. ,: .;-. m TECHNICAL NOTE 3782 HANDBOOK OF STRUCTURALSTABILITY PART II - BUCKLINGOF COMPOSITE ELEMENTS By HerbertBecker NewYork University I I 1 v 1 , Washington July1957 . H ‘1 :, #1, . . . . . ____ . . TECHLIBRARY KAFB,NM Illllllllllllunln OUbLbqA NATIONAL ADVISORY COMWITEEFORAERONAUTICS — TECHNICAL NOTE3782 HMJDBOOK OFSTRUCTURAL STABILITY PARTII - BWKH3VG OFCOMPOS~ EHMINB3 ByHerbert Becker SWMARY The localbuckling ofstiffener sections andthebuckling ofplates witheturdy stiffeners exereviewed, andtheresults aresummar izedin charts andtables.Numerical values ofbuckl~ coefficients arepresented forlongitudinally compressed stiffener sections ofvarious shapes, for Stiff mea plates loaded inlongitudinal compression andin shear, andfor stM?f enedcylhders loaded intorsion. Although thedatapresented consist primarily ofelastic-buckling coefficients, theeffectsofplastici@ are fora fewspecial cases. discussed RWRODUCTION Thebuckling behavior ofsimple plateelements isdescribed in partsI andIIIofthis“Handbook ofStructural Stability” (refs. 1 and components oftenconsist oftwoormoresimple plate 2). Structural elements soarranged thatthebuckling stress ofeachisincreased asa result ofthesupport provided by contiguous neighbors. Suchcomposite elements aretermed stiffeners because theyarefrequently usedto stiffen a plateinorderto increase thebuc~ingstress.A compact stiffener iS described as “sturdy” whenitisnotsubject tolocalbuckltng andthereforeonlytheaxial, bending, andtorsional rigidities ofthestiffener influence thebehavior oftheplate-stiffener comb@ation undera specified Thedatapresented inthisreport onthebuckling of stiffened loading. plates pertain to sturdy stiffeners. Thereport begins witha discussion ofcalculation oflocalbuckling stress of stiffening elements. Stiffener structural shapes incommon use, suchasZ-,channel, andhatsections, havebeenanalyzed forbucKMng andcharts arepresented tofacilitate buckling-stress computations. For sections whichbuckle elastically, failure mayoccuratloadsconsiderably Failure, orcrippling, of stiffening elements is inexcess ofbuckling. treated inreference 3. Whentheproportions ofa stiffener aresuchthatitissturdy with respect totheplatewhichitissttifening, itactsessentially asan . . — —.— —.. .- —-- —- -- . . 2 NACATN3782 elastic restraint totheplate.Itmayassist intheresistance toload, as dothespanwise stiffeners ina wingcover, or itmaybehave primarily asa support, suchasa transverse rib.“lheither case,itisnecessary to consider onlyitsaxial, bending, androtational spring properties in calculating thebuckling stress ofa“stiffened plate.Buckling ofthe composite willthenoccureither locally intheplateorgenerally, involving boththeplatesndstiffener. Theinformation onbuckling of stiffened plates appears inthesection entitled “Buckling ofStiffened Compression” foruniaxial loadandinthe Plates UnderImgitudinal section entitled “Buckling ofStiffened Plates UnderShearIoad”for shearload. Thebuckling ofstiffened curved plates involves thecomplication ofplatecurvature inaddition toaXLthepsmmeters affecting buckling of stiffened flatplates.Thebuckling ofUnsttifened curved plates has beendescribed h reference 2,inwhichitwasshownthattheory isin goodagreement withtestdataforshearloading andinpooragreement withdataforaxialcompression loading. Forcertain proportions, the curved plates approach cylinder behavior, whichpermits evaluation of theunstiff ened-plate results inthelimiting case.Analyses of stiffened curved plates arereported inthesection entitled “Buckling ofStiffened Plates UnderLongitudinal Compression” foraxialloadsandinthesection entitled “BucMing ofStiffened Plates Her ShearLoad”forshearloads. Znaddition, thelimiting caseoftorsional buckling ofa stiffened cylinder isdescribed inthelatter section. Theresults ofthetheory andtestdataarecompared withtheinformation on stiffened curved plates undershear. Thebuckling stress ofa stiffener ora stiffened platemaybe found fromthegeneral relationship (1) in Whichb pertains toa general. dimension. Itmaybe thewidthofa flange onanangle, thedepthofthewebona channel, orthewidthof oneofthesidesofa rectsmgulsr tube.Thebucuingcoefficient kb isthecoefficient tobeusedtogether withthisdtiension b equation (1). TIM? parameters uponwhichkb depends are a/b or A/b ofthe plate, theamount ofelastic rotational restratit alongtheunloaded edgese,theratiooftheareaofthestiffener tothatoftheplate A/bt,theratioofthebending rigidity ofthestiffener tothatofthe plateEI/bD, andthecurvature psxameter forcurved plates~. The . — . . NACAm 3782 3 figures discussed in thefollowing sections show kb asa function of theseparameters. Theeffects ofmaterial properties onthebuckling of simple elements werecovered h ref=ence1,inwhichstress-strain curves, Poisson’s ratio, andcladding andplasticity-reduction factors arepresented and discussed. Plasticity-reduction factors forcurved plates andshells are described inreference 2. Forconvenience, a summary ofpertinent information appears inthe“Application Section” andtables 1 to3. Thissurvey wasconducted s%NewYorkWversityunderthesponsorshipandwiththefinancial assistance oftheNational Advisory . Committee for-Aeronautics. , SYMlms A areaof st~enercrosssection, Sqim a len~ ofunloaded edgeonlongitudinally compressed plates ands~le elements orlonger sideofplates loaded in shear,in. b length ofloaded edgeonlongitudinally compressed plates and simple elements or shorter sideofplates loaded in shea”r,l in. . flexural rigidity ofplateperinchofwidth,E+2(. - ,3], in-lb D d widthofbulbofbulbflange E,Es,~ Young’s modulus, secant modulus, andtangent modulus, respectively, psi G shear modlihls, pSi h widthofrec tsmgubrtubestiffener (seefig.5(c)) %ymbolsa and b pertain todimensions between stiffeners on stiffened plates ortodistances between parallel edgesohunstiffened stress isfoundfora single element ofa stiffaed plates.Thus,buckling plateandnotb termsofovemlldimensions oftheplate,except for curved stiffened plates undershear.Inthislatter caseitismoreconvenient toutilizea and b as overall platedimensions foreaseof comparison withcylinder data. .. ... . .. . ... . . _ --— — .. ——. —-—— .