 Chord Betweenrivets 86,330Failureassociatedlamd2 withmetallographic

flawon surface1-1 2 chords Rivet3 137,&lo Catastrophicfailure2 2 chords Rivet3 75,3502-1 1 chord Rivet3 1,915,480Failuresassociated

1 web withsamerivethole

%ee figureI-8.

t

,

TAELE VIII

STRESSES IN I-J3EAM3

Specimen

11-122-1

Bending nlomentFatigue

Measured chordPa, 1,000 in-lb

life,0tresi3,ksl

~“c’e” LMaximum Mean (a) Maximum

I I 1253 133 E%,330 23.0249 U8 137,m l~.o256 135 75,330 15.8176 IJ8 1,915,483 E!.o

Mean

11,g;.;

8:0

Eased on gross

I

Based on netarea area I

Maximunl Mem M9xhlluln Meaq

26.6 lk.o ---- ---17.0 17.217.3 ;:; 17.8 ::?12. o 8.1 12.2 8.2

%ee table VII and figure 18 for location of failure.

bCalculatlonsbased on momnt of inertj.aat cross section associated with failure.

UNu

34 NACA‘m 4137d

TABLEIx

RESULTSOFFATIGUETESTSONSIMLJLATIONCOUPONS,TYPED,FORI-BEAM

Computedstresse,s, LoadingetressesSpecimen tiomstraingages,Lifetime

ksi ksi to failure

123C4

z

C7

11.5f 8.48.4& 8.38.3,&6,4

13.0 * 6.4

9.9* 8.310.9* 6.89,3& 7.1708f 6.87.3& 5.16.o ~ 4.5

468,000628,000738,000136,000

3,222,0002,507,0001,235,000

.

r

.

aCo utedstressesatrivetcenterlinewereobtainedfroms=; F

P+ ~, where P iseithermeanoralternatingloadand M = ~;

u

2 i:use’dontheassumptionthatthefirstfiverivetsofthegroup‘6ofsixrivetstakealtogether5/6P. Inthisexpressione and yrepresentdistancebetweencenterlineof chordandrivetrow.

bSeetextformethodofextrapolation.cIndication,fromothergages,ofunusualgradient.

1 r

I I4++++++++II I, +++9 ++++

P --’”’~””+

1‘+3= N% 21dril

Irt, $+Zrivet

,4 & u+,+,++ -b- * -

Figure l.- Schemtic drawing of box-beam specimen. For

A-A

section A-A: top skin, O.~-incheheet; bottm skin, O.C@-inch sheet; webs, O.Vjl-inch sheet; chord &les, -O.~ x 0.75 x

O.091-inch extrusion;stiffeners,1 x ~ - inch b~ck; moment of inertia (based on net area),

7.75 inch4; and moment of inertia (based on gross area), 8.~ inch4.

36 NACATN 4137

I,

L-77-3623

Figure2.-Testsetupforstaticandfatiguetestingofbox-beamspecimen.

8

●

—,

.t

f.

#

s’

----+-- “ ~ge ,8Gage 33

3E

Gage 34Goge3 ~’ Goge 7

— Goge4=, Gage 12

Gage 36

%

Gage23

‘-Goqe 28

Liz23 3:2840 36 32 26

\ Centerline of beam

o35

I I I20 16 12 8 4

Tenskm

+

All gages”wera SR- 4 ‘Nos 1-12, AR-2, ~ -inch length

Nos. 13-3< A-3, H -inch length

Nos 33-76, A-7, ~- inchlength —

Nos.79, 80, A-3,% - rnchImqth

NOS.W, 91, A-7,*- inti len9th

I4812 16 20 24 26 32364

Compmssirn

—

—

—

—

—

—

.

—

I

Stress, ksi

Uw

Figure 4.- 8tress distribution on sectionD-D for 90,000 tich-pomd bending mom?nt. For strain- ~gage ~cations see section-D-D in figure 8. w+

. ●

. t

❑

✎

1

d-x

z Gage 13= I‘Gage 18 _

,Gage 23 —

= I~

--’---.1Gage 29

Strain-gage Iocatians

I I I68101214

c

/

,

I I I I I22 24 26 28 30 32 34 36 30 40 42

Stress,ksi

Figure ~.- S%rest3variation of skin of section D-D with applied mulent. For fitraln-gagelgca.tions see section D-D in figure 8.

40 NACATN413’7

4

4

4

4

4

3

3

3

3

3

2

I

I

I

I

I

a-

,6—Goge91

4

2 —

o

8—

6

4 —

2

0—

8 Gage 901(longitudinalstress~

o

6“

4

2 —

o~

8—

6

4 “

2

0—

8 J

6 —

4

2 —

o0 18 36

BendinYMfiment,7;O00inch~%mds106 I26 1’

Figure6.-Stressvariationofbox-beamweb(betweenstiffenerrivets)

.

..-— withvariationinbendingmoment.

, # * ‘

Figure 7.-Resultsofbendingfatiguetestsonbox-beamweb8ectionat12.~-ksimeanstress.

4=ril

0 0 (q o,,~O’+-.Q. . .I

000 +0 o 00 Iw w w w w w w

HK J.

78 6

Figure 8.- Box-beam specimen, midspan-rivetpattern. Ihiberfbox beam.

‘4 \9

indicate locations of failure in’

,

I I

NACATN 4137 43*

.

L-57-3625

Figure9.- Fracturedsurfaceat fatiguenucleiofbox-beam2.

—- -,,.,,--—. -.,. -,=~—.=_- :..-

.-; _3’ y~”’”-:mfj)””~

=.-.. ~. __~----

.- “>>= __”__ =s!—s-—..——

. .

