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,
d
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
:
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
.——
.——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
10
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
—
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
—
bendingmoment.Tbro~houtthetest,.——
a numberofloadandstrainreadingsweretskento correctforloadchangesduringthetest.
—Crack-
detectionwiresalsowereusedto determineoccurrenceofthefirstcrack,thuspreventingcatastrophicfailure.ofthebeams.Whenthefirstcrackwasdetected,thetestwasconsideredcomplete.Thebeamthenwasturnedoverfora secondtest.
TwoI-beamsweretestedinfatigue.By usingthetechniquedescribedabove,foursidesofthebeamsweretestedandfourpointsontheS-N
.-
curvewereobtained.
TableVIIsummarizesthefatigue-testresults.Thetableindicateswhichmemberofthestructurefailedandthecracklocationby theuse *ofnumberedrivets.Thesenumberscorrelatewithnumberedrivetsinfigure18.
—
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
—
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
$pecimen
1
2
3
4
k-l
5
5-1
6
6-1
TABLB III
SUIMARYOF EOX-REAMFATIGUEFAILUREDATA
Data cm firstobservedfatiguecracks
Member
WebFlangeWebChordangle
WebCh6rdangleW&bChordangleWebCbrd angleWeb
WebChordangle
WebFlmge
aseefigore8.
crack
9
10
r +
I
Rivethole
~
2; 59
2; 5; 5; 52; 5; 5; 8
2; 5; 5; 75; 8
2; 5; 5; 85552
55
22
Fatiguelife,cyclee
289,00289,@193,T60193,[email protected]
36,67036,670265,3i?0265,3E!0624,700656,8&l
1,137,120
w>%
108,ooo
Final failm
Fatiguelife,cycle6
289,850
193,930
43,Ym
685,530
32,$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.
,’
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