- . .. . NACATN3782 4 I 4 bentlng moment ofinertia ofstiffener crosssection, in. J 4 moment ofinertia of stiffener crosssection, in. torsional k buclsUng coefficient kb general buckling coefficient ofstiffener pertaining to buckling stress ofelement ofwidthb %J% bucklhgcoefficients forcompression andshear, respectively length ofcylinder, in. moment applied to edgesofrotationally restrained element, in-lb number oflongitudinal stiffeners onplateoftotalwidthnb~ ornumber ofcircumferential rtigsoncylinder oflengthL number oftransverse buckles inlongitudinally stiffened plate lycompressed longitudinal . radius ofcurvature ofcurved plate, in. correction forpresence of stiffener on onesideofplate platestiffness (seefig.2 forcliff erenttypes ) thickness, in. platecurvature parameter, (b21+ - ‘e2)1’2 cylinder curvature parameter, (L’ld (1 - ,e2)l/2 factor h r dependent upon n and q (seefig.12) distance ofstiffener centroid frommidsurface ofplate, in. ratioofrigidity ofelastic restraint torotational rigidity ofplate; alsostrain plasticity-reduction factor rotation ofedgeof simple element, radians wavelength ofbuc=einshnple element orplate ~ in. .— . __— —— NACATN3782 5 Ve Poisson’s ratioinelastic range ‘cr general buckling stress; also,buckling stress ofcompressed element, psi ‘cr buckling stress ofelement loaded inshear, psi Subscripts: cr buckling e effective f flange L lip T topwebofhat-section stiffmers v web IOCAL13UCKLINGOF SKOWEMIMGELEMENTS Behaviorof Stiffeners Whena plateunderlongitudinal loadissupported bya stiffener in thedtiection oftheload,thestiffener participates tiresist~this thepossible buckling modesofthiscomposite are load.As a result, localinstability oftheplatealone, localbuckling ofoneormoresimple elements ofthestiffener, general Wtabili& oftheplateinvolving column action ofthestiffener, or somecombination ofthesemodes.The _ses perta~to stfifen~pl.ates a~lyto stm stiffeners only, and,consequently, thesecond modeisprecluded by theanalysis inthose casesdescribed h thelastsections ofthepresent paper.Howev=,in orderto insure thesturdiness ofthestiffener, itisfirstnecessary todetermine itslocalbuckling stress.Thisisthesubject tobediscussed inthepresent section, whichpresents thebackground foranalysis oflocalbuckling instiffeners andincludes charts forrapidcalculation ofbuckl~ stress forseveral comonshapes. Thelocalbucklhgstress ofa stiffener isthessmeasthatof its weakest element. Consequently, eachsimple element mustbeanalyzed for buckling under101@tUdb31 load. Oftentheweakest element isreadily evident by inspection. Theanalysis oftheelement involves detemdning thenature ofthesupports androtational restraints alongtheedgesand . .— ——.—._ -— . -—-.. —. ———__—— ——. ____ ._ _ _ ___ ._ 6 NACATN3782 thencomputing thebucKling stress oftheelement considered asa simple plateunderlongitudinal loadwiththeappropriate boundary conditions. Iugeneral, however, thereismutual restraint ata longitudinal jointamongallthemembers meeting alongsucha line.Ifthisrestraint couldbe converted directly intoa valueofrotational restraint e for thesimple element beinganalyzed, thenthebuckling-coefficient charts ofreferences 1 and2 couldbeusedtofindthebucliMng stress ofthe simple element, and,[email protected], the” buclding stress ofthestiffener. Because oftherotational interaction amongthesimple elements at each jotitline,whicharises fromthepreservation ofthecorner angles between element pairs (el= t12= . . . = en), howev=,therestraint imposed by eachupontheothers cannot befoundimmediately. Itisnecessary toanalyze theproblem asoneinthedistribution ofmoment among themembers ofa statically indeterminate Syst=. Whenthishasbeen d~e, e canbe foundand Ucr canbe calculated. libr themostpart,thestiffness ofoneelement h itsownplaneis sufficient toimpart support toitsadjacent elements perpendicular to theirplanes, although thecorner angles mqycliff erfromX“. Mostsimple elements ofa stiffener behave inthismanner.Ups andbulbsmaybetoo weaktoprovide complete transverse support toan element (invariably a flange). Theyactas columns thattendtoresist elastically thetransversedeflections oftheotherwise freeedgesoffI.anges and,consequently, . cannot be ticluded intheusualmethods ofanalysts oftheinteraction buckling problem. However, a flange witha lipor bulbalongitsfree edgemsytie analyzed asa stiffened platetodetermine therigidity of thiscomposite, whichthencanbeusedh theinteraction analysis. Calculation ofBuckling Stress !l!he buckling stress ofeachsimple element ofa stiffener meybe foundfromegyation (1).Cherts of ~ forseveral stiffener sections ticommon usearepresented h thisreport endarediscussed belowh thesection on “Numerical Values ofBuckling Stress. ” Thegeneral methods ofconstructing thesecharts andforftiMngthebuckling stress ofa new stfff enersection tivolve a successive approximation procedure suchasthe moment-distribution method ofLundquist, Stowell, andSchuette (ref. 4)or thestep-by-step procedure ofI@oK1., Fisher, andHetierl (ref. 5). methodisthejoint-stiffness Thebasisforthemcnnent-distribution criterion, whichrequires thatatbuctiing thesumofthestiffnesses of thesimple elements meeting ata jotntlinemustbe zero.Thisispredicted upona distribution of stiffnesses emongthejoint members such thatallhavethesamelongitudinal wavelength.Thevanishing ofthe jointstiffness atbuckling folhwsfromthefact-that stiffness iseqpal NACA m 3782 7 to M/e. Ehce e isthesameforallsimpleelements atthejoint line,stiffhess isproportional tothemoment carried by eachelement. However, sincethesemoments mustvanish atbucld.ing forsmalldeflectionsoftheelements, thejoint-stiffness criterion follows. Themoment-distribution analysis issimplified ~ theuseofchsz%s ofelement stiffness andcarry-over factor prepazed byKrollfordifferent typesofboundary conditions alongtheunloaded edges(ref. 6). Theseare described inthefollowi.ng section