Buckling of Thin Walled Cylinders under Compression of Tension and Torsion Citation Bridget, Francis Joseph (1934) Buckling of Thin Walled Cylinders under Compression of Tension and Torsion. Master's thesis, California Institute of Technology. doi:10.7907/3nqj-9h59. https://resolver.caltech.edu/CaltechTHESIS:09182024-203332146 Abstract No abstract. Item Type: Thesis (Master's thesis) Subject Keywords: (Aeronautical Engineering) Degree Grantor: California Institute of Technology Division: Engineering and Applied Science Major Option: Aeronautics Thesis Availability: Public (worldwide access) Research Advisor(s): Donnell, Lloyd Hamilton Thesis Committee: Unknown, Unknown Defense Date: 1 January 1934 Record Number: CaltechTHESIS:09182024-203332146 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:09182024-203332146 DOI: 10.7907/3nqj-9h59 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 16743 Collection: CaltechTHESIS Deposited By: Benjamin Perez Deposited On: 24 Sep 2024 16:54 Last Modified: 24 Sep 2024 16:57 Thesis Files PDF - Final Version See Usage Policy. 4MB Repository Staff Only: item control page

BUCKLING OF THIN WALLED CYLINDERS UNDER COMPRESSION OR TENSION AND 'IDRSION Thesis by F. J. Bridget In partial fulfillment of the requirements for the Degree of Master of Science in Aeronautical Engineering California Institute of Technology Pasadena, California 1934 BUCKLING OF THIN WALLED CYLINDERS UNDE..'i CCl,rPR1lSSION OR TENSION A.ND TORSION Introduction The loads received by a m.onocoque structure have led to this research, the original purpose of which was to investigate and, if possible, determine experimentally the relationship between axial compression and pure torsion on thin walled cylinders to cause buckling, as there is not much material of this type available for the de.s igner. This was done in the first six series tested, and when these followed a definite relationship an additional series of cylinders w~s tested under axial compression and pure torsion and axial tension and pure torsion. It was found that this re- lationship still held, and it was then planned to investigate the connection between axial compression and pure bending in conjunction with axial tension and pure bending. Further it was planned to investigate the relationship between pure bending and pure torsion. One series of cylinders was tested in axial compression and pure bending in conjunction with axial tension and pure bending, and, although the results of these tests show promise that a definite relationship exists, the data obtained were-for but one series with cylinders of but one diameter, thickness and length diameter ratio, and it is not felt that this relationship can be conclusively stated as existing for cylinders under axial compression-tension and pure bending or under pure torsion and pure bending. - 2 - Apparatus The tests were made on small scale models of steel and brass "shim stock". The technique of manufacture and the special testing machines used were those developed by Dr. L. H• .Donnell and described by him in N.A.C.A. Report 479. The figures mentioned in this paragraph only conform to the notation used in Report 479. As shown in this report, the results of small scale tests compare favorably with large scale tests. It is necessary to use great care in selection of stock and manufacture of specimens to secure uniformity of result, and despite this care it has so far been impossible to avoid scatter at high compression ioads. The thickness of sheet was measured in the thickness tester, Fig. 14a. The modulus of elasticity E was obtained in the special testing ma.chine and tensometer shown in Fig. 15a, and at the same time Clp 1the proportional limit stress,was determined for purposes of record. Sheets cut to 1/8 inch outside diameter greater than the diameter of the finished cylinder, were placed in a rolling machine around rods of such diameter as to obtain the proper curvature. These were then wrapped around an oiled wooden cylinder (to enable easy removal) and soldered. The rolled sheet was held tightly to the wooden cylinder by a special clamp and the edges soldered. (It has been found that buckling waves form freely over this soldered edge, and that the effect of the overlap, if small, is negligible). After removal