1、.!=.*ii,1“It:INATIONALADVISORYCOMMITTEEFOR AERONAUTICSTECHNICAL NOTE 3786HhDBOOKSTRENGTH OFOF STRUCTURAL STABIJJTYSI?IFFENED CURVED PLATES ANDBy Herbert BeckerNew York UniversityWashingtonJuly 1958SHELLS,-:,+)IIIIItI, . .-. . . . . .Provided by IHSNot for ResaleNo reproduction or networking permitte
2、d without license from IHS-,-,-TECH LIBRARY KAFB, NMMI.,. .-“ Iulllllllllllllllllllllllillll10bb701TABLE OF CONTENTSPage,-.rLSUMMARY . . .mollu(xtollSYMBOLS . . . . . .a71a15a15a71a15a15REVIEW OF EXISTING DATAIntroduction . . . .InstabilityMcx3es. .Panel instability .General instabilitytimum mode .
3、. .a71a15a15a15a15.a71a15a15a15a71.a71a15a15.a71a15a15a15a15a15a15.a71a71a15a15a15a15a71Historical Review of General InstabilityCurrent State of the Art . . . . .Emphasis of Present Investigation . .SIRENGTH OF SITmEmD cuRvEDPLATFs. .Introduction . . . . . . . . . . . .Axial Compression . . . . . .
4、. . . .ShW3J?. . . . . . . . . . . . . . . .ConibinedShesr and Axial CompressionBENDING GENERAL 1NSTABILIT% . .Introduction . . . . . . . .Theoretical Approach . . . .Basic differential equationTaylors theory . .Hoffs theory . . .Brazier instabilityEmpirical Approach .GALCIT . a71 a71 . . .PIBAL. .
5、. . . a71 .Physical Approach . .a71a15a15a15a15a15a71Frame spring constant ,Calculation of genersl instability stress. . . . . . . . .a71a15a15a15a71a15a15a15a71a15a15a15a15a15a15a71a15a15a71a15.a71a15a15a15a15.a71a15a15a15a15a15a15a15a15a15a15a71a15a15a15a15.a71a15a15a15a15a15a15a15a15a15a71a15a15a
6、15a15.a71a15a15a15a15a15a15a15a15a15a15a15a15a15a15a71a15a15a15a15Test Data . . . . . . . . . . . . . . .Section Properties . . . . . . . . . . . .Discussion of Taylors T23637394040404343454546;:4949494950:5154545454;54!55555656565757.4bProvided by IHSNot for ResaleNo reproduction or networking perm
7、itted without license from IHS-,-,-t.1.PageREFERENCES. . . . . . . . . . . . . . . . . . . . . . . . . . . . 58TAELE . . . a71 O a71 . . a71 . . . . . . . . . . .0 . . . . . . a71 C. 63FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .“.G.iii1- . .- .- . .- . . .-Provided by IHSNot
8、for ResaleNo reproduction or networking permitted without license from IHS-,-,-“.NATIONAL ADVEORY COWITIEE FOR AERONAUTICSTECHNICAL NOTE 3786HANDBOOK OF STRUCTURAL STABILITYPART VI - STRENGTH OF STIFFENED CUKVEDPIATES AND SHELLSBy Herbert BeckerA comprehensivereview of failure of stiffened curved pl
9、ates audshells is presented.Panel instability in stiffened curved plates and general instabilityof stiffened cylinders are discussed. The loadings considered for theplates are axial, shear, aml the conibinationof the two. For the cyl-inders, bending, externsl pressure, torsion, transverse shear, and
10、 colu-binations of these loads sre considered.General instability in stiffened cylinderswas investigated. Forbendiw snd torsion loads, test data and theory were correlated. Forexter.5moment of inertia of cutout cylinder cross section abouthorizontal diameter, in.4Jf i-Js, cu fi=distributed torsional
11、 moment of inertia of frame, f/d,Cu in.distributed torsional moment of inertia of stiffener,78/b,Cu in.torsionsl mment of “inertiaoftorsional moment of inertia offrsme spring constant per inchpsibuckling-stress coefficient forpressurebuckling-stress coefficient forbuckling-stress coefficient forleng
12、th of cylinder, in.frsme,in.4stiffener, in.4of effective span, P/bE,hydrostatic inwaxdtorsionradial inward pressureeffective length of axially cressed stiffener (fig. 2),in.bending moment, in-lbbending moment in uncut cylinder at general instability,in-lbaxial.wamformparameteraxial applied loading,
13、lb/in.shear applied loading, lb/in.applied circumferentialloading, lb/in. . .-. .-. .Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-6nPPcrP%Qt%qR%?%TTott=tftB%vvW)iiwwewx,yFNACA TN 3786circumferentialwaveform parameterconcentratedradial load applded
14、 to frsme to determineeffective spring constant, lbcriticel axial load for stiffener, lbpressure loading, psiparameter for bending general instabilityparameters for torsionsl general instabilitycylinder radius, in.shear. and compression-stressratiostorque, in-lbtorque at general instability, in-lbth
15、ickness of sheet, in.equivalent sheet thickness, in.distributed frsme sxea, Af/d, in.distributed stiffener area, As/b, in.effective thiclmess of sheet for shearingrigidity, in.shesr load, 1%tangential displacement, in.frame stiffnessparameters (eqs. (22) and (23)radial displacement, in.effective wid
16、th of sheet per side of stiffener, in.maximum radial U.splacement on inward-bulgebuckle, in.axial and tangential coordinates, in.distance from coordinate fiber to centroidal axis, in.,.-.-.-.-z .-. . - .-. . _ _ . . . .Provided by IHSNot for ResaleNo reproduction or networking permitted without lice