oqnumerical values ofbuckling stress. lhessence, thestep-~-step procedure forcalculating thebuclCling stress ofa simple element involves thearbitrary selection ofa buckling stress together withseveral arbitrary values ofbuckle wavela@h. llbr eachofthesevalues,Ucr iscalculated fromequation (1)untilits minimum valueisfound.Ifthisisdifferent fromtheinitially assumed buckling stress, theprocess isrepeated untiltheassumed andcalculated values a~ee. Thisisthebuckling stress ofthecomposite element. Charts of ~ (X/b, ~) areused(aspresented inref.1)together withtherigidity tables of~ol.1(ref. 6). ,, Thebuckling stress ofa flange witha liporbulbwasinvestigated byHuandMcCulloch (ref. 7),Gbodman and130yd (ref. 8),andGoodman (ref. 9)whoconsidered a largerangeoflip,bulb,andflsnge proporsimplified theanalysis by selecting thegeometries usually tions . Gerard encountered indesign anddefined therangeofsection proportions in whichtheelement undergoes thetransition froma flange toa webasthe rigidity oftheedgestiffener increases (ref. 10). RoyandSchuette havedemonstrated experimentally thatthelocal buckling stress ofthesection isunaffected although thesingle between adjacent elements isas smallas30°oraslargeas 120°(ref. 11). The principal effect ofchanging thecorner anglefrcmW“ istodecrasethe section moment ofinertia, tiichdiminishes itscolumn strength. Numerical Values ofBuckling Stress Thebuckling stress ofa stiffener isdetermined usingthebreakdownscheme offigure 1. Eqpation (1)isutilized to compute thenun@ricalvalueofthisstress fortheweakest element afterthebuckUng coefficient hasbeenfoundaccording toa method suchasthatdescribed inthepreceding section. Thecliff erentstiffnesses evaluated byRYoll intabular form(ref. 6)aredepicted infigure 2. Theeffects oflipsorbulbsareobtainable fromfigures 3(a)and 3(b)whichpresent thecharts developed by Gerard(ref. 10). Thebuckling —.. — .. ——------ —-— --- —..—.—. —— -— —— ——. .——— —- —-—---- 8 N/MA TN3782 strati isshownasa function oftheflangeb/t andtheedge-stiffener proportions, whichpermit deterndnation oftherigidity of sucha composite foruseintheindetermhacy analysis. Inthismanner, these charts serveasanadjunct toKroll’s tables. Buckling coefficients arepresented forccmnnon stiffener shapes suchas showninfigure 4, inwhichthedimensions ofwebsandflanges areshownforbothformed andextruded shapes.Thebuckliug-coefficient charts forchannel, Z-,W, andrectanguhr -tubestiffeners appear in figure 5. Theyweretakenfromthereport ofI&oll, Fisher, andHeimerl (ref. 5). Thedashed linesonthesecharts deftiethesection proportionsatwhichbothwebandfknge buckle simultaneously. Dataforhatsection stiffeners appear infigure 6. Thecurves, adapted fromthose ofVanDerMaas(ref. 12),covera rangeofflsnge” sizesforcliff erent widths ofcenter andlateral websofthehatsection. Itshould benoted thathatandlipped Z-andchaunel sections arestructurally equivalent. Effects ofPlasticity Theinelastic-buckling stress ofa stiffener maybe computed bya method suchasthemoment-distribution procedure ofLundqyist, Stowell, andSchuette forelastic-buclWng problems (ref. 4). Thiswasdoneby Stowell andPride(ref. u), whoobtained goalagreement withexperimental data(fig. 7),forH-section stiff eners.Theplasticity-reduction factor foreachsimple element ofthesection wasemployed incomputing thebuckling stress foruseinthemoment-distribution procedure, in whichthejoint-stiffness criterion controls thetheoretical buckling stress ofthesection. Itshould benotedthatthetestdataatthelarger strains lie about5 percent belowthestress-strain curve, whilethetheory band se- to tidicate that is3 percent belowatthemost.Thisanalysis theuseoftheplasticity-reduction factor fora clamped flange would be conservative. Useofthesecant modulus fora simply supported flange wouldbe slightly optimistic. BWKLCNGOF S~ l?IATllS UNDERLONGITUDINAL COMPRESSION General Background As discussed inthepreceding section, thegeneral caseofbuckling of stiffened panels involves localtestability ofthestiffeners aswell asthespring properties incompression, bending, sndtorsion.h this section thespecial caseofsturdy stiffeners isdiscussed, anda brief description oftheinfluence oftorsional rigidity ofthestiffener is -——.. ● Y NACATN3782 9 included. Thisisofsignificance sincethedesign datapresented in thecharts pertain to stiffeners withno torsional rigidi~. A description ofthebuckling behavior ofa supported andrestrained rectangular platemaybefoundinreference 1 forflatplates andinreference 2 forcurved plates.Thestiff eningelements, @ose localbuclCling behavior wasdepicted inthepreced~ section ofthisr@port, provide thesesupports andrestraints totheplates at intermediate positions in theplatespans.Theeffectiveness ofthesesupports depends uponthe axial, bending, andtorsional rigidities oftheplateandstiffeners. Representative arrangements ofplate-stiffener combhations areshownti figure 8. Eehavior ofStiffened Plates Her IOngitudhal Compression Thetwotestability modestobe considered inthissection arelocal buckling oftheplatebetween stiffeners andgeneral instabi~ty ofthe composite element. timostcasesthetorsional rigidi~ofthestiff =er isassumed tobenegligibly small., thusexcluding rotational restraint of theplatealongthestiff enerline. Thebehavior ofa platebuckling underlongitudinal loadandsupported by deflectional androtational springs isshownschematically infigure 9. Waveformsforthethreelimiting casesofperfectly flexible andperfectly rigidsprings areshown.b general, thewaveformsforfinite spring rigidities donotchange shapesignificantly, although theamplitudes of thewavesmayvary.Whenthestiff enerrigidity is sufficient to enforce a node,theplatewillreceive noadditional f1exural support fromthe stiff ener.Thisdescription parallels thatforcolumns whichwaspresented . by Budiansky, Seide, andWeinberger (ref. 14). Calculation ofBuckling Stress stress ofa stiffened plateunderlongitudinal loadis Thebuckling usually expressed intheformofequation (1)whereb isthewidthof stiffeners. theplatebetween Thebubkling coefficient ~ isa function ofthepsxameters ofthecomposite element: kC= kC(a/b,A/W,EI/bD, Zb) (2) Eoththeenergy-integral approach andthedtiferential-eqpation method ofsolution havebeenusedto solvetheproblem ofbuclCling ofa stiffened ofboththeseprocedures havebeendescribed in plate.Theessentials reference 1. -.. - ----- .