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TECHNICAL NOTE 3782
HANDBOOKOFSTRUCTURALSTABILITY
PART II - BUCKLINGOFCOMPOSITEELEMENTS
ByHerbertBecker
NewYorkUniversity
I
I
1
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TECHLIBRARYKAFB,NM
Illllllllllllunl
ATIONALDVISORYOMWITEEFORAERONAUTICS
OUbLbqA
TECHNICALOTE3782
HMJDBOOKFSTRUCTURALTABILITY
PARTI - BWKH3VGFCOMPOS~HMINB3
ByHerbertecker
SWMARY
The
ocalbucklingfstiffenerectionsndthebucklingfplates
witheturdytiffenersxereviewed,ndtheresultsresummarzedin
chartsndtables.Numericalaluesofbuckl~ coefficientsrepresented
forlongitudinallyompressedtiffenerectionsfvarioushapes,or
Stiffea
stM?fened
primarily
discussed
platesloadednlongitudinalompressionndinshear,ndfor
cylhdersloadedntorsion.
lthoughhedatapresentedonsist
ofelastic-bucklingoefficients,heeffectsofplastici@re
fora fewspecialases.
RWRODUCTION
Thebucklingehaviorfsimplelateelementssdescribedn
partsI andIIIofthisHandbookfStructuraltabilityrefs.and
2).
Structuralomponentsftenconsistftwoormoresimplelate
elementsoarrangedhatthebucklingtressfeachisincreasedsa
resultfthesupportrovidedycontiguouseighbors.uchcomposite
elementsretermedtiffenersecauseheyarefrequentlysedtostiffen
a plateinordertoincreasehebuc~ingstress.A compacttiffenerS
.
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.
2
NACATN
3782
elasticestraintotheplate.
Itmayassistintheresistanceoload,
asdothespanwisetiffenersna wingcover,ritmaybehaverimarily
asa support,uchasa transverseib.lheitherase,itisnecessary
toconsidernlyitsaxial,ending,ndrotationalpringropertiesn
calculatinghebucklingtressfastiffenedlate.Bucklingfthe
compositeillthenoccureitherocallyntheplateorgenerally,
involvingoththeplatesndstiffener.
heinformationnbucklingf
stiffenedlatesappearsnthesectionntitledBucklingfStiffened
PlatesnderImgitudinal
ompressionoruniaxialoadandinthe
sectionntitledBucklingfStiffenedlatesnderShearIoadfor
shearload.
Thebucklingfstiffenedurvedlatesinvolveshecomplication
ofplatecurvaturenadditionoaXLthepsmmetersffectinguckling
ofstiffenedlatplates.
ThebucklingfUnsttifenedurvedlatesas
beendescribedreference,inwhichitwasshownthattheoryisin
goodagreementithtestdataforshearloadingndinpooragreement
withdataforaxialcompressionoading.Forcertainroportions,he
curvedlatespproachylinderehavior,hichpermitsvaluationf
theunstiffned-plateesultsnthelimitingase.Analysesfstiffened
curvedlatesrereportednthesectionntitledBucklingfStiffened
PlatesnderLongitudinalompressionoraxialloadsandinthesection
entitledBucMingfStiffenedlatesHer ShearLoadforshearloads.
Znaddition,helimitingaseoftorsionalucklingfa stiffened
cylindersdescribednthelattersection.
Theresultsfthetheory
andtestdataarecomparediththeinformationnstiffenedurvedlates
undershear.
Thebucklingtressfa stiffenerra stiffenedlatemaybefound
fromthegeneralelationship
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ACAm
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figuresiscussed
theseparameters.
in thefollowingectionshow
kb asa functionf
Theeffectsfmaterialropertiesnthebucklingfsimplelements
werecovered ref=ence1,inwhichstress-strainurves,oissons
ratio,ndcladdingndplasticity-reductionactorsrepresentednd
discussed.lasticity-reductionactorsorcurvedlatesndshellsre
describednreference.
Forconvenience,summaryfpertinentnfor-
mationppearsntheApplicationectionndtables to3.
Thissurveyasconducted%NewYorkWversityunderthesponsor-
shipandwiththefinancialssistanceftheNationaldvisoryommittee
for-Aeronautics.
A
a
b
D
d
SYMlms
areaofst~enercrosssection,
.
,
Sqim
len~ ofunloadeddgeonlongitudinallyompressedlates
ands~le elementsrlongerideofplatesloadedn
shear,in.
lengthfloadeddgeonlongitudinallyompressedlatesand
simplelementsr
in.
flexuraligidityf
in-lb
shorterideofplatesloadednshear,l
.
plateperinchofwidth,E+2(. -,3],
widthofbulbofbulbflange
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NACATN3782
bentlngomentofinertiafstiffenerrosssection,n.
