REG NACA-TN-427-1932 Strength tests on thin-walled duralumin cylinders in torsion.pdf

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3、r networking permitted without license from IHS-,-,-Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICSTECHNICAL NOTE NO. 427STRENGTH TESTS ON THIN-WALLED DURALUMIN CYLINDERSIN TORSIONBy Eugene E. LundquistSUMM

4、ARYThis report is the first of a series presenting theresults of strength tests on thin-walled cylinders andtruncated cones of circular and elliptical section; itcomprises the results obtained to date from torsion (pureshear) tests on 65 thin-walled duralumin cylinders of cir-cular section with ends

5、 clamped to rigid bulkheads. Theeffect of variations in the length/radius and radius/thick-ness ratios on the type of failure is indicated, and asemi-empirical equation for the shearing stress at maximumload is given.INTRODUCTIONA survey made about a year ago of the available in-formation and the me

6、thods employed in the design ofstressed-skin structures for aircraft revealed that the de-sign of structures of this type is based largely upon theresults of experience and data obtained either from testson structures similar to the one under consideration orfrom tests on the particular structure un

7、der consideration.A study of the existing reports of static tests upon mon-ocoque fuselages and stressed-skin wings resulted in theconclusion that very little reliable informatiom of a funda-mental character concerning allowable stresses could be ob-tained from full-scale tests already made because

8、no men-tion was made of the properties of the material and be-cause failure of the structure as a whole was caused by avariety of different types of failure in the skin, rein-forcement, and connections. Consequently, the _TationalAdvisory Committee for Aeronautics, in cooperation withthe Army Air Co

9、rps, Navy Bureau of Aeronautics, and the Bu-reau of Standards, Department of Commerce, has outlined aresearch program to investigate stressed-skin structuresfor aircraft.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-2 N.A.C.A. Technical Note 5re. 4

10、27As a part of this research program an extensive seriesof tests on thin-walled duralumin cylinders and truncatedcones of circular and elliptical section is being made atLangley Field, Va. In these tests, the absolute and rela-tive dimensions of the specimens are being varied to studythe types of fa

11、ilure and to establish useful quantitatived_.ta in the following loading conditions: torsion, com-pression, bending, and combined loading.This report is the first of a series presenting theresults of these tests; it comprises the data obtained inthe torsion (pure shear) tests on thin-walled duralumi

12、ncylinders. Although the tests have not as yet been com-pleted, it was thought advisable to publishthe resultsthus far obtained.MATERI ALThe duralumin (AI. Co. of Am, 17ST) used in thesetests was obtained from the manufacturer in sheet form inthicknesses ranging from 0.0105 to 0.0228 inch. The prop-

13、erties of the material as determined by the Bureau of Stand-ards from specimens selected at random are given in TableI, Typical stress-straln curves taken longitudinally andtransversely to the direction of rolling are given in Fig-ures I and 2.Upon reference to the above-mentioned table and fig-uros

14、 it will be observed that the modulus of elasticity issubstantially the same in the two directions of the sheetbut that the ultimate strength and yield point are consid-erably lower transversely to the direction of rolling thanlongitudinally. However, as all the cylinders testedfailed at stresses co

15、nsiderably below the yield-pointstress, the difference in the strength properties in thetwo directions has no bearing on the results.SPECIMENSThe test specimens consisted of right cixcular cylin-ders of 7.5 and 15.0 inch radius with length_ ranging from2.25 to 45.0 inches, which were constructed in

16、the follow-ins manner. FSr_-t, a duralumin sheet _as cut to the di-mensions of the developed surface, The sheet was thenwrapped about and clamped to the end bulkheads, (See figs.iProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-q , ,N.A.C.A. Technical

17、 Note No. 4273, 4, and 6.) With the cylinder thus assembled, a buttstrap 1 inch wide and of the Same thickness as the sheetwas fitted, drilled, and bolted in place to close theseam. In the assembly of the specimen, care was taken toavoid having either “soft Spots“ or wrinkles in the wallswhen finall

18、y constructed_iThe end bulkheads, to which the loads were applied,were each constructed of two steel plates one-fourth inchthick separated by 1 inches of plywood core. The_e p_rtswere bolted together and turned to the specifled outsid_diameter. Steel bands approximately one-f0urth inch thickwere use

19、d to clamp the duralumin sheet to the bulkheads.The_e bands were bored to the same diameter as th_ bulk-heads.APPARATUS AND _ETHODThe thickness of each sheet was measured to an esti-mated precision of_.0003 inch at a large number of sta-tions by means of a dial gauge mounte_ in a special Jig.The ave

20、rage thicknesses of the sheets were used in allcalculations of radius/thlckness ratio and stress.A photograph of the loading appare.tus used in thetorsion tests is shown in Figure 3. The lead from thejack was applied through a thrust bearlng to a yoke. Bymeans of a flexible cable that passed over _.