-—. —____ .. . ____ . -_ . -.—-— — —..—- .- 10 NACATN3782 Numerical Values ofBuckling Stress Thenumerical values ofbuckling stress forstiffened flatplates andcurved plates underlongitudinal compression areasfollows: thebuckling coefStiffened flatplates .-SeideandSteincalculated ficients forlongitudinally loaded simply supported flatplates withone, two,three, andan infinite nmberoflongitudinal sttifeners (ref. 15). Theresults appear h figure 10inwhich~ isshownasa function of of coefficients for a/b fora rangeofvalues of EI/bD.A summary infinitely longplates ispresented infigure 11forconvenience indetermining buc~ingstresses forlongstiffened plates. Thecalculations ofSeideandSteinwerebasedupontheassumption thatthestiffener-section centroid waslocated atthemidsurfaee ofthe thecaseinactual practice, inwhichthe plate.Thisisnotusually sttifmeriscommonly located ononesideoftheplate.Thisproblem wasinvestigated ingeneral terms~ ~wallaandNovak(ref. 16). Seide alsoevaluated thiseffect(ref. 17)andevolved a correction forthe charts offigure 10applicable toplates witione,two,orinfinitely q stiffeners @J-/~)e . ~~ r = (EI/bD) I A~2I (3) 1 + (Zm#’bq fromwhichtheeffective bending rigidi~ratio (EI/bD)e maybeobtained. n, q) tifigure 12,inwhichA/b (Mb = a/qb, Thefunction&q = f(X/b, 10. A whereq = 1,2,and3) mustmatchthevalueusedto enterfigure trial-and-error a~roachmightberequired since (EI/bD)e ~ occurat a different valueof q infigure 10thandoesEI/bDatthe a/b originallyusedtogether with n (n= 1,2,and ~)to enterthesecharts. Whentherearethreestiffeners ontheplate, itisnecessary to satisfy an equation, otherthanequation (3),appearing inSeide’s report. compressive buckling Budians@ andSeide investigated longi~ oftransverse~ stiffened simqily supported plates(ref. 18). me data whichper&into a/b= 0.20,0.35,and0.50 appear infigure 13. The curves covera rangeofstiffener torsional rigidity, incontrast with thecurves foraxially stiffened plates forwhichGJ = O inallcases. Thepreceding datapertain to general instability of stiffened plates. Gallaher andBoughan (ref. 19)andBoughan andI?aab (ref. 20)determined localbuckling coefficients foridealized web-,Z-,andT-stfff enedplates. Thest~ener-web composites wereidealized as showninfigure 14,h which thebuckling coefficients szepresented asfunctions oftheproportions of theccunposite. —. .-. — .- —- .--. — NACA m 3782 . 11 . Stiffened curved plates .-Theinformation forstiff enedcurved plates relates to thatobtained fromsections ofcircular cyltiers.%tdorfand Schildcrout investigated thecompressive buckling ofa simply supported curved platewitha central cticumferential stiffener haxdng notorsional rigidity oraxialstiffness (ref. 21). b addition todetermining thetheoretical buckling stress, whichwasdoneusingltiear theory, thepercentageincrease inbuclil.ing stress overthetheoretical valuewasobtained ofthelowqerimentalvalues of andisshowninfigure 15. Because buckling stress compared withtheresults ofthelinear theory, I!atdorf andSchildcrout recommended a@@ng thetheoretical percentage increase totheqerimentalbuckling stress, values ofwhichmaybe foundinreference 2. Themaximum possible increase fora curved platewitha given valueof a/b and Zb isshowninfigure 15(a), whilean increase less thanthemaximum isobtainable fromfigure 15(b).Furthermore, thevalue of EI/bDrequired tocausea buckle nodeatthestiffener lineisobtainablefromthesefigures ~ cross-plotting. Notethatno gainisindicatel when a/b>0.7 orwhen ~ greater thanthevalues showninthetablebelow. is 9 a/b 0.600 0.500 0.417 0.333 0.250 0.167 % 28.o 14.0 7.8 4.1 0.7 1.9 4 !Ihe charts offigure 15weredesigned topermit an estimate ofthe increase inbuckling stress tobe expected inanaxially compressed curved platewhenthecentral circumferential stiffener haslessbendhgrigidity thanthatreq~ed to enforce a nodealongthestiffener line.Whenthe stiffener hasthisminimum rigidity, thelength oftheoriginal platemay be considered tobehalved, andthedatainreference 2 should beusedto obtain thebuckling stress. Thisapproach alsoapplies toplates withaxialstiffeners, which wereanalyzed by Schildcrout andStein(ref. 22). Thecurves forthis typeofpanelappear infigure 16,inwhich~ appears asa function of EI/bDfora rangeofvalues of a/b and ~. Tnordertoaccount forthedisparity oftestdatawiththeory forcurved plates, Schildcrout andSteinrecommend thefollowing procedure: (1)Determine thecliff erence between thebuckling stress ofthe stiffened panel(fig. 16)andthatoftheunstiffened. panel(ref. 2). (2)Tothisdifference, sddthelarger ofthetwofollowing stresses: (a)Thebuckling stress oftheunstiff enedpanel (b)Thebuckling stress ofthecorresponding flatplate .. .. . . . ..— —.. - . ..— ----- — — -—- .—-c -.. — —-— . . -. -. 12 NACATN3782 for Whenthecurved platewidthexceeds thelength, usethecurves cylinders. Usethecurved-plate buckling dataonlywhenthelength exceeds thewidth. Effects ofPlasticity Plastici@-reduction factors for stiffened panels depend uponthe factors pertinent to eachelement ofthecomposite. Forexmqle,the factor forsupported plates wouldbe ~ected toapplytotheplateelementsbetween stiffeners, whereas sturdy stiff enersbehaving ascolumns should follow thetsngent modulus.Iftheseconditions holdinthecomposite, theelastic-qepsrameter EI/bDkuld becomelZ#/qbDinthe inelastic range. Gallaher andl?Qu@an compared testdataon Z-stiffened panels subject to localbuckling withbuckling stresses computed usingthesecant modulus astheplastic i~-reduction factor andobtained theagreement showniu figure 17 (ref. 19). Someofthedatapertain toplates withsturdy stiffeners. However, a largeportion applies to composites inwhichthe stiffeners buckled locally. Effect ofTorsional Rigidity