REG NACA-WRL-67-1940 The Effect of Internal Pressure on the Buckling Stress of Thin Walled Circular Cylinders Under Torsion.pdf

1、A* $+*NATIONAL ADVISORY COMMITRE FOR AERONAUTICSWAlrmm IUNDOIW!ORIGINALLY ISSUEDMq 1944asAdvenoeRestrictedReportLkEZ27THEEE!EEcTa?ImERNALmoNTHE STRESSOF THIX-W- CIRCULARS _ TORSION!.By Hmold Crate,S.B. Batdorf,andGeorgeW. BaabLangleyMemorialAeronauticalLaboratoryLangleyField,Ta.NACAN A. c A li!?llji

2、jiy”LAIvGLEY MEMORIAL AERONAUTICALWASHINGTON LABORATORYLaey Field, v%NACA WARTIME REPORTS are reprints of papers originaLly issued to provide rapid distribution ofadvance research results to an authorized group requiring them for the W= effort. . They were Pre-viously held under a security status bu

3、t are now unclassified. Some of these reports were not tech-nically edited. All have been reproduced without change in order to expedite general distribution. .L-67k,$,IhProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA ARR Nom IM127NATIONAL ADVIS

4、ORY COMMITTEE- . -t-,- ., - ,-. VANCE RESTRICT$ZD”.,., . .FOR AERONAUTICSRZPORT . .,THE El?l?MITOF INTERNAL PRES ON THE BUCKLING STRESSOF THIN-WAILED CIRCUIJLRCYLIND-ZJK!UNDER TORSIONBy Harold Crate, S. B. Batdorf$ and George W. BaabsmtimThe results of a series of teets to determine theeffect of int

5、ernal pressure on the buckling load of athin cylinder under an applied torque indicated thatInternal pressure raises the shear buckling stress.The experimental results were analyzed with the aid ofpreviously developed theory and a simple interactionformula was derived.INTRODUCTIONThe curved metal sk

6、in of a modern airplane Inflight is subject to streses that may cause the skinto buckle, ar.dproper design of airplane structuresrequires a lmowledge of the tress conditions underwhich buckling will occur. The ability to etimate thebuckling point under combined loading conditions is ofparticular imp

7、ortance.In order to detennlne the effect that normal pres-sures or air loads, might have on the critical stressfor curved sheet, two preliminary tests were made (ref-ences 1 and 2). A pronounced increase in criticalstress with increase in normal pressure was found, andthe subsequent interest shown b

8、y the aircraft industryin this subject Indicated the desirability of furtherstudy,No well-established theories for buckling of curved-sheet panels either In torsion or under hydrostaticpressure are available; hawevers satisfactory theoriesfor buckling of complete cylinders under these loadingshave b

9、een advanced (references 3 and 4). In order toeffect some correlation between theory and experlment$.-. . .-. . . .Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-. .2 NACA ARR No. L4E27therefore, an investigation was made of the influence of:Interna

10、l pressure on the critical stresses of thincylinders in torsion. Experiments were conducted todetermine the critical shear stresses for four cylinderlengths at a number of different Internal pressures.The theories and the experimental data were used in con-junction to determine an Interaction formul

11、a for thebuckling of cylinders of moderate lenth under the com-bined action of torsion and internal pressure.EGLoLtdrP()cr Tcr()cr P=O%shear modulus of elasticity, pstlength of cylinder without rings, incheslength of cylinder between rings, inchesthickness of cylinder wall, inchesdiameter of cylinde

12、r, inchesradius of cylinder, Inchesinternal pressure of cylinder, consideredpositl.vewhen it produces tensle stressesIn cylinder walls, psicritical pressure in the absence of torsion(negative acc:iito sign conventionadopted for*shear stress In cylinder walls due to appliedtorque, psivalue of shear s

13、tress when cylinder is at thepoint of elastic instability, PSIcritical shear stress in the absence ofinternal pressure, psipressure ratio(*). . . - _ . .Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA. . . .iqeKsring3:.()cr“”-shear-stress -ratio

14、. ,.“” “exponent of R in the interaction formularotation of free end of cylinder, radianscoefficient used in Lundquist?s empiricalformula (appendix A)differences in straingage readingsPoisson?s ratioSpecimens AND TEST PROCEDUMDiagrams of the test-cylinder construction andsystems used are Klven in fi

15、ure 1. The cylinderwas-made from 0.032-inEh 24S-72al-minum-alloy sfieetclosely riveted around two heavy steel rings, one ateach end. The sheet was joined along an element of thecylinder with a butt joint covered with a single strapon the outside. RlnCs made of 24S-T aluminum alloywere added to this