21、 series of _,ul-leys, half of the load was tranBmltted to one end of thelower horlzonta_ beam as an up load and the other half wa_transmitted tu_,ugh the rectangular frame to the Otlo_r endof the same be(_m as a down load In this nanner tor_-_eunaccompanied by transverse shear, was applied to th_ _D

22、ec-imen. A shec_r load on the cylinder caused by the weightof the apparatus, including the forward bulkhead and b_nd,was balanced by a counterweight as shown in Figure S.In order to determine the possible errors caused byfriction in the joints of the frame, _ spe_isl test w_smade in which thu moment

23、 applied to the loJer beam wasmeasured directS y and compared with the monent calculatedfrom the force applied by the jack. Theso two momentswere found to _iree within i per cent throughout the r_ngcof moments applied.Loads were applied by the jack in increments of _bout1 per cent of the estimated l

24、oad at failure, except afterProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-4 N.A,G.A. Technical Note No. 427the first few tests had been made when the first incrementof lead was about half the estimated load at first wrln_;le.At first wrinkling Ohm

25、or more diagonal wrinkles began toform and greW, steadily in size and number until failureoccurred by a sudden increase in deformation and the for-matien of wrinkles in the complete circumference. (S_efig. 4.) In all the tests 6 to l0 minutes elapsed fromthe tlmo that lead was first applied to the s

26、pecimen untilf_.ilure occurred.For the very short specimens (length/radlus ratios of0.5 or loss) deformation following failurewas accompaniedby an increase in load, whereas for all other specimensdeformation following failure was accompanied by a decr_sein lead. (See fig. 6.) In order to insure that

27、 the record-ed loads at failure for the short specimens were correct,two dial gauges were used to measur_ the twist of the cyl-inder between bulkheads (fig. 6) and the load at which asudden increase in deformation occurred, as determinedfrom a lead deformation curve, was recorded as the lead atfailu

28、re.DISCUSSION OF RESULTSThe s_rength of thln-walled circular tubes subjectedto torsion has been treated theoretically in references 1and 2. In reference I equations are given from which itis possible to calculate tile critical stress but the compu-tations are tedious and Involved and have been made

29、onlyfor radius/thickness ratios far below those usually en-countered in stressed-skln structures for aircraft. Inreference 2 relatively simple equations are given for thecritical stress but these could not be checked by the re-sults herein reported. Consequently, no consideration iagiven to the corr

30、elation ef the 8xperlmental results withtheory in this report. However, when the general invest!-gatlon of the strength of thln-walled cylinders is com-pleted this correlation will be attempted.The results shown in Figures 7, 8, and 9 are self-explanatory. They show that for geometrically similarcyl

31、inders, the number o_ shear wrinkles, the angle betweenthe wrinkles and the cylinder elements when the wrinklesstart to form, and the shearing stress at failure, areconstant. For any given value of the radius/thickness ra-tio, the number of shear wrinkles, the angle between thewrlnkles and the cylin

32、der elements when the wrinkles startProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-N.A.C._, Technical: _3ot:_ _o. 487: 5to form, and the she_ring stress at failttra all decreasewith increase in the length/radius ratio. For any givenvalue of the leng

33、th/radius ratio, the number of shear wrin-kles increases with increase in the radius/thickness ratio,but the angle between the wrinkles and the cylinder“ ele-ments when the wrinkles start to form and the shearingstress at failure both decrease.As first wrinkling occurred in many of the specimensbefo

34、re ft,!lure, shearing stress at first wrinkle as a per-centage of shearin_ stress at failure has been plottedagainst the length/radius ratio in Figure i0. It will benoted that the points scatter widely but show a generaltendency for first wrinkle to occur at a lower percentageof stress at failure fo