ofStiffen=” Thebuckl~-coefficient charts discussed inthepreceding paragraphs wereprepared forstiffeners withnotorsional rigidi~.Actually all stiffeners havesometorsional rigidity, andclosed stiffeners, ofwhich thehatsection istypical, mayfuuction asfullyrigidstiffeners in torsion forscmeapplicatims. Inreference 1 a chartbasedupontest datawaspresented depicting theeffect onbuckling stress asthetorsional rigidity changes relative totherigidity oftheplate ‘being stiff enea . Thishasbeenreproduced hereb figure 18,inwhichmaybe seenthecomparative effects of stiffeners withlargeandsmalltorsional rigidi~. Thegaininplatebuckling stress realizable withstiffeners offinite torsional rigidity depends upontherotational restraint e provided by thestiffener. ~is isrelated to thecliff erence inbuckling stress between stiffmer andplate, wherethestiffener isnowconsidered tobe a simple element of specified elastic properties, inorderto satisfy thejotit-stiffness criterion iUEcuss&i = thesection entitled “Loc&l. Bucuingofstiffening Elements. “ Thus , ‘Crplate ) (4) d -———. —-——. . NACATIV 3782 u Thisissubstantiated by figure 18,whichshowslittle gainover simple support whentheplaterigidity ishigh(lowvalues of b/t). BUCKLING OF STIFFENED PIATES mm smm LOAD Behavior ofStiffened Plates UnderShear . . Whentransverse stiff enersareattached toa plateloaded inshear, theymayberigidenough to enforce nodesattheattachment linesorthey maybe soweakasto exertvirtually no influence ontheplatebuckle pattern.Theextreme caseofweakstiffeners wasexamined by Schmieden (ref. 23),Seydel(ref. 24),andWang(ref. 25)whilerigidstiffeners wereexsmined by Thoshenko (ref. 26). . Theintermediate rigidi@rangewasanalyzed byCrateandIawho demonstrated themmnerinwhichtheshearbuckling stress ofan infinitelylongflatplateisincreased longitudinally as stiffener rigidi~ risesuntilitissufficient toenforce nodesalongtheattachment lines thebuckle pattern ofthepl-.te changes (ref. 27). Duringthisprocess fromthewaveformforanunstiffened plateofinfinite length andof width (n+ l)b tothatofa platewidthb. Testdataobtained by . CrateandLofollow thetheoretical trendof ~ asa function of E1/bD Thescatter islargewithmostofthedatalyingbetween thecurves for simple support andclamped edges, as showninfigure 19(a). SteinandFYalich analyzed buckling oflongflatplates withtransversestiff enerssubjected to shearload. (ref.. 28). Thebehavior is analogous tothatofa longitudinally compressed platewithtransverse stiff en=s. tifigure 19(b)testdataareshowntoagreewiththethqq ofSteinandl?ralich. SteinandJaeger analyzed buckling ofa curved platewitha central stiff enerplaced either axially orcirctierentially (ref. 29). Although thegeneral behavior pattern corresponds tothatforflatplates, the additional factor ofcurvature modifies thebuckle pattezm, whichtends toward thatof a cylinder inwidecurved plates. A stiffened cylinder represents a limiting caseofstiffened curved pertaining tothiscasecovers ‘test results, plates.Mostoftheliterature themajorportion Ofwhichapplies towedcstiffeners’ thatbuckle locally or to stiffeners rigidenough to mforcenodesandthereby causethecylinder 2, tobehave asa groupofplates.Thesecasesareaiscusseain reference whichdealsspecifically withthisproblem. Stein, Sanders, andCrateinvestigated thebucklj.ng ofcylinders loaded intorsion andstiffened byringswithfinite rigidi@(ref. 30). .— . . . ——— .. . . . . . . —.— — .—— — .-— — - -- ——— --- —-— .- -- —. NACATN3782 14 A largerangeofvalues of % wascovered fora corresponding large wascompsxed withtestdatawith -e ofvalues of EI/bD.Thetheory 20, in whichthe&eoryisseentobe sliglrbly “ theresults showninfigure optimistic . Calculation ofBucklhgStress (1)inwhich Thebuckl@ stress isexpressed intheformof equation thebuckling coefficient ks isa function ofgeometry andloading. As h thecaseoflongitudinal load,thebasicparameters forflatplates are a/b, A/bt,and EI/bD, whileZb isanadditimal parameter for CUPRd pkteS d ZL 13~lieStO CyliIlderS . h the theoretical investigations thestiffeners wereassumed topossess notorsional rigidity, and thecentroids tiere assumed tolieh themidsurface oftheplate. Nmerical Values ofBuckling Stress Thenumerical values ofbuckling stress forstfif enedflatand curved plates andcylinders intorsion undershearloadssxeasfollows: Stiffened flatplates. - Thetheory ofCrateandb forlongflat plates loaded h shearandstiffened longitudinally (ref. 27)ispresented infigure 19(a), inwhichks isplotted asa function of EI/bDfor bothclamped andsimply supported plates withcmeortwostiffeners. The results ofStetiandIYalich (ref. 28) fortransversely stiffened flat plates appear h figure 21. Fromthislatter figure itmaybe seenthat theminimum valueof EI/bDremind to aforcea nodeatthestiffenerattachment lineincreases rapi~ @th a/b. Approxtite values areshown inthetablebelow. Ill a/b. . . . . . . . . . . . . . . . ...1 Minimum valueofEI/bD fornode . . . . . . . . . . . . . ..lOl~ 2 5 700 ofthetheoretical investigaStiffened curved plates. - Theresults oncurved plates loaded in shearandsupported tionofStetiandYaeger by a central stiff ener(ref. 29)appear inthecharts offigure 22. EOth axialsmdcircumferential stiffeners areconsidered together withwide plates andlongplates.me results areplotted intheformof ks as a function of EI/bD, inwhichb istheshortside.Thispermits comparison withthecurves f orunstiff ened plates p resented inreference 2. 0 -——. — — .. .— — — - NACATN3782 15 Thecurves areplotted forseveral values of Zb .- a/b= 1,1.5, plateaimlenand2 (where, forthiscase,a and b aretheoverall Sions ). Inaddition, thelimiting curves ofinfinite a/b forlong plates andthecyl~er curvefor-wide plates areinclud-ed. Thela~ter maybe checked against thecurves forcylinders to bediscussed inthe following paragmph andpresented infigure 23. Stiffened cylinders intorsion .