the cylinders were soldered to end rings in turn soldered to butt plates to fit in the special testing machine shown in Plate 1. The decrease in effective length due to the rings bas been allowed for in the following table. The testing ma.chine, Plate 1, is capable of testing specimens in any combination of axial compression or tension and in pure bending and pure torsion at the same time. The notation of figures, etc., from this point on applies to this paper. Conclusions and Results The relationship given by the empirical exponential fornrula: 1- ¾ Vo where: o =axial compression or axial tension in pounds = average of maximwn axial compression values {with zero torsion) in pounds 7 =pure torsion in inch pounds 7 = average of maximum pure torsion values {with zero como pression or·tension) in inch pounds. always positive. h{>1 )= slope of the line determined by plotting experimental values of % 0 vs. ?'z: on double log paper {see figures C 3 and 5) was determined conclusively to exist by experiment. . coordinates with the compression-tension or ordinate axis, and torsion or Using cartesian ¾o" axis as the ½. as the abscissae axis, it will be noted that values range from zero to unity for axial compression values, from zero to unity for pure torsion (when neither compression nor tension is applied), and from zero to values greater than unity up to the elastic limit of the material in the cylinders. illustrates these conditions. Figure 2 In Figure 1 a characteristic curve on cartesian coordinates is shown, and the crossing of the compression axis in a perpendicular direction while the crossing of the torsion axis at a definite slope is shown. That the curves are synn:netrical about the compression-tension axis is apparent as a change in the sign of shear for a symmetrical structure can make no difference. That the curve will pass through the torsional axis with a definite slope is physically apparent as the addition of tension obviously - 4 - increases the ability of the st~ucture to take a corresponding addition of torsion before buckling. Figure 2 is a plot on cartesian coordinates of the points obtained from series G .of Table I which in turn shows the physical characteristics of each series tested. is a cubic parabola (n = 3). In Figure 2 the solid line The dotted line represents that portion of the curve where the cylinders were stressed beyond their elastic limit. Figure 3 represents this Series G plotted on double log paper where the ·s lope {or n} ~ 3.3. Figure 4 represents a composite plot on cartesian coordinates of series A to G, while figure 5 illustrates the plots of series A to F inclusive, on double logarithmic paper. self explanatory. is attached. Figures 6-12 inclusive are In Fig. 11 it will be noted that the tension cage Table 2 tabulates the precise values attained on the individual cylinders of each series before failure by buckling. TABLE I b-operties of cylinders in series tested Series A B C D E F G Mat. Length Diam. Thick. Ex 10-6 Op X 10-3 n steel 5.315 brass 5.315 steel 5.315 steel 11.315 steel 5.315 steel 1.32 steel 5.315 .00204 .0032 . 00295 .00204 .00295 .00204 .00395 31.4 16.5 30.6 27 . 06 30.6 31.4 57.7 27.0 48.6 53.3 48 . 6 57 . 7 36.0 1.992 4.25 2.625 2.156 1.0 2.781 3.33 1 .88 1 . 88 3.75 1.88 1.88 3.75 1.88 29.6 - 5 - TABLE II Elcperimental Results Used in Plotting Curves Series A lbs. lb.in. O 20 40 60 80 100 120 170 172 230 192 218 231 55 49 47 40 39 36 30 20 10 0 0 0 52 Series B lbs. lb.in. 20 45 90 100 120 150 175 190 230 250 70 64 50 60 56 54 30 0 64 48 Series C lbs. 0 0 50 100 150 155 170 200 200 220 230 250 279 287 287 lb.in. 217 240 226 178 180 210 210 126 96 100 0 140 0 174 70 72 0 Series D Ths. 0 40 97 100 100 120 125 130 lb.in. 36 34 23 12 16 24 0 0 200 200 300 300 420 430 455 470 490 520 78 90 64 150 11 151 10 Series E lbs. 0 0 100 100 200 lb.in. 106 110 96 100 68 68 20 20 10 10 0 0 Series F lbs. O 25 50 75 lb.in. 160 170 128 130 100 96 132 0 Series G lbs. -980 -800 -800 -700 -600 -600 -500 -500 -400 -400 -300 -300 -200 -200 lb.in. 0 166 200 220 248 224 220 234 215 218 222 210 204 210 lbs. -100 -100 0 0 0 0 100 100 200 lb. in. 206 216 178 196 186 184 172 180 166 lbs. lb.in. 500 132 500 140 540 100 595 40 613 0 610 0 660 0 200 300 380 174 144 150 400 124 500 500 O 75 - 6 - Discussion The