35、r the thinner sheets than for thethicker sheets. This fact is attributed to the presenceof waves :and dents in the thinnez sheets which caused thecylinders constructed from this material to be, relativelyspeaking, less perfcc_ than cylinders Constructed fromthethicker material.As the experimental po

36、ints for shearing stress atfailure in Figure 9 plot _long smooth curves irrespectiveof the wide scattering of thepoints for stress at firstwrinkle in Figure I0, it Is concluded that the presenceof first wrinkling did not reduce the strength at failureto any appreciable extent.An examination of the d

37、ata plotted in Figure 9 indi-cated that the shearing stress at failure could be givenvery closely by an equation of the general form= (l)sst/where, for a given material, n is a constant and K isa function of the length/radius ratio of the cylinder. Inthis equation K has the dimensions of a stress. A

38、s the-oretical calculations always show that the stress at whichelastic instability occurs varies directly with E, themodulus Of elasticity, equation (i) will be written in thefollowing form:ss , (2)Ks E=T / f - ,Provided by IHSNot for ResaleNo reproduction or networking permitted without license fr

39、om IHS-,-,-6 N,A.C,A. Technical Note _o. 427where Ks is a nondlmensional constant. In all the cal-culations for the e_valuation of Es and n the secant modulus for Ss, the stress at failure, is substitutedfor E.The numerical value of n is established by the neg-ative slope of straight lines on the lo

40、garithmic plot ofSs/E against r/t in Figure ll. Actually, t1_e value ofn is not constant but varies somewhat with length/radiusratio. For the purpose of this report, however, an aver-age value of 1.35 was used.Values of Ks for n = 1.35 have been calculatedfor each test and plotted in Figure 12. In t

41、his figurethe greatest dispersion of the points occurs at a length/radius ratio of 1.0 for the 7.5-inch-radius cylinders withradius/thickness ratios between 830 and 700. Consequent-ly. the dispersion of all other points may be consideredto bewithin the experimental error.Strictly speaking, equation

42、(2) with the values of nand Ks derived from these tests applies only to duralu-min cylinders for the range of lengths, radii, and thick-nesses tested. It is now planned to extend the tests uponduralumin cylinders and also to make a few tests upon steelcylinders in order to generaiizo the conclusions

43、 or to makesuch modifications to them as may be necessary, particu-larly at low values of the length/radius r_tio.CONCLUSIONSI. For geometrically similar cylinders, the number ofshear wrinkles, the angle between the wrinkles and the cyl-inder elements when the wrinkles start to form, and theshearing

44、 stress at failure, are constant.2. For any given valne of the radius/thlckness ratio,the number of shear wrinkles, the angle between the wrin-kles and the cylinder elements when the wrinkles start toform, and the shearing stress at failure all decrease withincrease in the length/radlus ratio.3. For

45、 any given value of the length/radius ratio, thenumber of shear wrinkles increases with increase in theradius/thlckness ratio, but the angle between the wrinklesProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-N.A.C.A. Technical Note No. 427 7and the

46、cylinder elements when the wrinkles start to formand the shearing stress at failure both decrease.4. The presence of slight imperfections in the cylin-der may cause wrinkling to occur at loads considerably be-low the load at failure, but these imperfections apparent-ly 8o not reduce the strength at

47、failure to any apprecia-ble extent.5. The shearing stress at failure for thfn-walIed du-ralumin cylinders may be given very closely by an equationof the formK s ESs = where n is a constant and Ks varies with the length/radius ratio, %/r. As atentative value, n may be as-sumed equal to 1.35. Values o

48、f Ks corresponding to thisvalue of n are given by the faired curve in Figure 12 orby the following table:Z/r 0.2 0.25 0.3 0.4 0.5 0.751.0 1.5 2.0 3.0 4.0 5.0K s 3.3 2.75 2.45 2.02 1.78 1.451.27 1.06 .94 .78 .68 .61L.-.n_ley l_lemorial Aeronautical Laboratory,National Advisory Committee for Aeronautics,Langley Field, Va., July 25, 1932.REFERENCESi. Schwerin, E.: Die Torsions - Stabilit:_t des Dunnwand-igen Rohes. Z.f.a.?.L Vol. V, No. 3, pp. 235-243,incl. June, 1925.2. Sezawa, Katsutada, and Xubo, Kei: The Buckling of aCylindrical Shell under Torsion. Report No. 76,Aero. Res