02_1957beckerNACA-TN-3782 - Buckling of Composite Elements

8/11/2019 02_1957beckerNACA-TN-3782 - Buckling of Composite Elements

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TECHNICAL NOTE 3782

HANDBOOKOFSTRUCTURALSTABILITY

PART II - BUCKLINGOFCOMPOSITEELEMENTS

ByHerbertBecker

NewYorkUniversity

I

I

1


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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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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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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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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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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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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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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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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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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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NumericalaluesfBucklingtress

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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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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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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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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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14

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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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.


19/73

.

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


20/73

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.


21/73

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


22/73

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


23/73

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


24/73

23


25/73

24

NACATN

3782

s

s

s

s

c+

M

M


26/73

Y

NACATN3782

./c

T

4@ff

\

s

\

.


27/73

26

./0

a

Ce

Do/

NACATN 3782

~

.

\\

Y\

.

\

1

I


28/73

NACATN3782

27

r

b

L

1-

-J

r.+

.-

r

&f

bw

.


29/73

28

71 I 1 (

k

w

WEB BUCKLESFIRST

y

/

/

.4

fZAME BUCKLESFIRST

5

4

\\\\ \ \ \ \ \ \ \

I

\

.Pf

[v

UNGE, bf

2

~

t

WEB,bw

9

.

,


30/73

NACAN3782

7

6

5

4

w

3

2

/

7


31/73

NACATN3782

kh

.


32/73

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


33/73

32

NACATN3782

85

75

7G

C*,

ksi

65

6G

STRESS STRAIN

o

.


34/73

5Y

NACATN3782

33

LON61WWN44L

STIFFENER

TRANSVERSE

ST/F~AfEk?


35/73

34

NACATN

3782

EDGE

STIFFENER

El=

o

EDGE

GPO

I


36/73

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. )


37/73

kc

4

%

3

\+


38/73

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


39/73

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


40/73

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.


41/73

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


42/73

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


43/73

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

>

,


44/73

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.

. .


45/73

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.

. ,

*

,

,


46/73

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


47/73

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.

.

,


48/73

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


49/73

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


50/73

.

.

4

m

75

50

50

NACATN

3782


51/73

5C

-4

30

~

2C

51


52/73

2(

k

/6

5

52

NACATN3782


53/73

?

6

5

4

k,

3

2

/

.

.

.

.

53


54/73

.

..

.

7

6

5

4

k=

3

2


55/73

7

6

5

4

k=

3

2

.

.

NACATN3782

55


56/73

.

.

7

6

5

4

k.

3

2

d

BUCKUN6OFSKIN

EWRAWEOYSTIFFENER

8UCKLIN6WWIFFEWW

RWRAINEOeYWW

bf bfb~

~

4

56

NACATN 3782


57/73

7

6

5

4

k,

3

2

I

6

,t,

I

I

.

,


58/73

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


59/73

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


60/73

.

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


61/73

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


62/73

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


63/73

50

40

30

G5

ksi

20

/0

MAXIMUM

STRESSSTRAIN

CURVE

STRESS STRAIN

.

.

.


64/73

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


65/73

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-

.

,

,


66/73

/0

A

5

on

1.4

u

2 4

4 8

A

TH ORY

TEST

DATA

0/. =

L4, 2.4,4.8

0 0A


67/73

-

. -

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

.


68/73

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


69/73

.

NACATN3782

69


70/73

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


71/73

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.

.


72/73

I

300

b

z~

200

/ .~

CYLINDER

poo

100

60 f(~~

CYLINDER

100

40

20

/0

-1

N


73/73

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.)

,

Documents

02_1957beckerNACA-TN-3782 - Buckling of Composite Elements