I
4
J torsionalomentofinertiafstiffenerrosssection,n.
k
buclsUngoefficient
kb
generalucklingoefficientfstiffenerertainingo
bucklingtressfelementfwidthb
%J%
bucklhgcoefficientsorcompressionndshear,espectively
length
ofcylinder,n.
momentappliedoedgesofrotationallyestrainedlement,n-lb
numberoflongitudinaltiffenersnplateoftotalwidthnb~
ornumberofcircumferentialtigsoncylinderflengthL
numberoftransverseucklesnlongitudinallytiffenedlate
longitudinal
ycompressed
.
radiusfcurvaturefcurvedlate,in.
correctionorpresencefstiffenernonesideofplate
platestiffnessseefig.2 forcliffrenttypes
thickness,n.
platecurvaturearameter,
(b21+ - e2)12
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NACATN
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5
Ve
Poissonsatioinelasticange
cr
generalucklingtress;lso,bucklingtressfcompressed
element,si
cr
bucklingtressfelementoadednshear,si
Subscripts:
cr
buckling
e effective
f
flange
L lip
T
topwebofhat-sectiontiffmers
v
web
IOCAL13UCKLINGOFKOWEMIMGELEMENTS
Behavioroftiffeners
Whena plateunderlongitudinaloadissupportedya stiffenern
thedtiectionftheload,thestiffenerarticipatesiresist~this
load.Asa result,hepossibleucklingodesofthiscompositere
localinstabilityftheplatealone,ocalbucklingfoneormoresimple
elementsfthestiffener,eneraltabili& oftheplateinvolving
columnctionfthestiffener,rsomecombinationfthesemodes.The
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NACATN3782
thencomputinghebucKlingtressftheelementonsideredsa simple
plateunderlongitudinaloadwiththeappropriateoundaryonditions.
Iugeneral,owever,hereismutualestraintta longitudinal
jointamongallthememberseetinglongsucha line.Ifthisrestraint
couldbeconvertedirectlyntoa valueofrotationalestraint for
thesimplelementeinganalyzed,henthebuckling-coefficientharts
ofreferencesand2 couldbeusedtofindthebucliMngtressfthe
simplelement,nd,[email protected],heucldingtressfthestiffener.
Becauseftherotationalnteractionmongthesimplelementsteach
jotitline,whicharisesromthepreservationfthecornerngles
betweenlement
airs (el= t12= . . . = en),
howev=,therestraint
imposedyeachupontheothersannotefoundimmediately.tisnec-
essaryoanalyzeheproblemsoneinthedistributionf
momentamong
themembersfa staticallyndeterminateyst=. Whenthishasbeen
d~e,
e canbefoundand Ucr
canbecalculated.
librhemostpart,thestiffnessfoneelement itsownplaneis
sufficientoimpartupportoitsadjacentlementserpendicularo
theirplanes,lthoughhecornernglesqycliffrfromX. Mostsimple
elementsfa stiffenerehaventhismanner.Ups andbulbsmaybetoo
weaktoprovideompleteransverseupportoanelementinvariably
flange).
Theyactascolumnshattendtoresistelasticallyhetrans-
versedeflectionsftheotherwisereeedgesoffI.angesnd,consequently,.
cannoteticludedntheusualmethodsfanalystsftheinteraction
bucklingroblem.
However,flangeitha lip
or
bulbalongitsfree
edgemsytieanalyzedsa stiffenedlatetodetermineherigidityf
thiscomposite,hichthencanbeusedh theinteractionnalysis.
CalculationfBucklingtress
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NACAm 3782
7
,,
to
M/e.hce
e isthesameforallsimplelementstthejoint
line,stiffhesssproportionalothemomentcarriedyeachelement.
However,incethesemomentsustvanishtbucld.ingorsmalldeflec-
tionsoftheelements,hejoint-stiffnessriterionollows.
Themoment-distributionnalysisssimplifiedtheuseofchsz%s
ofelementtiffnessndcarry-overactorrepazedyKrollfordifferent
typesofboundaryonditionslongtheunloadeddges(ref.6). Theseare
describednthefollowi.ngectionqnumericalaluesofbucklingtress.
lhessence,hestep-~-steprocedureorcalculatinghebuclCling
stressfa simplelementnvolveshearbitraryelectionfa buckling
stressogetherithseveralrbitraryaluesofbuckleavela@h. llbr
eachofthesevalues,Ucr iscalculatedromequation1)untilits
minimumalueisfound.
Ifthisisdifferentromtheinitiallyssumed
bucklingtress,heprocesssrepeatedntiltheassumedndcalculated
values~ee. Thisisthebucklingtressfthecompositelement.
Chartsf ~ (X/b,) areused(aspresentednref.1)together
withtherigidityablesf~ol.1(ref.).
Thebucklingtressfa flangeitha liporbulbwasinvestigated
byHuandMcCullochref.7),Gbodmannd130ydref.8),andGoodman
(ref.9)whoconsideredlargerangeoflip,bulb,andflsngeropor-
tions
Gerardimplifiedheanalysisyselectinghegeometriessually
encounteredndesignnddefinedherangeofsectionroportionsn
whichtheelementndergoeshetransitionroma flangeoa webasthe
rigidityftheedgestiffenerncreasesref.0).
RoyandSchuetteavedemonstratedxperimentallyhatthelocal
bucklingtressfthesectionsunaffectedlthoughhesingleetween
adjacentlementssassmallas30oraslargeas120(ref.11).The
principalffectfchanginghecornernglefrcmW istodecrasethe
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N/MAN3782
stratisshownasa functionftheflangeb/t andtheedge-stiffener
proportions,hichpermiteterndnationftherigidityfsucha com-
positeforuseintheindetermhacynalysis.nthismanner,hese
chartserveasanadjunctoKrollsables.