L-57-3626Figure10.- Fatiguecrackinbox-beam.6-1.

0.19i-inch

\

diam

A-

Figure U_.- Detailed drawing

sheet; chord angle, 0.75

.-

.—

* lll--J

of the first shmilation element. For section A-A:

x 0.75 x O.091-tich extrusion;and rivets, ~ - inch

m ●

I ,;,1 ‘.!,

T3“

I

I

web, O.Ojl-inch

diameter.

. *

,11,:,

* , .,

G 1 1 1 I I I I I I \ I I 1 IZ I

$ Gage 2/~Gage I

,~4 & ~s ~7

Fatigue Life, cycles

Figure 12. - Results of axial-load fatigue tests on the first simtitirm element for bax beam.Mean stress,12.5 ksi.

~. 0.191-inch diem.

‘12-inch rad

I5“ +

It II Iii

4

Figure 15.- Detailed dxawing of second simulati~ element. Web, 0.051-inch

1 x ~- ~ch ~~i~; ~d ri~ets, _?_-inch ~~ter.—-28 16

.

I

stiffeners,

t .

47

36

32

26

.20

16

x

y ‘f’ ox,

x

w

// /

/ “x

/

/x

/

//

/

x

o SecondsimulationelementA

0’x Box beam

‘/

/

o I 2 3 4 5 6 7 8TransverseStress, ksi

Figure14.- Compsrisonof longitudinal-stress-transverse-stress reu.tionstip of second simulation element and box beam.

~4 ,.510’

~?

Fatigw Life, cycles

Figure 15.- Restits of sdal-lead fatigue tests on second simulation element for box bean.

,,.h-ddl-l4=03

. , . .

. Pm’

, ,

c+ sy mB + 4“~“

4

k Syln

Figure 16. - Schermtic

;4J ~A’c+

drawing of I-beam specimen.

I

-+

2Section A-A

Figure 17. - Eeam sections of speci.mn shown in

and Igg “

41.55inchesL;r~ secti~B-B,

I --

—

—

4

Section B-B

. , b

I

figure 16. Fm sectionAA, 1= . 40.88 inches4

In = 57-8 ~C~S4 ad Iu = 58.7 inches4.

1! I

*

,:

.

* , , ,

1 I I 1 1

@d’‘, e+ -—-——-----Center

Stiffener

3XR!R_--,----

4...-—_.L ----3-q&a

HD-@@-Q-_—_____ ____

Figure 18. - I-beam specimen,midspan-rivet

,

I I I

‘“9’57[’we”i ~ Goge 86

Goge4~ l— Goge 3

I-— Gage 20

1 1

50

r& Gage 18

l— Goge 16

Goge 2 —1 * Gage IJ ~Goge72

Goga 371 ~ G$%%5%0

‘Centerline of beom

All goges were SR-4

Nos. 1-12, AR- 1! ~-inch length

Nos. 13-55, A- 3, ~inch length

Nos. 56-87, A- 7, ~inch length37

36

I I I I I I I I40 36 32 20 24 201612 B40 -4-8 -12 +6 -20 -24 -Ze -32 -36 -40

Tension Stress, ksi Compression—

Figure 19. - Stress di@ribution on cross section at center of midspan of I-beem for270,000 inch-poundbending mcment.

, T 4 ,

,, ,,

NACATN 4137 !33.

.

.

.

\ \ -—-. x-- 2nd sideof first beam\\

\\\ –-~ Ist side of secondbeam

&\ ~ 2nd side of secondbeam

b \\+

\\

\\

\

\I

I u uo 4 8 12 16 - 20Tensile Stress, ksi

.

.

Figure20. - Tensile-stressdistribtiionat crosssectionthroughfirstrivetin shearplateof I-beamforappliedbendingmomentof240,0CQinch-pounds.

—,. .

54 NACATN4137*

.

—-.

shear p104‘--py5

,~*b -’- —,.

.’

...= .....L_. _.. .—. ...=.._ . .. . . ...= . . . . . . . . . ..—=

: – .7- .-=

.>: . . .. ..- ---- -—

. . +, _._. _&. _ -a F_y .1<: .. J--- --

_—_. . . ..._, -..

L-57-3627

Figure21.- FatiguefailureinsecondI-beam.

.

B!4~

12+

.-

2 10.

:

=

93

mw~

66

2g

E

:4

2

0104 IOs K+’ 10’ A-199eo

Fatigue Llfe,cycles

Figure 22.- Results of bending fatigue tests on I-beam chord section at 8-ksi measured meanstress. N

56 NACATN4137

I.I I

.I I

-I I

-I

-I I I 1 I

Iu u u u u u

I Thicknessofeachpiece=0.081w

II I 1 I

.1

nI I I 1 I1

n

I II I

I

u I Lu u I I IuI i

u u 1

I-10”

3“

I

Thicknessof eachpiece=(1081”

I I InII

It

n nI

nI I

nI I1

nI I

u u u u w ~~ J

TypeC

‘o”~ *,,,5,Figure23.- ElementsinpreliminarytestsforsimulationofI-beam.

[ +“ Types Aand Bb

L

Type A

.

II

, , . ,

Gages1,3 Gages5,7

Gages 1,2,5,6on front side

Goges %4,7,0 on reverse side

Figure 24.- I-beam element (type D) with location of eight strain gagesindicated.

U-1

12

.

G 10x$

a=~a

4n9~

3i6

G

z

Z4

2

010+ 105 10s 107

FutigueLife,cycles

Fi@re 25.- Results of fatigue tests on simulation elements for I-beam.

, . , . ,

1

-F=

G--J

Figure 26. - JRM.gua notch factors in beam tests.

Figure 27. - Fatiguenotch factors for simulationelements.

,’