1、/I iNATIONAL ADVISORY COMMITTEEFOR AERONAUTICSTECHNICAL NOTENo. 1197SOME INVESTIGATIONS OF THE GENERAL INSTABILITY OFSTIFFENED METAL CYLINDERS,_ VIII - STIFFENED METAL CYLINDERS SUBJECTED TOPURE TORSIONBy Louis G. DunnCalifornia Institute of TechnologyWashingtonMay 1947Provided by IHSNot for ResaleN
2、o reproduction or networking permitted without license from IHS-,-,-NATIONAL _LUVISORY COMMITTEE FOR AERONAUTICSTECHNICAL NOTE NO. iI_SoMEI_EmIGATIO_SOFT_ GmmRAL_S_ZL_Y OFS_IF_m_D_ CYL_VIII-STIF_ED_ CYLINDERSSUB_CTED_0PURE_O_IO_By Louis G. I%umSUMMARY .An experimental investigation of the general in
3、stability of reinforcedthln-walled metal cylinders was carried out at the California Institute ofTechnology. The basic parameters involved were the spacing and sectionalproperties of the stiffening elements, the wallthlckness, and_the die_e._ter of the cylinder. An analysis of the experimental _ata
4、led to a suita-ble parameter for estimating the genera_-instabillty stressof reinforcedmetal cylinders when subjected to pure torsion loading._IV2RODUCTIONThe present report deals with the experimental investigation of thegeneral instability of metal cYli2derssubjected tGpureotorsion loading.Reports
5、 on other loading conditions, that is, pure bending, combined bend-ing and transverse shear, and combined bending and torsion, have been pub-lishedpreviousl_ (references 1 to 7). _ _Inasmuch as a condition of a Puretorsional loadseldom arises in thedesign Of fuselage or wing Structures, _hepr0blem o
6、f pure torsion as suchmight not warrant ah investigation. However, under a C0mbinedloading ofbending and torsion (reference 7) the ultimate load of the stiffened cyl-inder is dependent on the ratio of_the shearing Stress atfailure for com-bined loading to the shearing stress _t failure for pure tors
7、ion. Hence,in order to predict the ultimatestrength of a Stiffened metalcylin_ersubjected to combimed bendiz_ and torsion, a knowledge of the ultimatestrength of the cylinderwhen subjected to a pure torsion loading is nec-essary._Because of the nonlinearity of the buckling problemof stiffened cylind
8、ers (cf. references _ and 8), noa_tempt has been made to give a theo-retical treatment of the problem. As given in the present report, theProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-2 NACA TN No. 1197 iparameter for predicting the ultimate streng
9、th of stiffened metal cylin-ders subjected to torsion loads is based on an analysis of the experi_-mental results and on the existing theory of unstiffened metal cylinders.This method was preferred over that of a linearized theory which cannotcorrectly describe the behavior of thestructure. Theresul
10、ts 0fa lin“ :ear theory would have to be modified and corrected to bring it intoagreement withtheexperimental observations and thus.thetheory _wouldimmediately be rendered an empirical method.This investigation was carried out by the California Institute ofTechnology under the sponsorship and with t
11、he financial assistance ofthe National Advisory Committee for Aeronautics. SYMBOLSMT applied.torsional moment, inch-pounds .MTcr applied torsional moment at skin bUckli_, Inch-pounds ._,Nr2z2_: applied torsional moment at failure, inc_-_olmds7 shearing stress in the sheet covering, pounds per square
12、 inch7cr buckling shear stress of the .sheetcovering, pounds per.square inch7msx shearing stress in the sheet covering at failure_ pounds persquare-inch “ “_- at tensile stress of diagonal-tenslon field, pounds per square inch -P tension load resultin N from _t acting, over a unit circ_Lfer_tial.wid
13、th of sheetl acts in the direction of cos._ pounds. 6PH longitudinal component of P_ pounds. .,. :PV circumferentlalcomponent of P,- pounds -angle0f diagonal-tension field with reference to a longitudina 1stiffenerCst strain in a longitudi_i stiffenerG shear modulus, pounds per square inchE Youngs m
14、odulus, pounds per square inchProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA TN No. 1197 3GE effective shear modulus, pounds per square incht thickness of sheet covering, inchesA area enclosed by sheet covering, square inchesR radiusof c_linder
15、, inches “ _,L length of Cylinder, inches _ :b spacing of 10Z4itudinals , inches d spacing of frames, inchesDx radius of gyration of a longitudinal and effectivesheet , ipches. - . .py radius of gyrat_0nof a frame and effective sheet_!nches .,“, ,DESCRIPTION OF APPARATUS.- . . -/ - .A.il tests were
16、conducted_in the combined bending and torsi0nma0hlneof the structures laboratory_at GALCIT This machine has a maximumcapacity of 900_000 inch-pbunds. Adetailed description of the machineis given in reference 2. A photograph (fig. l) shows a lO-inch-diametercylinder mounted for a pure-torsion test. _