Bucklingoefficientsrepresentedorccmnnontiffenerhapes
suchasshowninfigure,inwhichthedimensionsfwebsandflanges
areshownforbothformedndextrudedhapes.
Thebuckliug-coefficient
chartsorchannel,-,W, andrectanguhr
tubestiffenersppearn
figure.
TheyweretakenfromthereportfI&oll,Fisher,ndHeimerl
(ref.5). Thedashedinesonthesechartseftiethesectionropor-
tionsatwhichbothwebandfkngebucklesimultaneously.ataforhat-
sectiontiffenersppearnfigure.
Thecurves,daptedromthose
ofVanDerMaas(ref.2),covera rangeofflsngeizesforcliffrent
widthsofcenterndlateralebsofthehatsection.Itshouldenoted
thathatandlipped-andchaunelectionsrestructurallyquivalent.
EffectsfPlasticity
Theinelastic-bucklingtressfa stiffeneraybecomputedyamethodsuchasthemoment-distributionrocedurefLundqyist,towell,
andSchuetteorelastic-buclWngroblemsref.). Thiswasdoneby
StowellndPride(ref.u), whoobtainedoalagreementithexperi-
mentaldata(fig.7),forH-sectiontiffners.
Theplasticity-reduction
factororeachsimplelementfthesectionasemployedncomputing
thebucklingtressoruseinthemoment-distributionrocedure,n
whichthejoint-stiffnessriterionontrolshetheoreticaluckling
stressfthesection.
Itshouldenotedthatthetestdataatthelargertrainsie
about5 percentelowthestress-strainurve,hilethetheoryand
is3 percentelowatthemost.
Thisanalysise- totidicatehat
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NACATN
3782
included.
hisisofsignificanceince
thechartsertainostiffenersithno
9
thedesigndatapresentedn
torsionaligidi~.
A descriptionfthebucklingehaviorfa supportedndrestrained
rectangularlatemaybefoundinreferenceforflatplatesandinref-
erence forcurvedlates.
Thestiffningelements,ose localbuclCling
behaviorasdepictednthepreced~ sectionfthisr@port,rovide
thesesupportsndrestraintsotheplatestintermediateositionsn
theplatespans.
Theeffectivenessfthesesupportsependsponthe
axial,ending,ndtorsionaligiditiesftheplateandstiffeners.
Representativerrangementsfplate-stiffenerombhationsreshownti
figure.
EehaviorfStiffenedlateser IOngitudhalompression
Thetwotestabilityodestobeconsiderednthissectionrelocal
bucklingftheplatebetweentiffenersndgeneralnstabi~tyfthe
compositelement.
timostcasesthetorsionaligidi~ofthestiffer
isassumedobenegligiblymall.,husexcludingotationalestraintf
theplatealongthestiffnerline.
Thebehaviorfa platebucklingnderlongitudinaloadandsupported
bydeflectionalndrotationalpringssshownschematicallynfigure9.
Waveformsforthethreelimitingasesofperfectlylexiblendperfectly
rigidspringsreshown.
b general,hewaveformsforfinitespring
rigiditiesonotchangehapesignificantly,lthoughheamplitudesf
thewavesmayvary.
Whenthestiffnerrigidityssufficientoenforce
a node,theplatewillreceiveoadditional1
exuralsupportromthe
stiffner.
Thisdescriptionarallelshatforcolumnshichwaspresented
byBudiansky,eide,ndWeinbergerref.14).
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10
NumericalaluesfBucklingtress
NACATN
3782
Thenumericalaluesofbucklingtressorstiffenedlatplates
andcurvedlatesnderlongitudinalompressionreasfollows:
Stiffenedlatplates-
SeideandSteincalculatedhebucklingoef-
ficientsorlongitudinallyoadedsimplyupportedlatplatesithone,
two,three,ndaninfinitemberoflongitudinalttifenersref.5).
Theresultsppearh figure0inwhich~ isshownasa functionf
a/b fora rangeofvaluesf EI/bD.
A summaryfcoefficientsor
infinitelyongplatesispresentednfigure1forconveniencendeter-
miningbuc~ingstressesorlongstiffenedlates.
ThecalculationsfSeideandSteinwerebasedupontheassumption
thatthestiffener-sectionentroidaslocatedtthemidsurfaeefthe
plate.
Thisisnotusuallyhecaseinactualractice,nwhichthe
sttifmeriscommonlyocatednonesideoftheplate.Thisproblem
wasinvestigatedngeneralerms~ ~wallaandNovak(ref.16). Seide
alsoevaluatedhiseffect(ref.17)andevolvedcorrectionorthe
chartsffigure0applicableoplatesitione,two,orinfinitely
q stiffeners
@J-/ ~ e~~
I
~2I
r = (EI/bD)
1 + (Zm bq
3)
fromwhichtheeffectiveendingigidi~ratio (EI/bD)eaybeobtained.