-Stiffened cylinders h torsion represent a limiting case. ofstiffened wideplates inshear.Stein, Sanders, andCratecalculated thebuckling stress asa function ofthe cylinder andstiff enerparameters (r&.30). l?he curves appear infigure23,inwhichks isshownasa fuuction of EI/bDfora largerange ofvalues of ~ andforone,two,three, andfourhxtemmxliate rings. Thecurves pertaining toonerhg msybe seentoagreewiththe“cylinder curves offigure 22(d)forwideplates witha central cticumferential stiff ener , Theseresults wereobtained forstiffeners withno torsional rigidity, withthesection centroid inthemidsurface ofthecylinder ,Q1. Effects ofPlasticity . Theplasticity-reduction factors forstiffened plates undershear may befoundinreferences 1 and2 forflatandcurved plates withspecific boundary conditions . Thisinformation should applytoplates withstiffenersrigidenough to enforce nodesalongtheirattachment lines.Nodata exist, however, forplasticity-reduction -factors forplates stiffened by elem&tsofrigidi~lessthanthatrequired fora node. AEPIJCATION SEZ!KIDN plates has Theuseofbuckling chsrts forstiffeners andstiffened section beendescribed inthepreceding sections. Inthisapplication areexplained. andthetables theresults aresmmarizedforrapidreference loaded incompression. Table1 contains dataforstiffening elements Homation on stiffened plates loaded inlongitudinal compression appears intable2,anddatarelating to stiffened plates loaded inshearare fouudh table3. Inallcasesthebuckling stress canbefouudfrom equation (1): . .. . .... .. . . -.— .—— —— —- .— -. -.——--————.——— -- — . NACATN3782 16 Plasticity-reduction factors appear inthetables wheretheyareapplicable.Forfurther information onplasticity-reduction factors and information cladding reduction factors also,seereferences 1 and2. l?br onfailure ofstiffeners seerefer=ce 3. . I?&ring-stiffened cylinders intorsion, acr= &~~ Forthiscase,~ depends upon ~ tisteadof~, Itshould benotedthat a and b aretheoverall platedimensions comparison withthedata plates undershear.Thispermits forstiffened forring-stiff enedcylinders intorsion. Research Division, College ofEngineer-, NewYorkUniversi@, NewYork,N.Y.,April15,1955. —----- .-—. Y mm m 3782 17 1.Gerard, George, andBecker, Hqrbert:Handbook Of Structural Stability. PartI - Buckling ofFlatPlates.NACA~ 3781,1957. 2.Gerard, George, andBecker, Herbert:Handbook ofStructural Stability. ~ III- Buckling ofCurved Plates andShells.NACATM3783,195?. Stability. Partn - l?ailwe 3. Gerard,George:Hbook ofstructural ofPlates andComposite Elements. NACATN3784,1937. 4.Lundquist, Eugene E.,Stowell, Elbridge Z.,andSchuette, EvanH.: Principles ofMoment Distribution Applied to Stability of Structures Composed ofBarsw plates.NACAWl? L-326, 1943. (Former~ NACA~ 3K06. ) 5.Kkoll, W.D.,Fisher, Gordon P.,&d Hetierl, George J.: Charts for Calculation oftheCritical Stress forIota.1 hstabil.i@ ofColmns withI-,Z-,Channel, andRectangular-Tube Section. NACAWRL-429, 1943.(Formerly NACAARR3KD4. ) 6. fiO~, W.D.: Tables ofStiffness aadCarry-Over Factor forFlat Rectangular Plates WnderCompression. NACAWR L-3g8, 1943. (Formerly NACAARR3H27. ) 7. Hu,PaiC.,andMcCulloch, JamesC.: TheLocalBuckling Strength of Lipped Z-Columns With9nallLipWidth.NACATN 1335,15#+7. 8. Goodman, Stanley, andR@, Evelyn:Instability ofOutstanding Flanges Simply Supported atOne~ge andReinforced by BulbsatOtherEdge. NACATN1433,1947. 9. Goodman, Stanley: Elastic Buckling ofOutstanding Flanges Clamped at OneEdgeandReinforced by Bulbsat OtherFdge.NACATN1985,1949. Instability ofHinged Flanges Stiffened by 10.Gerard, George: Torsional Li.pSand Bulbs.NACATN3757,136. ofAngleoflknd 11.Roy,J.Albert, andSchuette, Eva H.: TheEffect Between PlateElements ontheIocalInstaBili~ ofFormed Z-Sections. ) NACAWRL-268, 1944. (FormerlyNACARB L4126. 1.2. vanDerMEU3S,Christian J.: Charts fortheCalculations oftheCritical Compressive Stress forLocalIhstabili@ ofColumns WithHatSections. Jour.Aero.Sci.,vol.21,no.6,June1954,pp.399-403. 13.Stowell., E1.bridge Z.,and~ide,Richard A.: Plastic Buckling of Extruded Composite Sections inCompression. NACATNlg71., 1949. . -. .- -.-—- _______... —.—. — - ..— _ —~---- — -.— -.—— ._ ___ .. _ _ NACATN3782 18 14.BuaisJls@, Bernard, Seide, Paul,andWeinberger, Robert A.: The ofa Column onEqually Spaced Reflectional andRotational Buckling Springs. NACATN1519,lW. Buckling ofSimply 15. Seide, Paul,andStein, Manuel:Compressive Supported Plates withlongitudinal Stiff eners.NACATN1825,1%9. 16. Chwalla,E., andNovak, A.: TheTheory ofOne-Sided WebStiffeners. R.T.P. Translation No.2501,I&itish Ministry ofAircraft Production. (FYom Bautechnic - SuQP1. dermbEUl, vol. 10,no.10,MSy7, 1557, pp. 73-76. ) ofIOngitudinal Stiffeners Located onOne 17. Seide, Paul:TheEffect Sideofa PlateontheCompressive Buckling Stress ofthePlateStiffener Combination. NACATN2873,1953. 18.hdiEUISky,Bermurd,and Seide, Buckl@ of Simply Paul:Compressive Supported Plates WithTransverse Stiffeners. NACATN1557,1948. 19. Gallaher,George L.,andI@u@an,RollsB.: A Method ofCalculating theCompressive Strength ofZ-stiffened Panels ThatDevelop Iocal NACATN1482,1947. Instability. 20.Boughan, RollsB.,andBaab,George W.: Charts forCalculaticm ofthe Critical Compressive Stress forIocalInstability ofIdealized Web-and ) 1944. (FmmrlyNACAACRL4H29. T-Stiffened Psnels.NACAWRL-204, Murry:Critical Axial-Compressive 21.Batdorf, S.B.,andSchildcrout, Stress ofa Curved Rectangular F%nelWitha Central Chordwise Stiff ener.NACATN1661,1948. . Axial-Compressive 22.Schildcrout, Murry, and%ein,Manuel:Critical Stress ofa Curved Rectangular PanelWitha Central Longitudinal stiff ener . NACATN1879,1949. 23. Schmieden, c.: TheBucklingofStiffened Plates inShear.TranslaWkshingtxm NavyYard, tion No; 31,U. S.lhsper~ental ModelBasin, June1936. Subjetted to Shear Plates 24.Seydel, Edgar:WMnklingofReinforced NACATM 602,1931. Stresses. Stiffened Plates UnderShear. 25 Wang,TsunKuei:BucklhgofTransverse Jour.Appl.Mech., vol.14,no.4,Dec.1947,p.A-269- A-274. ● ofElastic Stability. Firsted.,McGraw-Hill 26.Timoshenlm, S.: Theory EookCo.,MC., 1936. -—. — -— .. .. “ 19 NACATN3782 27.Crate, Harold, andIo,Hsu: Effect oflongitudinal Stiffeners onthe Buckling LoadofIongFlatPlates UnderShear.NACATN 1589,19$8. 