17、 The wire,strain-gage equipment, as used for the strain measurements,has been described in reference 6. The circumferential position of thevarious gages is shown in figure 2. Longitudinallythe gage is mountedat the centerof the speclmen_ :-._- TEST PROCEDURE“? f “The test specimens were all circular
18、.reinferce_metaX cylinders,Two sizes of specimens were tested, one series having a diameter of 32inches and a length of 64 inches, and the other series, a diameter of 20inches and a length of 40 inches. The sheet covering was 0.010-3 0.01_-, and 0.020-inch-thick 24ST dural. The:longitudinal reinforc
19、ing membersconsisted of round 24ST dural tubing drawn to an elliptical shape andthe frames consisted of rectangular bars of 24ST Alclad. Longitudlnals- of three different wall thicknesses and frames of two different sizeswere used. A sketch of the reir_forcingmembers is presented in figure 3.Provide
20、d by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-4 NACA TN No. 1197A diagram showing a sheet panel bounded by two longitudinal stringers andend mounting rings is presented in figure 4(a). The relationship of theforces acting on an element of sheet of unit wi
21、dth is given in figure 4(b).In table I the sheet thickness, the reinf0rclngmembers, and their spacingare listed for each specimen. Stress-strain curves of the materlals usedin the tests are shown in figures _ to 12.All test specimens were tested in the combined torsion and bendingmachine mentioned p
22、reviously. In the pure torsion loading, the bendingarms and one torsion arm were locked In place, the load beingapplied tOthe second torsion arm. In all tests_ shear stresses, in the sheet cover-ingwere not measured_ inasmuch as itwas assumed that a Calculation ofthe shear stresses based on the clas
23、sical formula“ 7 = MT/2At _ (!)would be sufficiently accurate. Strain measurements of the_inducedstresses in the longitudinal members were made on all specimens, thestrain measurements being made by means of electric strain gages as de-scribed in reference 6. For a number of specimens_ the unit angu
24、lardeflection as a function of the applied torque was measured. By measur-ing the differential displacement between two pointers mounted on thecylinder, the unit angular deflectioncould be calculated. Thepointersconsisted of triangular frame structures and are shown mounted on thespecimen in figure
25、13, _Mountlng these pointers on the cylinder just in-board-of the end-rings ensured that the entire measured deformation oc-curred in the cylinder. : ,The effective shear modulus was calculated in the following manner:If “ :2 length of the pointer measured from the center of the cylinder,inches5 mea
26、sured differential displacement between the two pointer, inchesZ distance between the pointers3 inches ._ . then the unit angular displacement is given .by_: . . . .and the effective shear modulus IsProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NAC
27、A TN No. i197 5MT_tGE- (2)Some attempts were made to measure the wave form of the buckledsheet as a function of the applied torque; however, considerable diffi-culty was encountered in these measurements, primarily because of thenonuniform buckling which occurred over the cylinder, it was found that
28、,in the testing of a cylinder, buckling of individual Panels, that is, asheet panel bounded by two frames and two longitudlnals, would vary by asmuch as 100 percent. For this reason it was thought that a measurementof the wave form and wave amplitude _as a function of the applied loadwould be rather
29、 meaningless. Photographs of a number of typical failuresare shown in figures 13 to 17. TESTP SULTS .Results of the induced longitudinal strain as a function of the ap-plied torsional moment are shown for 17 specimens in figures 18to 34.Each curve represents the average of two strain gages mounted o
30、n diamet-rically opposite sidesof the longitUdinal stiffener. _The induced strain is associated with the shear buckles in the sheetcovering. It can be readily seen that upon buckling of the sheet, longi-tudinal forceswhich act on the end mounting rings are introduced by thesheet covering. These forc
31、es have a tendency to pull the end mountingrings together and, since such a motion is resisted by the longitudinalstiffeners, the result is an induced strain in thesemembers. In theappendix some calculations have been worked out on themagnitude of theresulting strains. The calculated values do not a
32、gree too wellnumeri-cally with the measured values; however, the order of magnitude is cor-rect.The results of induced strain as a function of applied torque havebeen cross-plotted as shown in figures 35 to 46. The strain wasplottedradially outward with thecylinder circumferences asthe zero referenc
33、eline. These curves indicate that in general the induced strain is dis-trlbutedunlformly around the cylinder.In addition to the foregoing test data, the measurements of the ef-fective shear modulus as a function of the shearing stress in the sheetcovering are given in figures 47 to 93, Atthel0wer sh