16、cylinder and divided it into shortercylinders, the lengths of which were equal tc the ringspacings.Figure 2 is a photograph of the apparatus used totest the cylinder. The ends of thelcylinder wereclosed by heavy flat steel plates in order that aircould be maintained under pressure inside the cylinde

17、r.The weights of the steel plate and test ring at thefree end of the cylinder were neutralized by an upwardload on one of the torque arms. Rotations of the freeend of-the cylinder relative to the floor were measuredby a pair of dial gages.Observed buckling loads at zero and at low internalpressure w

18、ere determined as the loads at which therewas a sudden snap of the cylinder to the buckled state.This snap action was in many cases preceded by a slowgrowth of visible wrinkles in the cylinder walls as theload increased and a greatly increased rate of growthof the wrinkles at close ,proximity to the

19、 snap-bucklingload. With increases in the Internal pressure, theProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-.,;“ I4 2-TACAARR ITo.L4E27snap decreased in violence until it was no longerobservable. In these cases the buckllng load was esti-mated, o

20、n the basis of visual observations, to be thatload at which the rate of growth of wrinkles with loadwas cmparable with the rate of growth of wrinkles justprior to buckling In those cases in which snap bucklingQld oeeur.The Southwell method of detemlnln this figure indicates that the buclclingstresse

21、s increase as pressure increases. The resultswere essentially the same whether the visual or theSouthwell method of determining buckling loads wasused, although the Southwell method usually gaveslightly higher loads than the visual.The buckled cylinder could be returned to theunbuckled state.either

22、by decreasing the torque or byincreasing the pressure. The loads at which the bucklesdisappeared were determined visually for cylinders 1,2, and 3a, and are also shown in figure 5. These loadswere not recorded, however, for the remaining cylindersbecause of a large scatter in the readings. ThisProvi

23、ded by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-6 NACA ARR No. L4E27scatter is attributable to the fact that, as the cylln-ders became shorter, the disappearance of the bucklesbecame more gradual and the visual selection of a“ became difficult. In the cas

24、e“point of disappearanceof cylinder 2, in which the readings are relativelydefinite, the location of the curve indicating disap-pearance of buckles was the same for elther”an increaseof pressure or a reduction of torsion.The method used to find the interaction formulabest representing the experiment

25、al data is given inappendix A. The analysis leads to a formula of thetypeRsq+y=lwhere the value of the exponent q depends upon theassumptions made for (Per).=o and (Tcr=O- orcyllnders of moderate length, which according toDomells analysis satisfy the inequalitythe exponent q ts equal to 1.89 to 2 Us

26、ing crderived from Donnell!s theoretical curve, the exactvalue depending on the value of L2/td concerned.When Tcr derived from Lundquist!s empirical formulaIs used, q = 2.17.In figure 6, curves representin the exponents1.89$ 2, and 2.17 are drawn through the experimentaldata of figure 5 replotted by

27、 a method explained inappendix A. The three curves lie close together and,so far as fit of deta is concerned, llttle basis existsfor a choice among them. Simplicity and proximity tothe average value; however,The equation then becomesRa2 +recommend use of q = 2.%=1Provided by IHSNot for ResaleNo repr

28、oduction or networking permitted without license from IHS-,-,-NACA ARR No. L4E27 7The parameter L2/td, which according to theory. detelngs buckling behavior, may be varied by cngingthe lerth*hlckiess, diameter,”or any combination ofdimensions. For this reason, the restriction of thetests to one thic

29、kness and one diameter probably doesnot constitute a significant 10ss In generality.The question of theappllcabllity of the formula tocurved panels is dlscusaed briefly in appendix B.CONCLUSIONThe critical stress of a cylinder in torsionIncreases as the internal pressure increases. The fol-lowing In

30、teraction formula was found to representapproxtiately the buckling of a cylinder of moderatelength under the combined effects of torsion and internalpressure:Rs2+Rp=lwhere Re Is the ratio of crltlcal shear stress withInternal pressure to critical shear stress withoutinternal pressure and P Is the ra

31、tio of internalpressure to the critical pressure In the absence oftorsion.Langley Memorial Aeronautical Laboratory,National Advisory Committee for Aeronautics,Iangley Field, Vs .: . .Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-. .8 NACA ARR No. L