28.Stein, Manuel, andFYalich, Robert W.: Critical ShesrStress of Infinitely Long,ShplySupported PlateWithTransverse Stiffeners. NACATN1851,1949. DavidJ.: Critical 29. Stein,Manuel, ShearStress ofa Curved andYaeger, SW?fener.MACATN1972,1949. Rectangular PanelWitha Central Harold:Critical 30.Stein, Manuel, Sanders, J.well,Jr.,andCrate, Cylinders inTorsion. NACARep.989,1950. Stress ofRing-Stiffened ----- ____ ________ .__, - ...— —.. —-- -- --— NACATN 3782 20 TABLE 1 STIFFENER ELEMENTS IN COMPRESSION [See fig. I for breakdownof typicalsectionsintotheir component elements] Buckling coefficient Section Fig. Plasticity-reducfion factor 5(a) 12c ‘w ‘E;:;:J~] bw j(b) kw Nonereported kh Nonereported k+ Nonereported t-i j(c) bh ‘ D bt 6 JY — ..- -— .. . —.— NACATN 3782 TABLE 2 STIFFENED PLATESUNDERLONGITUDINAL COMPRESSION GJ=O] [ Seefig.8 for sketchesof plate-stiffener arrangements; Section Pfg. - Plasticity-mductIonfactor (a) Endview 10 A w x v A A w n=l,2,3,a) End view 4(a) WhenMfenersenforcenodes, ~ Infinitelywide Endview 4(b) ~=(i)(a ~+,[++’ = Infinitelywide Endview 4(c) T T T T 4(d) Infinitelywide Side Wew Endview 15 - :=: . Whenstiffenersenforcenodes, Endview usedata in ref. 2 16 4 an, numberof stiffenerson plate; ~, .. —..-. —. ●, sturdy ~ffen% transversesupportwithno restraintof lateralmovement. -- —-—————-———— --—— __._- —- ..— .— -.. ...— .-—.-. . - NACA TN3782 TABLE 3 STIFFENED PLATES UNDER SHEAR 1 See fig.8 for sketches of plate-stiffener arrangements. GJ=O Fig. Section (a) 1 Plastlclty7eductIon factor Endview 9(a) n=l,2, co Lomplates only Side view Endview 21 iv ~ 1A ~6 :; v Lowplates only Endview :2(0) ❑nd 2(b) When stiffeners enforcenales, 7 = (%/E) (l~e2)/(i 4 Endview :2(C) and4 2(d) = - V2~ Sideview . w u A 23 m n=l,2,3,4 Simply SUpprted ends %, numberof stiffenersan plate; ~, ●, sturdy stiffener; transverse support withnorestraint of lateralmovement. —-.—. .. 23 Figure l.- Breakdownofsngle andZ-stiffeners intocomponentplate as,simply supported. elements. — —. .. .——.—— .- —. . —.—. .—— —- - -—- -—. NACATN 3782 24 s ‘c+ . s’ s“ s’” . S’v JW3- M M M M stiffnesses offlatplates withdifferent boundary 20- Rotational conditions . Momenti varysinusoidally alongplatelangth. . .—. . ——._ Y NACATN 3782 ./c T s 4@ff . \ \ \ , /m . (a)Lipflanges. Figure 3.- Buckl@ stratiofhhgedflanges. Lfi = 3.5; . %@2 t 2.Ve = 0.3 (dataofref.10). E cr=12(l -.—. —.—..... . _ __ - _ )() z=’ Ve .._ ___ __ _ —. —-. — ———— . .— 26 NACATN 3782 ./0 ~ “ a Ce Do/ . . Y\ . \\ uNs77wEMm FLANGE ~\\ .000< “/0 \ 1 I “ /00 (b)Bulb” flanges. =e 3*- Concluded. —— NACATN 3782 27 r b ‘1--J L b .+ r r &f “ -m .- bw LJ bf . (a)Extruded sections. (b)Formed sections. Figure 4.- Typical formed andexlamded stiffeners. . . .. . .. . . . ____________ ___ —-—- —. ——- .—— —:. —— -- . 28 71 I WEB BUCKLESFIRST 1 ( / . / y .4 fZAME BUCKLESFIRST— 5 4 kw [v \\\\ \ \ \ \ \ \ \ I , .P’f \ FUNGE, bf 2 ~ t “ WEB,bw 9 ‘&l-l s EO)IIIIIJ .2 I 4 20’.8 .6 ● (a.) ChannelandZ-section stiffeners. acr= 8!0 I 12 I$#E t# 12(1- Vez)r lllgure 5.-Buckling coefficients fcmstiffeners (data ofref.5). -—-—-—— —— —-———-— — —-. — —. . .— -.. . NACA TN3782 ● 7 7 6 5 4 kw 3 2 / FLAh@&bf o 1111111111 .2 o # .8 /2 10 ; &w (b)H-section stiff eners.Ucr= ~2E %2 .12 (1- ~e2) ~ Figure 5.- Continued. 0 . ..— ...- ___ ___ . ——. -.—— _ __ . ..— “ NACATN 3782 kh l-+--i . I I I stiffeners. am = (c)Rectangular-tube-section *($ Figure 5.- Concltid. 0 -- — . 1 i 6 I 5 I u 4 I 1% 4 k, 3 2 1 0 Figure 6.- I 1 Eucklingstcessfor hat-sectionstiffeners. t = %=%=%; ~21J t2 —. (E&a of ref. 12.) % = U!(1 - Veq bq? NACATN 3782 32 85 . STRESS- STRAIN o 75 7G C*, ksi 65 6G 55 .005 .0/0 .0/5 of buckling ofthecmy andtestdqtaforinelastic Figure 7.- COmpsrison H-section stiffaers.ecr= %+%2 Q= 1.(); +$ =0.5 ~ 12(1- ve2)b#;~ 0.8. (I%ta ofref.13.) . —- —. .—.. .. .. 5Y NACATN 3782 LON61WWN44L STIFFENER AXIAL STIFFENER 33 TRANSVERSE ST/F~AfEk? — —. CA?CUMFEW6AL STIF=NER combinations underionFigure 8.- IIIYPiCal arrangements ofplatestiffener gitudinal compression. ._ —..-. .——. -.— ——-— ...— — — - - -. NACATN 3782 34 EDGE STIFFENER El= EDGE GPO o I . me behavior ofaxially compressed flatplatesuppofied 90- BucKling bydeflectianal androtation~ springs. ___ .. 5 4 \ 3 k. 2 ‘2 / -0 / 2 3 4 56 7 8 o“b (a) One stiffener. A/bt = O. Figure 10.- Ccmqressive-buckling coefficientsfar shply sqpportedflet plateswith lcmgitudinelEtiffenem ● of ref. 15. ) ... .*Y. (Data . 4 ‘% \’+<:;—---J” \_ 40 3 kc 2 / / - ~ ~/b=a/b+ F [ Lllllllld ‘o A/b=oA2b +A/b=o/3b / 2 3 ~ 4 db (b) One stiffener.A/bt = ().2. m lo. - Continued. , 6 7 I 8 . 5 4 3 kc 2 / . L,,l,l,ll 00 / 2 I 3 I , 4 I 5 o/b I (c) one stiffener. A/bt = 0.4. Figure10.- Chtin’ued. I I I 6 7 8 I w 5 0) “4 3 kc 2 \ / Axb=a/b-#-- IIlllllil 0 0 / 2 3 4 b+=wa’ 5 6 .’ 1“ 7 8 (24) M !3 6tiffener6.A/m = o. F’Uwe 10.- Continued. , , s . T 5 )’ 4 A 1 3 k= \ 2 20— \G ‘/0 I ,’2” \ / I \l \ I hl~ \ I - I J 7 8 —. ti o 0 / 2 4 3 5 0/’ (e) Two stiffeners. A/bt = Figure10.- Ccmtimed. 6 5 -T 4 3 k= 2 \ 2 / o ( 11111111 / 2 3 5 4 6 7 4 (7A5 (f) Twu Stiffeners.A/bt= 0.4. Figure 10.-Continued. , w -1 al n) * , , 5 4 I,. 3 kc 2 I { i / ! 0( i “\ / 2 3 4 5 oh k) Three stiffeners.A/bt = O. Figure10.- Continued. I 6 7 8 J 5’ 4= Iv 5 4 1 3 kc 2 / q 11111111 / z 3 4 5 6 7 8 u/b (h) Three stiffeners.A/bt.0.2. -10”- -tfi~d” > , 5 El 4 3 4 2 / o o / 2 3 4 5 6 7 8. Cvf!b (i)Three Stiffe?mra.A/bt .0.4. II . . F@u.’e lfl. - Contintid. 5 I I l\ I I 4 3 4 2 I / o 0 / 2 3 4 U/b (J) Infinite nunberof Fil!3m= 10. - 5 6 7 8 ‘Mb stiffeners. A/bt = O. Continti. . , * , , 5 I w 4 4 Is 3 & 2 / \.1 o 111,,11~ \ 75 I 0 / 2 4 3 OA 5 ‘ 6 7 Mb (k) Ihflnitenumberof stiffeners.A/bt = 0.2. Figure10.- continued. I I I g 5 4 3 2 I _ o / 2 3 4 5 6 O!!b ‘M (2) IMtnite numberof stiffeners.A/bt -0.4. Figme 10.- Concluded. 7 8 . , 5 4 3 k 2 / o ./ /0= / /oa .g FigureIL- C!cmpresslve-buckJ.lng coefficients for infinitelylong with lcmgltudiw 1 stM&ners. . shlp~ S~ flat — plates k#E ‘m= K!(1 - ve2) o. .