NASA-CR-1160-1968 The buckling of thin-walled circular cylinders under axial compression and bending《在轴向压缩和弯曲下薄壁圆柱体的屈曲》.pdf

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1、NASA CONTRACTOR REPORT NAS :- LOAN COPY: RETURN T AFWL (WLIL-2) KIRTLAND AFB, N THE BUCKLING OF THIN-WALLED CIRCULAR CYLINDERS UNDER AXIAL COMPRESSION AND BENDING by F. R. Stnurt, J. T. Goto, und E. E. Sechler Prepared by CALIFORNIA INSTITUTE OF TECHNOLOGY Pasadena, Calif. for NATIONAL AERONAUTICS A

2、ND SPACE ADMINISTRATION WASHINGTON, D. C. . SEPTEMBER 1968 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-/ NASA CR- 1160 TECH LIBRARY KAFB, NM 00b037b THE BUCKLING OF THIN-WALLED CIRCULAR CYLINDERS UNDER AXIAL COMPRESSION AND BENDING /- “ “-? By F.

3、 Rr Stuart, J. T. ,dotognd E. E. Sechler “_I.“- / - .“ Distribution of this report is provided in the interest of information exchange. Responsibility for the contents resides in the author or organization that prepared it. /Prepared under Grant No. NsG-18-59 by CALIFORNIA INSTWWM? OF TECY Pasadena,

4、 Calif. for NATIONAL AERONAUTICS AND SPACE ADMINISTRATION For sale by the Clearinghouse for Federal Scientific and Technical Information Springfield, Virginia 22151 - CFSTI price $3.00 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-THE BUCKLING OF T

5、HIN- WALLED CIRCULAR CYLINDERS UNDER AXIAL COMPRESSION AND BENDING By F. R. Stuart, J. T. Goto, and E. E. Sechler California Institute of Technology SUMMARY A series of tests was conducted on both electroplated copper and Mylar cylinders under combined axial compression and bending. Great care was t

6、aken to assure that the cylinders were as perfect as was possible and loading and boundary conditions were carefully controlled. For the Mylar cylinders, corrections were made for both area and stiffness of the lap joint. Under these conditions, much higher values of the buckling stress have been ob

7、tained than had been reported on by previous investigators. INTRODUCTION As an extension of the work on the buckling stress of thin- walled circular cylinders, it was desirable to determine the effects of combined loading conditions. One of the most important of these from a structural design standp

8、oint is the combination of axial load and bending. By using an electroplating technique discussed in References 1 , 2 , and 3 , thin- walled cylinders could be made without seams , with a high degree of dimensional accuracy, and which had a minimum of initial deformations. In addition to the tests o

9、n these “perfect“ metal cylinders, a number of tests were run on cylinders made from Mylar. These cylinders had a lap seam whose dimensions were varied. The main difference between these tests on Mylar specimens and those carried out by other experimenters lay in the fact that the effect of both the

10、 area and the stiffness of the seam were taken into account in reducing the experimental data. Loading and boundary conditions were carefully controlled and any anomalies in the data were systematically investigated. Provided by IHSNot for ResaleNo reproduction or networking permitted without licens

11、e from IHS-,-,-The combination of axial compression and bending, even though it is a common loading for both aircraft and missiles, has not been extensively investigated. References 4 and 5 give interaction data for this loading condition for celluloid and Mylar cylinders with a few check points in

12、reference 4 for metal specimens. Even the case for pure bending has been in doubt since, until recently, the theoretical value of critical bending stress was accepted as that presented by Fltigge, namely 1.3 uc (Ref. 6). It has been shown (Ref. 7) that Fliigges calculation was quite restricted and a

13、 more general investiga- tion has led to the conclusion that the maximum stress to cause bending failure is the same as that necessary to cause failure under uniform axial compression. In the past, experimental investigations have been discouraging. The correspondence with theory was poor (Ref. 8) a

14、nd the scatter has been great. However, it has been shown by Babcock that careful fabri- cation of the test specimens and good control of the experimentation will lead to more satisfactory results. These controls have been practiced in the current set of tests. The Metal Specimens The electroforming

15、 process discussed in Reference 1 was used. Briefly, the method consists of plating a copper shell on an accurately machined 8.0 inch (20.3 cm) diameter form which has been coated with silver paint. After plating, the shell is cut to a length of 10 inches (25.4 cm) and is removed by melting the wax.