Thefunction&q =
f(X/b,,q) tifigure2,inwhichA/b (Mb = a/qb,
whereq = 1,2,and
3) must
matchthevalueusedtoenterfigure0. A
trial-and-error~roachmightberequiredince(EI/bD)e occurat
a differentalueof q infigure0thandoesEI/bDatthe a/b origi-
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NACAm 3782
11
. .
Stiffenedurvedlates-Theinformationorstiffnedcurvedlates
relatesothatobtainedromsectionsfcircularyltiers.%tdorfand
Schildcroutnvestigatedhecompressiveucklingfa simplyupported
curvedlatewitha centralticumferentialtiffeneraxdngotorsional
rigidityraxialstiffnessref.21). b additionodetermininghethe-
oreticalucklingtress,hichwasdoneusingltiearheory,hepercent-
ageincreasenbuclil.ingtressverthetheoreticalaluewasobtained
andisshowninfigure5.
Becausefthelowqerimentalvaluesof
bucklingtressomparediththeresultsfthelinearheory, atdorf
andSchildcroutecommended@@ng thetheoreticalercentagencrease
totheqerimentalbucklingtress,aluesfwhichmaybefoundinref-
erence. Themaximumossiblencreaseora curvedlatewitha given
valueof a/b and Zb isshowninfigure5(a),hileanincreaseess
thanthemaximumsobtainableromfigure5(b).Furthermore,hevalue
of EI/bDrequiredocausea buckleodeatthestiffenerineisobtain-
ablefromthesefigures cross-plotting.
Notethatnogainisindicatelhen a/b>0.7 orwhen ~ is
greaterhanthevaluesshowninthetablebelow.
9
a/b
0.600 0.500 0.417
0.333
0.250
0.167
28.o
14.0
7.8
4.1 1.9
0.7
4
Ihehartsffigure5weredesignedopermitanestimatefthe
increasenbucklingtressobeexpectednanaxiallyompressedurved
platewhenthecentralircumferentialtiffeneraslessbendhgrigidity
thanthatreq~ed toenforcenodealongthestiffenerine.Whenthe
stiffenerasthisminimumigidity,helengthftheoriginallatemay
beconsideredobehalved,ndthedatainreferenceshouldeusedto
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12
Whenthecurvedlatewidthexceedshelength,se
cylinders.sethecurved-plateucklingataonly
exceedshewidth.
EffectsfPlasticity
NACATN3782
thecurvesor
whenthelength
Plastici@-reductionactorsorstiffenedanelsdependponthe
factorsertinentoeachelementfthecomposite.orexmqle,the
factororsupportedlatesouldbe~ected toapplytotheplateele-
mentsbetweentiffeners,hereasturdytiffnersbehavingscolumns
shouldollowhetsngentodulus.Iftheseconditionsoldinthecom-
posite,heelastic-qepsrameterI/bDkuld becomelZ /qbDinthe
inelasticange.
Gallaherndl?Qu@anomparedestdataonZ-stiffenedanelssubject
tolocalbucklingithbucklingtressesomputedsingthesecantodulus
astheplastic~-reductionactorndobtainedheagreementhowniu
figure7 (ref.19).
Someofthedatapertainoplatesithsturdy
stiffeners.owever,largeportionppliesocompositesnwhichthe
stiffenersuckledocally.
EffectofTorsionaligidityfStiffen=
Thebuckl~-coefficienthartsiscussedntheprecedingaragraphs
werepreparedorstiffenersithnotorsionaligidi~.Actuallyll
stiffenersavesometorsionaligidity,ndclosedstiffeners,fwhich
thehatsectionstypical,ayfuuctionsfullyrigidstiffenersn
torsionorscmeapplicatims.nreferencea chartbasedupontest
datawaspresentedepictingheeffectnbucklingtresssthetor-
sionaligidityhangeselativeotherigidityftheplatebeing
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NACATIV
3782
u
.
Thisissubstantiatedyfigure8,whichshowslittleainover
simpleupporthentheplaterigidityshigh(lowvaluesf b/t).
BUCKLINGFSTIFFENED
IATESmm smmLOAD
BehaviorfStiffenedlatesnderShear
Whentransversetiffnersareattachedoa plateloadednshear,
theymayberigidenoughoenforceodesattheattachmentinesorthey
maybesoweakastoexertvirtuallyoinfluencentheplatebuckle
pattern.
TheextremeaseofweakstiffenersasexaminedySchmieden
(ref.3),Seydel(ref.24),andWang(ref.25)whilerigidstiffeners
wereexsminedyThoshenko(ref.
26).
.
Theintermediateigidi@rangewasanalyzedyCrateandIawho
demonstratedhemmnerinwhichtheshearbucklingtressfaninfin-
itelylongflatplateisincreasedongitudinallysstiffenerigidi~
risesuntilitissufficientoenforceodesalongtheattachmentines
(ref.27).
Duringthisprocesshebuckleatternfthepl-.tehanges
fromthewaveformforanunstiffenedlateofinfiniteengthndof
width(n+ l)b tothatofa platewidthb. Testdataobtainedy
CrateandLofollowhetheoreticalrendof ~ asa functionf
E1/bD
Thescatterslargewithmostofthedatalyingbetweenhecurvesor
simpleupportndclampeddges,sshowninfigure9(a).