&~ b (Date d ref. 15. ) a34 4 n=2, UA!FAUZED STURDYS77ffEWRS 3 / \ z—w + 2 /“- n=l, q=f I n=2, q4 r fpw c J/b Ilgure 12. - l/~q aa a functionof (m/bD)e pattern. r=—= (EI/bD) stiffenedplate proportions 1+* crosssection. (Dataof ref. 17.j VI -a 0) N stiffener A ‘s”=’” . ‘Y 49 NACA . m . # 75 4 50 e, u I I I [ --- 100 (a) . Zm a/b= 0.20. Figure 13.- Longitudinal-compressive-b~ coefficients forsimply supported withtransverse T= = stiffeners. J21 ( - ~e2b2” ) (Data ofref.18.) . . . ..— ------ —.—- -.—. ..— — &x2~2 ._. — -—. —— —.—— _— NACATN 3782 50 5C -4 30 ~ 2C /c a La w E] n (b) a/b= 0.35. Figure 13.- Conttiued. . . .— —. —. t 51 2( k /6 5 6 (c) a/b= O.50. Figure 13.- Concluded. .— —— .-..-— .—. . .-— NACATN 3782 52 . ? . 6 5 4 k, 3 2 / 1 IJlllllllll 2 4 00 I I .6 .8 I D bp/b* (a)Websttifeners. 0.5< ~/ts <2.0 (Data ofref.20.) wide coefficients forinfinitely Figure 14. - Compressive-local-buckMng idealized stiffened fkt p~teS. am = *:7” . .— — -. .— ..- .—. -- .-. . .-— — . . 53 “ 7 . 6 5 4 k= .. 3 . 2 / o z u .4 s .8 10 M bw ~ Z-section stiffeners. ofref.19.) %/% =0.50snd0.79. (Data Figure 14.- Continued. .. . ...— ..__ _ ___ — ——. ——.. —— —— ———. —.. . . 7 . 6 5 4 k= 3 2 / 00 2 .8 .6 LO b~ ~ (c) = 0.63 enaLO. Stiffalers . i#ts Figme14.- Continued. . (l)ata ofref.19.) 55 NACATN 3782 . 7 . 6 5 d BUCKUN6 OFSKIN ‘EWRAWEO BYSTIFFENER 4 k. 8UCKLIN6WWIFFEWW RWRAINEOeY WW 3 bf bf b~ 2 ~ . / 4 m’ TTr o0 .2 .6 .8 L2 . bf %? 0.25. t_& = 1.0;~> 10;~> (d)T-section stiffeners. s (Data ofref.20.) Figure14.- Continued. .-—. .—._ ----- . ——. . —— —.. . . . .—— —. .- ———.—— —.—- -. . - --- 56 NACATN 3782 7 6 5 4 k, 3 2 I 1 .8 40 .6 m I o o mm ,t, .2 4 .6 b/b Ws I E “ (e)T-section stiffeners. tw/tf= 0=7;bf/tf> 10;%/bs >0.25. (Data ofref.20.) Figure 14.- Concluded. . , 1 I I 0 (a)Maximumincrease. I I I I .2 .3 .4 (~ti~)(~b)” i I ./ (b) IiuxeaseXor given stiffbms. stressfor siqplysupportedcurvedplateswith a Figure15.- Increasein compressive-buckldng centercircumferential stiffener. (Dataof ref. 21.) 58 NACATN 3782 . 6 5 I A/bf=O . A/bt =C12 _ “ . k. 3 . oo~ 4 /2 /6 . 12 048 16 6 I t A/bt-+.4 _ 5 A/W =0.6 4— ~= 3 2 / 00 { 4 8 /2 /2 A? 048 B ~gure 16.- Compressive-buckling coefficients forsimply supported, curved plates withcenter longitudinal stiffener. am = *Y” (Data of ref.22.) - NACATN 3782 59 . I A/bt=O.2 \ oo~ 24 3? 08 6 I A/bf =0.6 I ● 1. A/bt=O.4 . 5 + \ 3 2 f ‘O . 8 /6 24 32 08 < tf524 32 . (b) a/b= 2. Figure16.- Continued. . . -. .——. -.--—- — —-—... —.— ——— . ..— —. — .—— . ..— — NACATN3782 60 DxzIl” 6 5 4 kc 3 2 / 0 I ) 6‘ I I I I . A/bt=O.4 5‘ 4 i /6 32 48 64 A/bt=0.6 \ zg250 1 k. 3’ / 2 I 324w&? O /6 324864 . (c) a/b= 3. ~gure 16.- continued. . 61 6 5 _ ai N. 4 Zpfjo kc 3 1 I > o 2 ///!//////zw/z/ / =b - /ww///wzu’ f I I I I I I Ot~163?486480$W[ 6 I /6 32 48 64 80 96 _ 5 I I#Mbt=Q6 \ 4 3 2 A / ‘O16324864&U96 O /6 324864 8096 El m (d) a/b= 4. Figuqe 16.- Concluded. .. —.-— — .—.— —.. .— .—-— — .—. — ..-— .. . _. _. 62 . 50 MAXIMUM 40 – STRESS- STRAIN CURVE . . 30 STRESS-STRAIN- G5 . ksi . 20 /0 q .002 .004 .006 .Ot ? oftestdatawithsecaut-modulus theory for Figure 17.- Comparison inelastic-locsl-buckMng stress ofZ-stiffened flatplates uuder ofref.19.) compressive load.(Data . . I 8 I 7 I I UWG,EDGES CLA@’A?5D TORS1O)WL Y – RIG/D S7iFi5ENEf? 6 5 — LONG EWES SYMRY w’PmrED&-4.oo) 4 — 3 I -o 50 /50 ItLgure 18.- Effdct of torsionalrigidityof stiffeneron bua ficiemk fm flat plateB. (Dataof ref. 1.) A?50 300 coef - m —m m I 7MWY o nmj -------- n ~.p ——— / v / n am 40 ❑ If*30 o m, O/w s77FFEm - 0 m CLAMR5Z Em NY SU+0R7ED EDsm — /0 o EI/bD (a) C1.aqedand shply Slqpcrted plates;longitudinal m . stiffeners. 19.- Cmqparimn of theoryaud. test“datafor shearbucklingcoefficients of long flat plates with stiffeners. , , /0 on 0 ‘1.4 u .2.4 A“ .4.8 5 A DATA L4, 2.4,4.8 TEST THEORY 0/. = 00A 0 E//bD stiffeners. (b)Wmplysupported plates; trsnmerse ----- ... . . . . ..— —— —— -.— ----——- -. ————— __— —_. — ..- ———— q.~=o —- .— - 7 --T———~— —=s - –––– ~= “-–f ___ 4* ● 137 N~OFUAWS Ch!w#n ON M o u Sro?lw ON ONEW Mm- me Qkl ● 0 .1 I 10 SEcm WOE 10= . . 10” 10’ E.I_/iiD FigureZO.- Comparisonof theoryend test data fm dmply sqpported circuhr cyMnd.ersstHfened by rings and loadsdin torsion. NACATN 3782 67 . m u — 48 4 00 ‘ S/m r bYJPmR KAn%s G!ED+4“ 8‘e :1 16 m so E1/bD (a) a/b= 1. # 6 . / 4 z k, . J_ m b #- –-r 00 40 “ “ 80 L?o#oma ,11 E1/bD (b) a/b= 2. ., E7/bD a/b= 59 Shear-buckkn coefficients forlongshplysupported flat . (c) @dH3 withtiEUM3VETSe StiffeI,IerS.Tm= lsf#r2E&2 )() “ I-2(1- Ve2b (wta of ref. 28.) .. - .—.—— .—— ——— —. -. — .. ..-— — —. NACA?CN 3782 68 ● . w 0 1 I .-II I I 1111111 I I IlllllJ 1 I 1111111 / ./ /d - /0 El. -m (a) Centersxial stiff~j axial , /03 -.- .‘.+. .,-*,-“: %.>> .. , -. length greaky~hsncircbnferential width. -j :...,, Figure 22.- Shear-budding coefficients for” si&# &zppdr$ed curved plates ofZ&b 29,.) .; withC(?31ti Stiff tie)?● (Data $ -.. .. --—— —---- .—— —-. —____ ____ ._ ._. . ~ ‘ -7 NACATN3782 / CYUWER /00 50 Woo / z M 20 100 CYLL4D /0 I [ / 30 20 tts “z~ b 200 69 CYLJ!E 10 ! – “ - 30 20 10 6 30 L5 /0 I 48 CYLINDER ! : “- “ 0 J / ‘ - . d /03 (b)Center axialstiffener; circumferential widthgreater thau”sdsl length. .. —.-. . . ..— .—— —. . . . . . — -— ——.—. — - —. --- 70 NACATN 5782 200 /m 60 30 20 /0 I 40 r 20 k, m /0 2 R ‘= 30 M ‘ . 30 / 20 45 2 /0 6 /0 “1 :zz‘II: 30 20 m i: I “ “ 44 “ 1 10 6 4 ‘5 m / 0 .f / (c) Centercircumferential. sti&ner; t--al ——— { /7-b \UJ ——. w /0 fop /03 axial length greater thancXrcum- ferential width. Figure 22.- Conttiued. —. J . NACATN 3782 . n. I‘ ‘ Q / .~ 200 100 60 40 20 /0 z~ b 300 CYLINDER f(~~ CYLINDER poo 100 (d)Center circumferential stiffener; ci&muferentialwidthgreater than -al length. Figure 22.- Concluded. . . ... . -- - .——. --—. -- — ----- .. —— - ..—- -1 N I .I t /v- #v {U” I EV20 Figure 23. - BuckMng coefficients for t3imply supportedcticulercylinders stiffenedby r*6 and loadedin torsion. Ta = &-#r” (Ik&a of ref. 30.) ,
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