16、 Specimen dimensions are shown in Table I. The average thickness of the shell was found by accurately weighing the shell and dividing this weight by the surface area and density. A density of 8.9 grams/cc (8900 kg/m ) was used for this purpose and checks of the actual thickness using a comparator on

17、 samples confirmed the method. Spot checks on typical cylinders indicated that the variation in thickness over the shell area was not greater than t 3 /o. See Table I1 for typical results. 3 0 - Poissons Ratio was taken as 0.30 and the modulus of elasticity was measured by specimens from each shell

18、which were tested in 2 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-uniaxial tension on an Instron testing machine. A typical stress-strain curve is shown in Fig. 1 which indicates good linearity up to a stress value of about 13, 000 psi (89.6 MN/

19、m ). The value of Youngs modulus used to reduce the data is an average of several tests conducted on specimens from each shell. These values are shown in Table 111. Table 111 also indicates the scatter obtained during these tests. Similar values for electroplated copper were obtained by Read and Gra

20、ham (Ref. 9) and they explained the scatter by the grain size of different specimens. 2 After mounting the base of the specimen in the testing machine, measurements were taken to determine the deviation of the cylinder generators from a straight line. The pick-up was an iron-core reluc- tance unit w

21、ith an output of approximately 25 volts/inch (10 volts/cm) and had a working range of 0.200 inches (7.87 mm). It was mounted on a vertical slide that could be placed at any place desired around the circumference, Fig. 2. Figs. 3, 4, and 5 show typical data. Test Procedure for Metal Cylinders The cyl

22、indrical shell was first mounted in a brass end ring with a low temperature melting point alloy, Cerrobend. After the Cerrobend hardened, the other end of the shell was mounted in the load ring of the testing machine with the same material. The testing machine was then rotated to the testing positio

23、n (horizontal) and the free end of the shell (that opposite to the load ring) was rigidly attached to the machine end plate with Devcon Plastic Steel. Figure 6 shows the testing machine and shell in the testing position. Although the testing machine was originally designed for axial loading it was p

24、ossible to apply a bending moment by varying the end plate displacement through non-uniform adjustment of the three loading screws. Close control of the end plate movement was possible since a single revolution of the loading screws corresponded to 0.025 inch (0. 635 mm) and the screw could be adjus

25、ted to one tooth of the 180 tooth loading gear. The total applied load and the load distribution was obtained from the loading ring, Fig. 7. This was a brass cylinder 8.00 inches Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-(20.32 cm) in diameter,

26、 2.50 inches (6.35 cm) long and 0.0107 inches (0.271 mm) thick. Twenty-four strain gages were mounted around the inside and outside circumference at equally spaced stations - inside and outside gages being directly opposite each other. The load ring gages were connected into a bridge circuit with du

27、mmy gages on a brass plate to give temperature compensation. The output was connected to an amplifier and read out on a Leeds and Northrop voltmeter. The load ring was calibrated to determine the load and moment as a function of gage output. Typical calibration curves are shown in Fig. 8. The actual

28、 testing was carried out in the following manner: After the shell was mounted, the desired difference in strain gage readings was adjusted at diametrically opposite points in the shell. Once the desired moment was applied, all three loading screws were operated simultaneously to apply uniform axial

29、compression. Data were taken at approximately 50 /o of the anticipated buckling load and at small increments thereafter. If necessary, individual screw adjust- ments were made to maintain the desired bending moment. The axial compression load was increased until buckling occurred and the highest str

30、ain gage readings were recorded. 0 Test Results on Metal Cylinders A total of 16 shells were tested. Table I gives the description of the specimens and Table V a summary of the results. The data are shown plotted in Fig. 9 in which b ubR/Et C C = ucR/Et C U = 0.6 = ucjR/Et where ub = maximum bending

31、 stress u = uniform compressive stress uce = classical buckling stress C 4 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Buckling occurred in all tests with complete failure and subse- quent large load reduction. There were no visual indications of

32、 local buckling before failure. The postbuckling state was the familiar diamond shaped pattern occurring in several rows around the circum- ference in most cases. When high moments were present, buckling was restricted to the high stress side of the shell. Strain gage data was reduced by a Fourier a

33、nalysis carried out on an IBM 7094 computer. The method employed was that of Reference 10. The data were presented in the form 6 strain gage reading = A. t B COS (0 - +n) 0 n M= 1 and the constant and the first harmonic coefficients were used to calcu- late the applied loads and stresses. Table IV g

34、ives the results of this analysis and Figs. 10 and 11 show typical correspondence between the actual strain gage readings and the Fourier representation used to calculate the buckling stresses. A few metal cylinders were tested under dead-weight loading, in contrast to a fixed displacement loading.