manufacture, test and choice of material for these experiments must be carefully done or results will not be uniform or accurate. As a general rule the rolled metal stock is not isotropic and is definitely anisotropic as shown by the different moduli of elasticity in series D cut longitudinally from the sheet stock and F cut across the sheet. Any attempt to condense the physical charac- teristics of the cylinders by formL11.g parameters of the several variables to be accurate would of necessity consider this fact. In the construction of the curves for this paper the values of maximwn compression and maximum torsion have been chosen as the mean of the maximum values secured experimentally. The use of the maximum torsion ( lo ) as calculated from Technical Report No. 4?9, N.A.C.A. 1933, by Dr. L. H. Donnell, and the use of maximum compression ( <S:;;, ) as calculated from Technical Report No. 4?3, N.A.C .A. 1933, by E. E. Lundquist, would change the value of n but not the nature of the relationship. In Figure 2 it will be noted that compression decreases the ability of the cylinder to resist torsion while tension increases it. The empirical equation represents this relationship definitely. In Fig. 2, the value of the point at which this relationship breaka down, namely ~imum tension and torsion values at the elastic limit, about ~.8 is interesting in comparison with the maximum compression and mininrum torsion value of 1.0 at the stability limit. Further expert~ mental work 1night develop a bona fide relationship between these points which would be of value. - '( t t The author wishes to thank Dr. Th. von Karman, Director of the Guggenheim Aeronautics Laboratory at the California Institute of Technology, for the opportunity for making these researches. The researches were suggested by and carried out under the direction of Dr. L. H. Donnell. Acknowledgment is also due to L. Secretan, who cooperated in the first r~search, and to Dr. A. L. Klein and E. E. Sechler (all of the staff of the Institute) for numerous helpful suggestions,and to Dr. E. E. Lundquist of the N.A.C.A. for his suggestion as to the choice of maxinnun torsion and compression values. 1 <5 -&~ 0 I T To .·· (A) ' .• -, - 1 - 0 0 •<>o · Fig . 1 ..,... · T~ (B } •. 0 --T 0 0 0 I r - ~:::::::f--t---f-______;_+-----+--_J I 1.4 '·0 I 1.21 oo .2 B z -0 6 V) (/) w ~ a. 2 .4 u0 .2 I .0 I .4 -.6 I. .8 SHEAR (TORSION) I I •o o -er Do I ·I -.2 -.41 I I 0 \0 I I I I ...I-"// / I /11 / /J I I I I• I .~ _. ....+- - o l 2z -.8 I L I , - BUCKLING OF CYLINDERS ~. _ 10 UNDER COMBINED TORSION oI .~· • , . ANO COMPRESSION OR TENSIONj1 -1.21 . . -1.4 -l.6c!,.:: . -- -- - --- Fig. 2 1 I J - -l /_ .. ' .10 ' : I g, _j . I - I r/ ,- -% C, -~ I f ' ~ · ·~ . cP 1.0 i I SERIES j l G lI . - L ' - 1 ! I +I ...1.' .1 J ~ .J ... o. I .I 5 J ; _j , ! ' j .1 .1 t.O T Fig. 3 Ta -- .,- 0 It'> • ~ 1-:,;j I-'• -6'Do E E OD --c 1 I 6 Al D G IC A(j 1c rs C 6'. 0 • .2 B B .. . 2 .--r .A. .u ~ . To r - - ·8 C A\ 6-G ~~ 0 F 1.2 I 1.0 GACEOFEG---~---J B B-c-+----t--~ -- AND COMPRESSION OR TENSION UNDER COMBINED TORSION rl cf E C _. _ .'GF . BA B UCK LING -OF CY LI NDERS E A-.--t---+---__L__ G :M ·. 0 .6· l ---+----'---,--~---,- . E:~E A. . . .8 I I G A D ? I• Q Cf i~ I E A 6 ! I I I I .10 I I I _/ I /' ·• I I SERIES A ) V .. I I I ·p I - . ,. ... : .. 1.0 t : i /o I ,.. <. ... ~ •-·· ,-···-- -~- ; ··--- - • _L.1 .! .. .......... _ I , .10 . 'T' 1.0 0 _ I 0 I V 0 J t of p•, SERIES C I I V ) SERIES B 0/ 0 .,o ;. . I I 0 u I - I 1.0 'T .10 'I .,..._ 0 'T To 1.0 To Jo 1.0 .10 • • I J I I C) I ) / J I 0 I I ' I; / 0 / 0 : / + f-;i + + - - - + - - - + - - - - + - - - - - - 1 j i I +-+/+--+--+--+--+-~-----I - / SERIE5 F /"' I V 1 7 - 10 0 -···-·· I I. To Fig. 5 .10 ·· ! I /" '1. - .I I V ~"' -~ I / t-+--+--+-,·TJ ' : V / I 0 SERIES E SERIES D ---+-!-+ - + - - - + - - - + - - - - - •. I J ,' , l O 1-1-+-+-+---+---+-+-+---+------1 .10 I i 1.0 I I. To ·- - .10 r.o Fig . 6 A Typical Specimen "G" Series ,' Fig . 7 Compression and Torsion Buckling Series uA" Fig. 8 Axial Compression Buckling Series "C" Fig . 9 Compression and Torsion Buckling Series "D" Fig. 10 Compression and Torsion Buckling Series "F" Fig. 1.1 Tension and Torsion Buckling Series "G" Ten5ilJIJ ression dec.rer.1.Hf1J Fig. 12 "G" Series Cylinders After Test