32、4E?7APPENDIX ADERIVATION OF IN1ERACTIONFORMULAIntroductory DiscussionAny attempt to detemnine whtch of the conventionaltypes of interaction formulas best fits the experimentaldata presented h this paper Is complicated by the.questlon of which values to use for (C,),=. dUcr)=.o Experimental values fo

33、r (dt=o- ereobtalfied,but the corresponding experimental values of()cr T=O were not InvestlSated because of the destruc-tive effects on the cyllnder Involved In such a test.A stiple experimental result makes possible a derivationof an interaction formula without necessitating assump-#tlons concernin

34、g stress rattos or the type of formulato be used.The experimental data appear to indicate that theinteraction curves far the four cylfnders tested areIdentical, dlfferlng only In posttlon. (See fig. 5.)The effect of a change of length appears to be a shiftof the curve parallel to the pressure axis.

35、In fig-ure 6 this effect Is made clearer by pl.ottlnga 1 theidata to a common p-intercept. The curve for = 1.43Is shifted parallel to the p-axis a distance eqal to-(per).=o (as given by equation (5) which follows) Inorder to make the p-intercept zero. Each of the othercurves 3s then shifted the prop

36、er distance for bestsuperposition. The relatively slight scatter showsthat the experimental curves are nearl superposable.If .ttis ased that the interaction curves fordifferent lengths of cylinder are for practical pur-poses identical, a computation of the equation for thecurves from theory is possi

37、ble. Among the points onthe curve of figure 6 arc four, indicated by modifiedsymbols, representing the special case p = O for thefour values of the length. Because the curve of figure %represents Tcr ( crT=Oplotted against p- p these four()points represent Tcr plotted againstp=o ()- cr T=O. .Provide

38、d by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA ARR NO. L4E27m . fon varlos, yalues of the length, The fotiacurve can therdfofie”-”beobtained”by eliminatinglength from the equations expressing (7cr)p=09fo”tithist%?. -and()pcr =o in terms of L, d, and t

39、. The inte?actloncurve for a cylinder of given dimensions can then beobtained by shifting the origti to make the p-interceptequal to pcr)T=Oformula may then besions for rdp=oand transforming tofor that-cylinder. The Interactionderived by ftndtng simplified expres-and ()cr T=os eliminating L,give the

40、 final fomula.Simplified Expressions for ()cr P=OTwo simplified expressions for (Tcr)p=o arederived, the first based on Donnell?s curve (reference 3)and the other on Lundquists formula (reference 6).Donnells theoretical result for the shear bucklingstress of thin-walled cylinders with simply support

41、edends subjected to torsion is given by the solid curve offigure 4. For cylinders of moderate length, the curveis nearly a strai?t line given by the equation()cr P=o = 1a44+J0”53($J1265 la)while for extremely large values of L2/td a betterfit is given by the equation of the asymptote()Cr p=() = 1=27

42、E($-0”5(w”25This essentially straiht portionincluded between the limitsof the curve is()L2 0.5,0-0.46 .KS = 1.27 ;At L/r = 0.35 (approximately the lower llmlt ofInequality (2) for the cyllnder tested), the error inthis formula js about 7 percent. Use of this value ofKS leads to the formulaTCr p=o =

43、20364ir”4($-1”35Simplified ?ZZpressionfor ()pcr =o(3)A formula based on work by von Mises and developedat the David Taylor Model Basin (equation (10) of refer-ence 7 for the bucklin of a closed cylinder underhydrostatic pressure may be writtenIf, as in the inequality (2),#(4)(Y34.7.0-%“ - Figure 2.-

44、 Test setup. ,zo.%J.dFlat sheet valuy / “,” Tabte3, referenca3 “1 ,.”/ - Recommended fordesign;reference 340 e - STmighT line apptmximaion .-/ A* I. A ,.O- usect his paper,/ I,/I II , * Assufhed lower limit of validily of approximationI i10 W$ 10+ .810$Figure 4.-CrMca! Sheur W%?ss for thhwakd cyhk?r

45、65”r 0.081” Appmv(. 53”8Section of rib at center Uned panelfigure8.-Curved-5hQet ,.-, , -,., ,. , ., .,.,-,-ll-panels of reference2., ,Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-108(64 a71c200Figw/Intemctkmckw, R+kp=lo TestntsNATIONAL ADVISORYCO

46、MMITTEE FOR AERONAUTICS.1 2 4PreS9&, psi9.- I nkmction fbrmla oppliadto curwdof refar4mcu 2.s 6panel SpOcimanszo.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-If *., 0 ,v.,Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-