SteinandFYalichnalyzeducklingflongflatplatesithtrans-
versestiffnerssubjectedoshearload.ref..
8).
Thebehaviors
analogousothatofa longitudinallyompressedlatewithtransverse
stiffn=s. tifigure9(b)testdataareshowntoagreewiththethqq
ofSteinandl?ralich.
.
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A largerangeofvaluesf
-e ofvaluesf EI/bD.
theresultshowninfigure
optimistic
The
20,
NACATN3782
wascoveredora correspondingarge
theoryascompsxedithtestdatawith
in whichthe
CalculationfBucklhg
Thebuckl@ stresssexpressednthe
&eoryisseentobesliglrbly
Stress
formofequation1)inwhich
thebucklingoefficients isa functionfgeometryndloading.s -
h thecaseoflongitudinaload,thebasicparametersorflatplates
are a/b,A/bt,and EI/bD,hileZb isanadditimalarameteror
CUPRd pkteS d ZL 13~lieStO CyliIlderS
h the theoreticalnvesti-
gationshestiffenersereassumedopossessotorsionaligidity,nd
thecentroidsieressumedolieh themidsurfaceftheplate.
NmericalValuesfBucklingtress
Thenumericalaluesfbucklingtressorstfifnedflatand
curvedlatesndcylindersntorsionndershearloadssxeasfollows:
Stiffenedlatplates.ThetheoryfCrateandb forlongflat
platesoaded shearandstiffenedongitudinallyref.27)ispresented
infigure9(a),nwhichks isplottedsa functionf EI/bDfor
bothclampedndsimplyupportedlatesithcmeortwostiffeners.he
resultsfStetiandIYalichref.
28)
fortransverselytiffenedlat
platesppear figure1. Fromthislatterigureitmaybeseenthat
theminimumalueof EI/bDremind toaforcea nodeatthestiffener-
attachmentineincreasesapi~ @th a/b.Approxtitealuesre
inthetablebelow.
shown
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.
NACATN3782
Thecurvesreplottedorseveralaluesf
Zb .- a/b
and2 (where,orthiscase,
a and b aretheoveralllate
Sions.
Inaddition,helimitingurvesfinfinitea/b for
15
= 1,1.5,
aimlen-
long
platesndthecyl~er curvefor-widelatesreinclud-ed.hela~ter
maybecheckedgainsthecurvesorcylindersobediscussednthe
followingaragmphandpresentednfigure3.
Stiffenedylindersntorsion-Stiffenedylinders torsion
representlimitingase.fstiffenedideplatesinshear.
Stein,
Sanders,ndCratecalculatedhebucklingtresssa functionfthe
cylinderndstiffnerparametersr&.30). l?heurvesppearnfig-
ure23,inwhichks isshownasa fuuctionf
EI/bDfora largerange
ofvaluesf ~ andforone,two,three,ndfourhxtemmxliateings.
Thecurvesertainingoonerhg msybeseentoagreewiththecylinder
curvesffigure2(d)forwideplatesitha centralticumferential
stiffner
Theseresultsereobtainedorstiffenersithnotorsionaligidity,
withthesectionentroidnthemidsurfacefthecylinderQ1.
EffectsfPlasticity
Theplasticity-reductionactorsorstiffenedlatesndershearmay
befoundinreferencesand2 forflatandcurvedlatesithspecific
boundaryonditions
Thisinformationhouldpplytoplatesithstiff-
enersrigidenoughoenforceodesalongtheirattachmentines.Nodata
exist,owever,orplasticity-reductionfactorsorplatesstiffenedy
elem&tsofrigidi~lessthanthatrequiredora
AEPIJCATIONEZ KIDN
node.
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16
Plasticity-reduction
.
NACATN3782
factorsppearnthetablesheretheyareappli-
cable.Forfurthernformationnplasticity-reductionactorsnd
claddingeductionactorslso,seereferencesand2. l?brnformation
onfailurefstiffenerseerefer=ce3.
I?&ring-stiffenedylindersntorsion,
.
acr=&~~
For
for
for
thiscase,
~ dependspon ~ tisteadof~,
Itshouldenotedthata and b aretheoveralllatedimensions
stiffenedlatesndershear.
Thispermitsomparisoniththedata
ring-stiffnedcylindersntorsion.
Researchivision,ollegefEngineer-,
NewYorkUniversi@,
NewYork,N.Y.,April15,1955.
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mm m 3782
17
1.Gerard,eorge,ndBecker,qrbert:Handbookf Structuraltability.
PartI - BucklingfFlatPlates.
NACA~
3781,1957.
2.Gerard,eorge,ndBecker,erbert:
HandbookfStructuraltability.
~ III- BucklingfCurvedlatesndShells.
NACATM3783,195?.
3. Gerard,
George:
Hbook ofstructuraltability.artn - l?ailwe
ofPlatesndCompositelements.
ACATN3784,1937.
4.Lundquist,ugene.,Stowell,lbridge.,andSchuette,vanH.:
PrinciplesfMomentistributionppliedoStabilityfStructures
ComposedfBarsw plates.