35、These are also shown in Fig. 9 and the data show the same trend as those obtained earlier. Another method of presenting the data is shown in Fig. 12 where crTOT/cce is plotted against rb/uce whe re Conclusions Concerning Metal Cylinders Figures 9 and 10 indicate that careful testing of carefully mad

36、e metal cylinders will give much higher values for the buckling stresses than have been reported on previously. In general, the total stress that can be developed lies between 0.65 and 0.95 times the classical buckling stress, the higher vhlues being obtained for loads approaching pure bending. Ther

37、e may be two reasons for this trend namely: 5 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-a) The high stresses for pure bending are acting over a smaller percentage of the total shell and, b) The effect of the fixed boundary as discussed in Refer

38、ence 3 may be different for bending than it is in uniform axial compression and may not be as effective in lowering the buckling stress. The Mylar Specimens A second program on the same problem was set up using cylin- ders made of Mylar. The advantage in using this material is that, if postbuckling

39、is not carried too far, the specimen does not suffer permanent damage upon buckling and can, therefore, be used to obtain many data points. The specimens were 8 inches (20.32 cm) in diameter and 10 inches (25.40 cm) long and had thicknesses ranging from 0.00475 to 0.0103 inches (0.1206 to 0.2616 mm)

40、. The ends were cast in a circular slot in an aluminum end plate using Cerrolow, a low melting point alloy. In order to assure that the Mylar did not slip in the alloy (particularly when the sheet was in tension) it was found necessary to add a locking device to the edge. This was easily accomplishe

41、d by putting a row of paper staples around the edge so that they would be buried in the Cerrolow. Loading was through a ring dynamometer and was accomplished by a hand-turned, fine thread screw attached to the frame of the testing machine. The ring dynamometer was calibrated with dead weights. Load

42、points all lay along a diameter containing the seam and the combined loading consisted of an axial compressive load equal to (See Fig. 13) PA = PL + PH where PL = the load read by the dynamometer plus the dynamometer dead weight and PH = the dead weight of the loading head. 6 Provided by IHSNot for

43、ResaleNo reproduction or networking permitted without license from IHS-,-,-1- f To this is added a bending moment given by M = P xe+ P xse L - H where e = the distance of the loading point from the experimentally determined neutral axis and 6e = the distance from the center line of the specimen to t

44、he neutral axis. The seams were made as an overlap cemented with an Epoxy cement. Since the combination of Epoxy and Mylar did not have the same Youngs modulus as the Mylar alone, typical seams were cut from specimens and tested in uniaxial tension to determine the seam mo dulus , Es. From this valu

45、e and the seam dimensions a theoretical neutral axis and an effective area could be calculated as indicated in the Appendix. In addition to the theoretical neutral axis, an experi- mental one was determined by finding that loading point which gave the maximum axial load carrying ability of the speci

46、men. Curves for the 7 specimens tested are shown in Fig. 14. Since the experimental determination of the neutral axis also took into account any effect of seam initial waviness, the experimental value was used to calculate the bending moments and the bending stresses. Test Results on Mylar Cylinders

47、 Table VI1 gives the stress ratios for the seven Mylar cylinders tested and the results are plotted in Figs. 19 to 21 inclusive. In general, there is a linear relationship between rc/rc$ and crb/rc n = 1, 2 . . . 0 n Shell A. B1 51 B2 t2 B3 53 B4 54 B5 I5 B6 t6 S-1 145,4 96. 8 -24 9. 6 -26 2. 5 -66

48、0. 8 -81 3, 9 2 0.4 0 S-2 340, 1 6. 5 10 8. 9 31 9. 3 -86 5, 3 -31 3.4 -69 1. 9 0 5: S-3 264.4 63, 5 -35 10. 9 58 8, 6 -80 3.2 -45 1. 9 64 0.2 0 0 S-4 209. 9 145. 6 -25 13. 9 25 4. 0 75 2,2 68 2.2 -88 2.1 0 7. 5 -37 3. 4 40 1. 5 -22 2. 9 0 S-5 282. 7 44. 4 -19 11. 2 -59 S-6 11 1. 7 204 -30 16. 8 -77 4, 4 24 2. 4 -79 1. 8 48 0. 5 0 0 s-7 108. 1 249.7 -32 19.6 -67 3,8 23 2.4 -37 3.0 -19 0. 7 0 5-8 268. 3 118.8 -34 18. 6 51 9. 1 55 3. 6 -45 0. 9 -46 1.2 Oo S-9 213, 0 150, 1 -29 9, 3 -67 11.5 - 4 14,2 73 5. 4 -72 5, 3 0 S-10 165. 0 232.2 -33 28.4 77 6. 1 69 5.0 -31 3.0 -82 0.2 0 Provided by IHSN