1、A Reproduced CopyOFNASAReproduced for NASAby theScientific and Technical Information FacilityFFNo 672 Aug 65Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-
2、,-,-Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-REPORT No. 479STABILITY OF THIN-WALLED TUBESUNDER TORSIONBy I. H. DONNELLCalifornia Institute of Tec
3、hnologytfProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICSNAVY BUILDIN6. WA3fl/NGTON. D.C.(An Independent Government t_tablkhn_nk created by a_ of Congress appoved March 3, 1915,forthe su_rvkion and dkec_on o
4、tthe _ientfflcstudy o! tl_l l_obloms of flight. I_ memb_ahll_ was Iacr_a_d to 15 by act approved March 2, I_r29(PtlbHe, No. _, T0thContrQm). It omL1t_ot raemberswho are appoLutodby the Prestdeu;, all of wlaom _rve u such without eoml_asatloa.)JOSEPH S. AMirs, Ph.D., Chairman,President, Johns Hopkins
5、 University, Baltimore, Md.DAVID W. TArLOn, D.Eng., Vice C“hairman,Washington, D.C.Cs.,aLze G. Anc_r, Se.D.,Secretary, Smithsonian Institution, Washington, D.C.LrMAS J. BnzoGs, Ph.D.,Director, Bureau of Standards, Washington, D.C.AaTHUR B. CooK, Captain, United State8 Navy,Assistant Chief, Bureau of
6、 Aeronautics, Navy Department, Washington, D.C.WLr-zAM F. Du_tA_m, Ph.D.,Profe_or Emeritus of Mechanical Engineering, Stanford University, California.BzsJAms D. Fovcom, Major General, United States Army,Chief of Air Corps, War Department, Washington, D.C.H_mav F. Gvooz._szm, M.A.,Port Washington, Lo
7、ng Island, New York.E_eT J. Kmo, Rear Admiral, United States Navy,Chl_, Bureau of Aernnauties, Navy Department, Washington, D.C.CaaaLss A. Lz_-vsmaos, LL.D.,New York City.WrLLL_M P. MAcCaAcExN, Jr., Ph.B.,Washington, D.C.Cs._.aczs F. MAavm, Se.D.,Chief, United State_ Weather Bureau, Washington, D.C.
8、Hz_mr C. PaA_, Brigadier General, United States Army,Chief, Mat all the N.A.C.A.tests (reference I) were on specimens 15 inches and 30inches in diameter. Comparison of the results indi-cates that there is no great disadvantage or danger inusing such small specimens. In all tests the propor-tions wer
9、e such that the stresses were always well be-low the elastic limit.The material was carefully rolled around rods ofproper diameter to give it approxhnately the desiredcurvature, the longitudinal seams were soldered, andthe tubes were then soldered to heavy, end piecesJigs were used to hold the mater
10、ial in a true cylindricaiform and prevent local waving while these solderingoperations were performed. The specimens havingthe smallest t/dratiosshowed some initialwaves, duechieflyto lack of flatnessin the stock from which theywere made; but in the specimens with largert/drationo departure from tru
11、e cylindricalform could be de-tectedby the eye or fingers.The longitudinalseams were lapped about _I inchand were formed with _ littlesolder as possible.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-8 REPORT NATIONAL ADVISORYThere is no theoretical
12、 reason why such a seam shouldhave an appreciable effect in this type of loading.Buckling deflections seemed to occur across seams asfreely as anywhere, so the stiffening effect of the doublethicknem at the seam was probably negligible in allcases except possibly for the few tubes which were only_6
13、inch in diameter. For these tubes an attempt wasmade to correct as much as possible for this stiffeningeffect by taking the thickness as the total cross-section-al area of the tube wall divided by the circumference.The end conditions of the tubes were as shown infigure 5. The medium length tubes (6
14、to 30 incheslong) were soldered to heavy end plates as shown at(a). Heat was applied only to the end plates and care.l.oose _/tffn_, ringY_ba,S_tlx_. O_k$(b)Er_ #/_ off_ting m_hine5/6.“ ro_ .rubec) (d)F_Ull ,_.- Kd_ c_mdit km_ o( t_t s_.utm.was taken to heat them symmetrically to avoid produc-ing in
15、itial strains in the tube. The loose ring shown inthe figure fitted the tube just closely enough to keepthe tube cylindrical during the soldering. .ks therewas always a certain amount of clearance between thering and the tube wall and buckling deflections werenot appreciable at a distance from the e
16、nd many timesthe width of the ring (see fig. 6), the effect of the ringon the end conditions was ne_ected and the distancebetween the end plates was taken as the length of thetubes.Several extremely short specimens were made, totest the theory at small values of/-/. .ksboth theoryand common sense in
17、dicate the greater importance ofCOMMrIrEE FOR AERONATTICSend conditions for such a case, great care was taken toobtain definite end conditions. One side of a strip ofmaterial _ inch wider than the desired tube length wastinned on one side with a very thin coating of solderThe mechanical properties o
18、f similar sheet materialwere measured after tinning and found to be the sameas before tinning, as nearly as could be determined.Two disks were turned the size of the desired tube,their edges were thinly tinned, the tinned strip wastightly clamped around them as shown in figure 5 (b),and the whole he
19、ated so as to sweat the tube to thedisks. Examination after testing showed a perfectjoint between the tube and the disks right up to theedges of the disks.The _6-inch-4iameter tubes were merely sweatedover the end of a steel rod as shown in figure 5 (c)The 27-inch tube had bolted joints, and its end
20、s wereembedded in concrete, held between steel hoops, asshown at (d). The Ltoops were clamped to the heavyend plates of the testing machine, and the length ofthe tube was measured as shown.The medium and very short specimens were testedon the special testing machine shown in figure 6.a FI-. t l_OVll
21、 7.-Dta_rammatl top VllW of tonl|oo-b_nd/n_-ecmprt._sion t_i_g _hloQ.This machine is capable of testing specimens in torsion,uniform or varying bending, and axial compression,separately or in any combination. The three types ofloadareappliedby threeconvenientlylocatedcranks,and the load applicationi