NACAWl?L-326,1943.(Former~
NACA~ 3K06.
5.Kkoll,.D.,Fisher,ordon.,&d Hetierl,eorge.:
Chartsor
CalculationftheCriticaltressorIota.1stabil.i@fColmns
withI-,Z-,Channel,ndRectangular-Tubeection.NACAWRL-429,
1943.(FormerlyACAARR3KD4.
6. fiO~,
W.D.:
TablesfStiffnessadCarry-OveractorforFlat
RectangularlatesnderCompression.ACAWRL-3g8,1943.
(Formerly
NACAARR3H27.
7.
Hu,PaiC.,andMcCulloch,amesC.:
TheLocalBucklingtrengthf
Lipped-Columnsith9nallLipWidth.NACATN1335,15 +7.
8. Goodman,
tanley,ndR@, Evelyn:
InstabilityfOutstandinglanges
SimplyupportedtOne~ge andReinforcedyBulbsatOtherEdge.
NACATN1433,1947.
8/11/2019 02_1957beckerNACA-TN-3782 - Buckling of Composite Elements
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.
18
14.BuaisJls@,
Buckling
Springs.
NACATN3782
Bernard,eide,aul,andWeinberger,obert.: The
ofa ColumnnEquallypacedeflectionalndRotational
NACATN1519,lW.
15.Seide,aul,andStein,anuel:
CompressiveucklingfSimply
Supportedlatesithlongitudinaltiffners.NACATN1825,1 9.
16.Chwalla,E., andNovak,.: TheTheoryfOne-SidedebStiffeners.
R.T.P.Translationo.2501,I&itishinistryfAircraftroduction.
(FYomautechnic
SuQP1.ermbEUl, vol. 10,no.10,MSy7, 1557,
pp.73-76.
17.
Seide,aul:TheEffectfIOngitudinaltiffenersocatednOne
Sideofa PlateontheCompressiveucklingtressfthePlate-
Stiffenerombination.ACATN2873,1953.
18.hdiEUISky,Bermurd,
and Seide,aul:
Compressiveuckl@ ofSimply
SupportedlatesithTransversetiffeners.ACATN1557,1948.
19.Gallaher,George.,andI@u@an,RollsB.: A MethodofCalculating
theCompressivetrengthfZ-stiffenedanelshatDevelopocal
Instability.ACATN1482,1947.
20.Boughan,ollsB.,andBaab,George.: ChartsorCalculaticmfthe
CriticalompressivetressorIocalInstabilityfIdealizedeb-and
T-Stiffenedsnels.
NACAWRL-204,1944.
(FmmrlyNACAACRL4H29.
21.Batdorf,.B.,
andSchildcrout,urry:
Criticalxial-Compressive
Stressfa Curvedectangular%nelWitha Centralhordwise
Stiffner.
NACATN1661,1948.
22.Schildcrout,urry,and%ein,Manuel:
Criticalxial-Compressive
Stressfa CurvedectangularanelWitha Centralongitudinal
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NACATN3782
19
27.Crate,arold,ndIo,Hsu:Effectflongitudinaltiffenersnthe
BucklingoadofIongFlatPlatesnderShear.NACATN1589,19$8.
28.Stein,anuel,ndFYalich,obert.: CriticalhesrStressf
Infinitelyong,ShplySupportedlateWithTransversetiffeners.
NACATN
1851,1949.
29.Stein,
Manuel,ndYaeger,
RectangularanelWitha
30.Stein,anuel,anders,.
StressfRing-Stiffened
DavidJ.:
CriticalhearStressfa Curved
CentralW?fener.MACATN1972,1949.
well,Jr.,andCrate,arold:Critical
CylindersnTorsion.NACARep.989,1950.
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20
NACATN
3782
TABLE1
STIFFENERELEMENTSIN COMPRESSION
[See fig. I for breakdownof typicalsectionsntotheir componentlements]
Fig.
Section
Buckling
Plasticity-reducfion
coefficient factor
5(a)
12c w E;:;:J~]
t-i
bw
j(b)
kw
Nonereported
j(c)
D
bh
kh Nonereported
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NACATN3782
TABLE 2
STIFFENEDPLATESUNDERLONGITUDINALOMPRESSION
[
Seefig.8
for sketchesof plate-stiffener arrangements;
GJ=O]
Pfg.
Section
- Plasticity-mductIonactor
(a)
Endview
10 x
A A v
w
w
A
n=l,2,3,a)
Endview
WhenMfenersenforcenodes,
4(a) ~
Infinitelywide
Endview
~=(i)(a
4(b)
=
~+,[++
Infinitelywide
4(c)
Endview
T T
T
T
4(d)
Infinitelywide
Endview
Side Wew
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NACAN3782
TABLE 3
STIFFENED PLATES UNDER SHEAR
1
ee fig.8 for sketchesof plate-stiffener arrangements. GJ=O
1
Fig
Section
(a)
Plastlclty7eductIonactor
Endview
9 a)
n=l,2, co
Lomplatesnly
Endview
Sideiew
21 :;
iv ~
v
1A 6
Lowplates
nly
Endview Whentiffenersnforcenales,
:2 0)
nd
4
7 = /E) l~e2)/ i - V2~
2 b)
Endview
Sideview
:2(C)
and4
2(d)
. uw A
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23
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24
NACATN
3782
s
s
s
s
c+
M
M
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Y
NACATN3782
./c
T
4@ff
\
s
\
.
