1、1,1+SiE7J1J.NATIONALADVISORYCOMMITTEEFORAERONAUTICSTECHNICALNOTENo. 1559 -.-BUCKLJNGSTRESSESOF CLAMPED RECTANGULARFIJIT PIATES IN SHEARBy BernardBudianskyandRobertW. ConnorLangley Memorial AeronauticalLaboratoryLangley Field, Va.Washington_ May 1948LIBRARYCOPY!. .-. . _n iAFR3LANGLEYRESEARCHCENTERHA
2、MPTON,VIRGINIA * ?J ACA LIBrtilRyProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-. - .ByNATIONALAJXL30RYCOMMITTEEFORAERONAUTICSTECHNICALNOTENO.1559BVXIJXGSTRESSESOFCLAMFEDRECTAI?WMRm PM- m smByBernemiBudiandqandRobertW.ConnorconsiderationSUMMARYofsnt
3、isymmtrical,a8wellassymmetrical,bucklingconfigurations,thetheoretical-shearbucklistresses-ofclampedrectangularflatplatesareevaluatedmorecorrectlythaninpreviouswork.Theresultsgiven,whichrepresenttheaverageofuppeandlower-llmitsolutionsobtainedbytheLagraqgienmultipliermethod,arewithin1 percentofthetrue
4、bucklingstresses.$ThetheoreticalbucklingINTRODUCTIONstressinshearofa clampedrectangularplatehasbeenfoundexactlyonlyforthecaseofaninfinitelylongplate(reference1);forplatesoffiniteaspectratio,approxlmtesolutionsofuncertainaocuracyharebeenpresentedbyseveralinvesti-gators. reference2,Coxgivesbuckling-tr
5、esscoefficientscomputedbytheRayleigh+litzenermethodforseveralaspectratios,butnodetailsofsolutionareincluded.Iguchi(reference3)”obtainsapproximateresultsbymeansofa seriesmthodthat,esSmithpointsoutinreference4,doesnotprovidedefiniteinformationastowhethertheresultsobtainedaretoohighortoolow. Smiththeno
6、btainsupperlimitstothetruehuckl.iwstressbyusiw IguchiSsdeflectionfunctionintheRayleim+itzmthod. Thenumericalresultspubldshedbytheseinvestigatorsdifferbyasmuchas10percentatsomevalues of,plateaspectratio.Furthermore,theseresultswereallapparentlybesedontheassumptionthat,foreachaspectratio,thecriticalst
7、resscorrespondstoabucklingpatternsymmetrical(ratherthanentisymmetrical)abouttheplatemidpoint. Thepresentpapergivestheoreticalbuckling+%resscoefficientscomputedfromananalysis(referenoe5) “bytheLagraanmultipliermthod. Bothupperandlowerlimitstothetruebucklingstresswerea71 calculated,sothatthemeximumemo
8、r inthefinalresultsisdefinitelylmown.Furthermxe,inthepresentpapertheassuqtionisnotmadethatthes,ymmtrioalbucklinupatterngoverns atallaspectratios.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-.2 NACATNNo.1359 .Inreference6 ft is shownthat,inshearbuc
9、klingofarectangularplatesimplysupportedattheedges,anS.ntisymmliricalbucklingpatternis .criticalatcertainaspectratios.Theantley.mmtricalpatternwasaccordi includedinthepresent.investigation,endtheresultsIndicatearae ofaspectratiosinwhichthelowestbucklingstressdoesoccurwitha configurationofantiswmetry.