34、ear-stress values,the results are not very reliable because of the difficulty in measuringthe resulting small deflections, At the higher values of T the resultsare sufficiently accurate to indicate the order of magnitude of theProvided by IHSNot for ResaleNo reproduction or networking permitted with
35、out license from IHS-,-,-_. _ 97effective shear modulus which may result in an actual structure. It isof interest to note that the effective shear modulus GE is considerablyless than 0.625G, which Is the theoretical value for the fully developeddiagonal-tension field of a flat plate.In presenting th
36、ese experimental data, it would be More apporpriateto use the ratio T/Tcr rather than_ T or MT since all the measuredquantities are associated with buckling. However, as previously men-tioned, for the cylinders tested3 buckling.did not occur uniformly over.the cylinder at a definite load. The buckli
37、ngprocess was progressiveanduniformbuckllng occurred, forsome specimens, atmore than twice theload at_hich the first buckles appeared, For this reason, it was notpossibleto establish a definite observed buckling value.In determining a parameter for predicting the general instabilityfailure in torsio
38、n, the same general procedure was followed as was usedin the pure-bending investigation of reference 5. The variables to beconsidered are the same as those of the pure-bending problem and canagain be divided into two groups_ namely, those dealing with the geo1_-etry of the str_cture and those involv
39、ing the sectional propertiesofthe stiffening elements as well as the sheet covering. The geometricalvariables are the longitudinal spacing b, theframespaCi_ _,_ thediameter, and the length of_thecylinder. The second group of_vazlablesincludes the section properties of the longitudinals and frames an
40、d thethickness of the sheet covering. _ . ! _.A number _of specimens: were _tes_e_d_in which the geometr_c_l _a_iablesb and trial cal-culations indicated that the best results were obtained if the totalwidth of sheet was used. For this reason Dx and py were calculatedwith the entire width of sheet a
41、ssumed to be effective. The variation of0x and Dy, with flat sheet assumed, as a function of the effectivewidth of sheet we is shown in figures 59 to 63.Specimens were also tested in which both the sheet thickness and sec_$ional properties of the longitudinals were _aried. The results of all-tests a
42、re shown plotted in figure 64. It is seen that up to values oflO,O00 pounds per square inch all test values scatter closely_oout astraight line. For higher values of Tmax there is a sudden shift inthe experimental values. However_ the majority of tests again follow astraight line having the same slo
43、pe as the line corresponding to thelower values of Tmax. Since the observed diagonal-tension field variedbetween about 30o to 50O, it is seen from equation (3) (see appendix)that for a shear stress of lO_000 pounds per square inch the correspond-ing tensile stress would be between 20,000 and 23,000
44、pounds per squareProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-8 NAOA TN No. 1197inch. It was thought that this tensile stress might be sufficiently closeto the _roportional llmit of the sheet:cowering $o explai_ t_e suddenshift in the experimental
45、 values. However1 an examination of the stress-strain curves (figs. 9 to 12) indicates that the tensile stress at ashear stress of I0,000 pounds per square inch is well belowthe propor-tional limit.A more desirable presentation of the test data would be to plotshearing strain 7. Such a presentation
46、would be more general a_d wouldallow for materials of different physical properties or for changes inthe physical properties abov;ethe proportional limit. It had not been re-alized at the beginning of the test program that it would be desirable toobtain a measure of 7/GE at f_,ilure. For this reason
47、 angular deforma-tions were measured on only a _u_ber of specimens. Not enough measure-ments are available to make such a plot. A plot of _max/E as a func-tion of is given in figure 6_. The value of Ebd R Yin this figure corresponds to that of the sheet covering and was taken aslO7 pounds per square
48、 inch, since this is very close to the actual testvalues obtained for the sheet.It should be noted that the curve of figure 69 as presented isstrictly applicable to the alun_inum alloys tested. However, an estimateof the failing stress of a reinforced cylinder of different material canbe obtained bl
49、 calculating the numerical value of the parameter and as-certaining the value of 7max/E from the curves of figure 65.CONCLUSIONSThe over-all generalinstability test program was undertakem to fur_-nish the designer with sufficient information to enable him to make azestimate of the allowable general-instabilit_stress of a reiz_omcedmetal cylinder. Wi