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26
./0
a
Ce
Do/
NACATN 3782
~
.
\\
Y\
.
\
1
I
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NACATN3782
27
r
b
L
1-
-J
r.+
.-
r
&f
bw
.
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28
71 I 1 (
k
w
WEB BUCKLESFIRST
y
/
/
.4
fZAME BUCKLESFIRST
5
4
\\\\ \ \ \ \ \ \ \
I
\
.Pf
[v
UNGE, bf
2
~
t
WEB,bw
9
.
,
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NACAN3782
7
6
5
4
w
3
2
/
7
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NACATN3782
kh
.
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1
i
I
I
I
6
5
4
k, 3
2
1
0
Figure 6.-
Eucklingstcessfor hat-sectionstiffeners.t =
%=%=%;
~21J t2
% =
. (E&a of ref. 12.)
U (1 - Veq bq?
u
4
1%
I
1
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32
NACATN3782
85
75
7G
C*,
ksi
65
6G
STRESS STRAIN
o
.
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5Y
NACATN3782
33
LON61WWN44L
STIFFENER
TRANSVERSE
ST/F~AfEk?
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34
NACATN
3782
EDGE
STIFFENER
El=
o
EDGE
GPO
I
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5
4
3
k.
2
/
\
2
-0
/
2
3
4
56
7
8
ob
(a)One stiffener.A/bt = O.
Figure10.-Ccmqressive-bucklingoefficientsfar shply sqpportedflet
plateswith lcmgitudinelEtiffenem
... .*Y. (Data
.
of ref. 15. )
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kc
4
%
3
\+
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5
4
3
kc
2
/
L,,l,l,ll
.
I
I
,
I
I
I
00 /
2
3 4
5 6 7
8
o/b
(c)n e
stiffener.
A/bt=
I
Figure10.- Chtinued.
0.4.
I
I
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5
4
3
kc
2
/
\
IIlllllil
Axb=a/b -- b+=wa
0
.
1
0 /
2 3 4 5 6 7 8
w
(24)
3
M 6tiffener6.
A/m =
FUwe 10.-Continued.
o.
, ,
.
s
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5
4
3
k=
2
/
o
.
ti
T
A
\
20
\G
/0
I
\l hl~
I
\
I
\
I
-
I J
,2
\
3
4
5
6
7
8
0
/
2
(e)
0/
Two
stiffeners.
A/bt=
Figure10.- Ccmtimed.
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5
4
3
k=
2
/
o
(
-T
\
2
11111111
/
2 3 4 5 6 7 4
(7A5
(f)Twu Stiffeners.
A/bt= 0.4.
Figure0.-Continued.
w
-1
al
n
,
,
,
*
J
5
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I
,.
I
{
i
5
4
3
kc
2
/
0(
\
i
/
2
k)
3 4 5 6 7 8
oh
Threestiffeners.
A/bt= O.
Figure10.- Continued.
I
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1
kc
5
4
3
2
/
q
11111111
/
z
3 4 5
u/b
(h)Threestiffeners.A/bt.0.2.
-10- -tfi~d
6
7
8
4=
Iv
>
,
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I
I
5
4
3
4
2
/
o
El
o
/
2
3
4
5
6
7 8.
Cvf b
(i)Three Stiffe?mra.A/bt.0.4.
[email protected] lfl. - Contintid.
. .
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5
4
3
4
2
I
/
o
0
I
l\ I
I I
/ 2
3
4
5 6 7
8
U/b
Mb
(J) I n f i n i t e nunberof stiffeners.
Fil 3m=10.- Continti.
A/bt = O.
. ,
*
,
,
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I
5
4
3
&
2
/
o
0
\.1
\ 75
111,,11~
/
2
3
(k)Ihflnite
4
OA
Mb
5 6
numberof stiffeners.A/bt = 0.2.
Figure10.- continued.
7
w
Is
g
I
I
I
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5
4
3
2
I _
o /
2 3 4 5 6 7 8
O bM
(2)IMtnite numberof stiffeners.A/bt -0.4.
Figme 10.- Concluded.
.
,
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5
4
3
k
2
/
o
./
/
/0=
/oa
.g
FigureIL- C cmpresslve-buckJ.lngoefficientsfor infinitelylong
shlp~
S~ flat plates
ithlcmgltudiw1 stM&ners. .
k E .&~
o
. (Date d ref. 15. )
m=K (1 -
ve2
b
a34
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4
3
/
zw
2
c
UA FAUZEDTURDYS77ffEWRS
+
\
/-
n=2 ,
n =l , q=f
I
n =2 , q4
r
fpw
Ilgure12. -
l/~q aa a functionof
J/b
stiffened
plate
proportions
(m/bD)e
pattern.
==
(EI/bD)
1+* A s=
crosssection.
(Dataof ref.17.j
stiffener
.