17、nse from IHS-,-,-N.AC.ATN 3786“7.,.z, Z.%!zz?8f%vw Yx%Puu=UcrYsection modulus for cut and uncut cylinders, cu in.cylinder curvatureparameter, (L2/R) (1 . v2)1/2(b2/Rt)(1 - #) 1/2plate curvatureparameter,distance to neutral axis of frsme plus effective sheetmeasured from sheet center, in. thalf angle
18、 of cut cylinder, radianspanel efficiency coefficientparsmeter related to wave-length ratio, n/mradial deflection of frsme uuder concentratedradial load,in.Solidityplasticity-reductionfactorangle of cutout, radianspsrsmeter for evaluating bending general instabilityPoissons ratio for isotropic struc
19、turesx and y Poissons ratios for orthotropic structuresframe section radius of gyration, in.stiffener section radius of gyration, in.stress,psicompressive stress at bending general instability,psicompressivebuckling stress of sheet, psicircumferentialnormal stress under external pressure atgeneral i
20、nstability,psi- . . . . . . . - . _ _ _Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-I8CrvSubscripts:0avcCYfsYNAcA TN 37%fshearing stress at torsional general instabilitygeneralizedplasticity-reductionfactorsheer buckling stress of sheet, psisheari
21、ng stress at shear genersl instability,psigeneral singleon cylinder cross section (fig. 2), radiansangle to terminus of inward bulge (fig. 2), radiansoptimum designaveragecompressioncompressiveyieldpertaining to framepertaining to stiffenery-dectionI.T,8.REVIEW CI?EXISTINGW!TAIntroductionThe present
22、 knowledge concerning the failure of stiffened curvedplates and shells is difficult to apply to engineeringproblems. Notonly sre *here discrepanciesbetween theory and test data, but in thecase of bending of stiffened cylinders,for example, two different setsof test data are in conflict.As a prelude
23、to the analysis of the existing data, which is theintent of this report, a review of these data appesxs in this section.The modes of tistsbility sre described, and a historical review of thetheoretical and experimental data relating to general instability ispresented. The information in this review
24、permits an assessment of thestate of the art in applying data on general instility to the solution “I-13. ._ _ _ . _ .Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-9.NACA TN 3786of engineeringart are listedproblems.in summaryThe deficiencies in the
25、 present state of thefOrmoThe emphasis of the present report is derived from this evaluationand is des it was found that a linear relation existed at low elastic stresslevels (ref. 13).Current State of the ArtTo summsrizethe state of knowledge:(1) A large mass of test data is avaikble on general ins
26、tabilityOf Cylid.erSunder bending and torsion hXdS . .(2)For bend, both GALCIT and PIBAL test data yield linear rela-tionships between failure strain and the GALCIT empirical parameter forthis case, although the two lines have different slopes.(3) For torsion, the GALCIT test data yield a linear rel
27、ationshipbetween fail.urestrain and the GALCIT parsmeter for this case at lowelastic fail.urestrains.(4) Mathematical theories for axial buckling predict general-insta-bility stresses sev=al times as great as the test values for bending.(5) Mathematical.theories exist for general instabilityunder ex
28、ter-nal pressure. However, no published test data are availablewith whichto ccmpsre them.(6) There are differtng views on the smount of notiinesrity associ-ated with bending instability of stiffened circular cylinders.Emphasis of Present Investigation.This report is devoted primarily to a examinatio
29、n of the methodsfor predicting bending and torsional general instability in stiffenedcircular cylinders. In addition, various theories on bWkling underpressure loadhg sre ccaupared.a71“ . Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-N1-xwm 3706 15
30、“IIThe principal targets are the apparent lack of agreementbetweenmathematical theory and test data and the difference between the GALCITand PIBAL test data, for bending loading. These discrepancies appear tobe attributable to the choice of section properties to be used in Taylorstheoretical bucklin
31、g stress expressions. The primary problems, in thisregsrd, seem to be the selection of effective values for the torsionalrigidities of the axial and circumferential stiffeners smd the shesrrigidity of the sheet. The frsme stiffness 6riteria of Hoff smd Shanleyaxe also discussed. Lack of suitable dat
32、a prevents an examination ofthe question of nonlinearity.The results obtained from the various theories for general insta-bility of ring-stiffened cyltiders under external pressure are camparedto determine the range of predicted stresses. The GALCIT test data formoderate-length cylinders in torsion