10、SmaolsDTlengthofplatewidthofplateplateaspectratio(a/%)thicknessofplateYoungtsmdulusformaterlslPoissonsratioformaterialflexuralstiffnessofplate(JtMcriticalshearstresssr?DcriticalshearstresscoefficientintheformulaT =kab2tRESULTSANDDISCUSSIONThecritfcslshearstressforarectangularflatplatewithclampxledge
11、sisgivenbytheequationi%T.k$b2tThesolidcurveinfigure1givesthevaluesoftheshearstresscoefficientks forvaluesofaspectratioB from1 to3. Asshownin figure 1, thesolidcurveconsistsofpartsoftwodistinctcurves,oneofwhichcora?espondstosymmetricalbuckl!ng,theothertosntl-symmtricalbuckling,about-theplatemidpoin-T
12、hegoverning.9Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-. .,- . , -NACATNNo.1559 3.configurationatsnyaspectratio,givenbythesolidline,isthatwhicheldsthelowerbucklingstress.Thevaluesof ks plottedinfigure1representtheaverageofuppeandlowen+lmitsolut
13、ionsobtainedfromtheanalysisofreference5. (See table1.) Innmstcases,theloweu+imitresultswereobtsinedfromeleventh-orderstabilitydeterminants,andtheupper-limitresultsfromninth+nderdeterminants.(Seereference5.) Theevaluationofmny termsinthedeterminantswasconsiderablysiqliffedbymansofthecomputationaltidi
14、scussedintheappendixtothepresentpar.Asisseenfromthedataoftable1,thefinalresultsobtainedmustbewithin1 percentofthetruebucklingstresscoefficients.iItistobeexpectedthatforvaluesof 13between3 snd thebucingstressescorrespondingtos,ynmetricalandantisynmetricalbucklingwillbeveryclosetoeachother.Hence,the8o
15、lidcurveof ks againsttable1,canbel/13showninftgure2,fairedthoughthedataofusedtoestimateks foranyvalue of j3between1 endm.I%oma considerationofpatterns,theshearbucldlngclsmpededgeshavebeentireCONCZUDII?3REMARKSlmthsymmetricalandantisyrmretricalbucklingstressesofrectangularflatplateswithcorrectlyevalu
16、atedthaninpreviousworkwhereinonlysymmetrical buckllngpatrnswereconsidered.Throughtheuseoftheiagrengisnmultiplier?#dmd,whichpetitsthecomputationofbothuppersndlowerlimitstothetruebucklingstress,valueslmowntobewithin1*percentofthetrusbucklingstresscoefficientshavebeenohtalned.LangleyMemorialAeronautica
17、lLaboratoryNationalAdvisoryConmitteeforAeronauticsLangleyField,Va.,Septeniber18, 1947Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-.+, -. theareNACATNNo.1559 .AWENDIXCOMPUTATIONAIDSJnthedeterminantswhiohformthestabilityoriteriafromwhichbucklitressc
18、oefficientssrederived(reference5)Amanytermsgivenintheformofinfinitesummations;thatis, x.%mawhereAmn% =%n2- %26+n2Thissumation,fora givenvalueof n, convtirgesveryslowly,approfimatel.yas 1“ however,thetermsofthesummationapproachthe2 .W=3%ullthOlaar detemlnant; p3, q=2“ZEleventhcader dd81511b31tj P.3,-
19、dm dt; p+, lp2 (See refemnoe 5.)w%leventh order detemlnimt; , q=2%1.eTWRihOZd81?detj 7, qd? J)btalned flun erect solution in referenoe 1.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-16 I IT141 .Qb 11aI=. b:12 1A Lk -I .1 s10 - %. AA Antisymrnetric
20、a buckling .A -.S Symmetrical buckling I0018 “ t 1 1 I ! I I I I1,0 1.4 L8p= ; 2“2 : 3.0 FOROERawmcsFigure I.-Buckling stresses of clamped rectangular plates in shear.1. . .IIProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-16 t,- ! .!.4 ! 1t I I I I
21、I /)/MPI-ill Is/y I I -H10 I / I I I IkllA I A Antisymmeiricol buckling It L-l-=-F “” -1S Symmetrical buckling8 Io .2.4, ,.6 .8 1,0Figure 2.-Buckling stresses of clamped rectangular plates in shear.II ( )L as function of ks.BIProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-