VI
-a
0)
N
Y
NACA
49
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.
.
4
m
75
50
50
NACATN
3782
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5C
-4
30
~
2C
51
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2(
k
/6
5
52
NACATN3782
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?
6
5
4
k,
3
2
/
.
.
.
.
53
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.
..
.
7
6
5
4
k=
3
2
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7
6
5
4
k=
3
2
.
.
NACATN3782
55
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.
.
7
6
5
4
k.
3
2
d
BUCKUN6OFSKIN
EWRAWEOYSTIFFENER
8UCKLIN6WWIFFEWW
RWRAINEOeYWW
bf bfb~
~
4
56
NACATN 3782
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7
6
5
4
k,
3
2
I
6
,t,
I
I
.
,
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1
I
I
i
I
I
0
./
.2
.3
.4
(~ti~)(~b)
(a)Maximumincrease.
(b)IiuxeaseXor
given
tiffbms.
Figure15.-
Increasein compressive-buckldngtressfor siqplysupportedcurvedplateswith a
centercircumferentialtiffener.
(Dataof ref.21.)
I
I
I
58
NACATN
3 7 8 2
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k.
6
I
5
A/bf=O
.
3
oo~
4 /2 /6
6
I
5
A/bt-+.4 _
4
~= 3 -
2
A/bt
=C12 _
. .
048
12 16
t
A/W
=0.6
.
.
NACATN
3782
59
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.
oo~
24 3?
6
5
A/bt=O.4
.
+
3
I
A/bt=O.2
\
08
I
1.
I
A/bf =0.6
\
60
NACATN3782
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6
5
4
kc 3
2
/
0
k.
I
i I I
)
/6 32 48 64
DxzIl
6
I
I
5
A/bt=O.4
4
1
3
A/bt=0.6
\
zg250
/
.
61
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6
5
4
kc 3
2
/
Ot
N
I
Zpfjo
f
ai
_
// //////zw/z/
=b
-
/ww///wzu
I
I
I
I I
I
~163?486480 W[
6
I
5
\
4
3
2
A
>
1
/6 32 48 64 80 96
I
I
_
Mbt=Q6
62
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50
40
30
G5
ksi
20
/0
MAXIMUM
STRESSSTRAIN
CURVE
STRESS STRAIN
.
.
.
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I
8
7
6
5
4
3
I
I
I
TORS1O)WL Y
UWG,EDGES CLA@A?5D
RIG/D S7iFi5ENEf?
LONG EWES SYMRY
wPmrED&-4.oo)
I
-o 50
ItLgure
8.-
/50
Effdctof torsionalrigidityof stiffener
ficiemk fm flatplateB. (Dataof ref.
A?50
on bua
1.)
coef
300
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m
m
40
If*30
m
/0
o
m
7MWY
I v
o
nmj
--------
/
/
n
~.p
n am
o
m, O/ws77FFEm -
0
CLAMR5Z
Em NY SU+0R7ED EDsm
(a) C1.aqedand shply
EI/bD
Slqpcrtedlates;
longitudinal
stiffeners.
m 1 9 .- Cmqparimn of theoryaud
bucklingcoefficientsf longflat
plates with
stiffeners.
.
testdatafor shear-
.
,
,
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/0
A
5
on
1.4
u
2 4
4 8
A
TH ORY
TEST
DATA
0/. =
L4, 2.4,4.8
0 0A
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-
. -
7
q.~=o ___
--T~
=s
* -
~=
-f
137
N~OFUAWS
o
Ch w n SEcm
ON M WOE
u Sro?lw
me
ON ONEW
Qkl
Mm-
. .
0 .1
I
10 1 0 =
10
10
E.I_/iiD
FigureZO.-
Comparisonof theoryend testdatafm dmply sqpported
circuhr cyMnd.ersstHfened by ringsand loadsdin torsion.
NACATN3782
67
.
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m
u
S/m r bYJPmR
48
KAn%s
4
G ED+-
00 4
8
e :1
6
so
m
E1/bD
(a) a/b= 1.
6
/
k, 4
.
m
J_z
b
-
-r
00
40
,11
80 L?o oma
E1/bD
(b) a/b=
2 .
.
.
68
NACA?CN
782
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.
NACATN3782
69
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t t s
[
-7
~
z~
200
/ Woo
CYUWER
/00
50
/
z M 100
20 CYLL4D
/0
I
30
-
/
30
20
L5
CYLJ E
10
30
: - -
I
/0
20
48
10
6
CYLINDER
70
NACATN 5782
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200
/m
60
30
20
/0
k,
40
R =
I
r
30
20
2
M
/0
m
3 0
i :
4 4
/
/0
20
45
/0
2
6
m
0 I
1
J
20
10
5 t--al
.
NACATN3782
n.
.
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I
300
b
z~
200
/ .~
CYLINDER
poo
100
60 f(~~
CYLINDER
100
40
20
/0
-1
N
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I
.I t
v
/v-
{U I
EV20
Figure 23. -
BuckMng coefficientsor t3implyupportedcticulercylinders
stiffenedby r*6 and loadedin torsion. Ta =
&- r
(Ik&a of ref.30.)
,