33、are compsredwith the explicittheoretical result obtained in reference 43.As willbe seen in the section on torsion general instability, atheoretical approach leads to an expression for the instability stressthat agrees with test data. There is also a theory available for generalinstability under exte
34、rnal pressure for which case experimented.dataare not available. In the case of bending general testability, compari-son of the theory of Taylor with a large amount of test data has revealedpoor agreement. The principal effort in the section entitled “BendingGeneral Instability” is devoted to a crit
35、ical examination of the testdata and of Taylors theory to determine whether inconsistenciesexist.If Taylors theory csn be shown to agree with test data, then a unifiedtreatment of general instability is possible since the differentialequations employed for bending, pressure, and torsional general in
36、sta-bility-are vhtudly the ssme. It would then remain to obtain test dataon pressure general instability for correlationwith theory.STRENGTH (IFSTHTENED CURVED PLAmsIntroductionPanel instability can occur in stiffened curved plates in any ofthe mode shapes pertaining to stiffened flat plates. As has
37、 been sug-gested previously, reference should be made to Part V (ref. 5) for adetailed discussion of this latter case for axial loading.In this portion of the report panel instability is discussed foraxial compression and shear loadings on stiffened curved plates. Eachtype of loading is discussed se
38、parately, after which interactionbetweenthese two loadings is described. . _ . . .Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-16Axial CompressionNACA TN 3786.When the strebgth of a flat stiffenedpanel is known, then it ispossible to select.transv
39、erse stiffeningto support the panel over anyspecified length. One approach to this procedure is through the assump-tion that the transverse ribs act as reflectional and rotational springs.When the minimum required spring constant is found the ribs can bedesigned.The proportions of the sheet and stif
40、feners are selected from dataon the buckMng stress and failure of curved webs and on the bucklingstress and failure of stiffeners,which may be found in references 1 to4. The freme regyimments may be satisfiedwith the aid of the datapresented in the section entitled :GeneralInstability.”When a flat p
41、anel is bent to a cticular curve the buckling stressof the sheet is increased. This leads to an increased effectivewidthof sheet acting with each stiffener,which tends to alter its columnstrength. This effect is small for practical structuralproportions,and the net gain in load-carrying capacity of
42、a curved stiffened sheetis little different from that of the correspondingflat sheet. Thisresult is demonstratedby Sechler and Dunn (ref. 46), who used the flat-sheetbuckling stress to determine we. Theti calctitions of ultimateload-carrying capacity of stiffened curved sheet panels agreed fairlywel
43、l with data fr 32 tests covering a large range of panel curvatures. .The relative insensitivity of panel instability stress to the effectof curvature is apparentfrom figure 3, in which data obtainedby Ramberg,.Levy, sndl?ienup (ref. 47) are shown. The ratio of curved- to flat-panelfailure stresses i
44、s plotted as a function of the curvatureparameter = b2/Rt. The change in failure stress is seen to be small, on theaverage, and appears to decreasewith increasing curvature.Additional data are provided by Sechler snd l)unn(ref. 46). How-ever, the scatter is large, and the end-fixity data are not inc
45、luded.Consequently, although an increasing trend of failure stresswith is indicated, it cannotbeIt must be noted thatcurved stiffenedpanels inevaluated accurately.there is a serious need for test data oncurrent use.shearThe analysis of stiffened curved plates smd shells in shear wasdevelopedby Kuhn
46、and his collaboratorsat the NACA through the.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-.a71NACA TN 3786 17modification of pure tension field theory by means of the reduction oftest data. This has resulted in a semiempiricalmethod of analysisdes
47、cribed by Kuhn and Griffith (ref. 48).The analysis devised by Kuhn and Griffith involves a sequence ofcomputationswhich require special charts that include the effect ofR/t, Tu/T, and the stiffener and frsme section properties. Thatreport should be consulted for a description of this method and for
48、asummary of the test data upon which it is founded.ConibinedShear and AxisllCompressionThe failure of curved stiffened sheet under conibinedaxial compres-sion sad shear was investigatedby Melton and Ensrud (ref. 49). means of an experimentalprogrsm on J-stiffened psnels of differentsheet thicknesses, they obtained curves of shear l