22、sextremelysmooth. Theloadisreaddirectlyininch-poundsand pounds,onthreedialgages. These dialgagesmeasure thede-flectionsof cantileverspringswhich are designedinsuch a way as toeliminatepracticallyallhysteresisand areartificiallyaged. Provisionismade foradjust-ing the positionofthe dialgages lengthwis
23、eof thespringssothat,incalibrating,apositioncan befoundat which they read the loads directly.The principle of the machine is shown by the dia-grammatic top view (fig. 7). The specimen is attachedto two L-shaped members abc and de/ which arebalanced on practically frictionless universal joints atb an
24、d e. The ends of the specimen are therefore freeto rotate in any direction. When a.,dal loads are usedthey are applied through these universal ioints andthis insures a definite line of action of the load. Thespecimen is subjected to bending by applying down-ward forces at d and ; these forces are ap
25、plied through.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-STABILITY OF THIN-WALLED rUBES UNDER TOI_IONwhich extend down to a cross bar dc under thespecimen. A crank is used to press down on a ful-crum mounted on the bar dc; the crank and fulcruma
26、re movable along the length of dc, and in this waythe ratio between the forces at d and c, and thereforethe bending moments at the two ends of the specimen,can be varied at will. Torsion is applied to the speci-men by pulling down on f through a wire, by means ofa crank; the point a is prevented fro
27、m vertical (butnot from horizontal) motion by vertical wires. Axialload is applied by moving point b to the left with ajoint takes loads in two directions, a_lows rotation inany direction with almost no friction, and is extremelycheap and satisfactory. The whole testing machineis built of structural
28、 shapes, assembled largely bywelding, with a minimum of machining. It cost very.little to build and has proved very satisfactory andconvenient to use.The 27Anch diameter specimen was tested on aspecial testing machine similar to the one just describedbut much larger (fig. 9). No prevision for a_al l
29、oadingis made on this machine, and the loads are measuredcrank; is mounted on one of the cantilever springsand thus the axial load is measured. The arms bc andab are in themselves cantilever springs and their de-flection measures the bending and torsion momentsrespectively. The dial gages which meas
30、ure the de-flections of the springs are mounted on unstr-=_d arms.The universal joints at b and are of the type shownin figure 8a, consieting only of a spherical cup, a centralball and six loose balls (the weight of the member abcor def issufficientto keep the hallsin position). Thisby the lateral d
31、eflection of tension members that axeinitially bent, which permits the measurement of verylarge forces with a light measuring device. This ma-chine takes specimeas up to 3 feet in diameter and 15fast in length, and has a capacity of 500,000 inch-pounds in bending and in tordon.The _0oinch diameter s
32、pecimens, used to test thetheory for long slender tubes, were loaded as shown infigure 10. Toshaped pieces were attached to the endsof the specimen. The_ were balanced on a knife-edgcProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-STABILITY OF THIN-W
33、ALIJD T_BE$ UNDER TORSIONwires which extend down to a cross bar dc under thespecimen. A crank is used to press down on a ful-crum mounted on the bar dc; the crank and fulcrumare movable along the length of dc, and in this waythe ratio between the forces at d and c, and thereforethe bending moments a
34、t the two ends of the specimen,can be varied at will. Torsion is applied to the speci-men by pulling down on f through a wire, by means ofa crank; the point a is prevented from vertical (butnot from horizontal) motion by vertical wires. Axialload is applied by moving point b to the left with a9joint
35、 takes loads in two directions, allows rotation inany direction with almost no friction, and is extremelycheap and satisfactory. The whole testing machineis built of structural shapes, assembled largely bywelds, with a minimum of machining. It cost very.little to build and has proved very satisfacto
36、ry, andconvenient to use.The 27-inch diameter specimen was tested on aspecial testing machine similar to the one just describedbut much larger (fig. 9). N o provision for axial loadingis made on this machine, and the loads are measured1ilrcrank; e is mounted on one of the cantilever springsand thus
37、the axial load is measured. The arms bc andab are in themselves cantilever springs and their de-flection measuree the bending and tormon momentsrespectively. The dial gages which measure the de*fleetious of the springs are mounted on unstressed arms.The universal joints at b and are of the type show
38、nin/igure 8a, con_i_tiug only of a _pherical cup, a centralhall and six loose balls (the weight of the member abcor def is sufficient to keep the bn,Usin position). Thisby the lateral deflection of tension members that areinitially bent, which permits the measurement of verylarge forces with a light
39、 measuring device. This ma-chine takes specimens up to 3 feet in diameter and 15feet in length, and has a capacity of 500,000 inch-pounds in bending and in torsion.The _0-inch diameter specimens, used to test thetheory, for long slender tubes, were loaded as shown infigure 10. T-shaped pieces were a
40、ttached to the endsof the .qpecimen. The_ w_re b_lanc_d nn a knife-edgcProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-10 R_PORT _ATIONA/d ADVISORYat one end and on a loosevertical_tripat the other,sothat the ends of the specimen were freeto rotate i
41、nany dizectionor to approach each other (asw_s alsothecase with the testingmachines previously described).The long arm of the T at one end was held down witha string,while weights were applied to the other untilbuckling occurred, as shown in the figure.The wall thickness of the specimens being so sm
42、all,itwas nece_ary to measure itwith much more thancommon accuracy. The instrument shown infigure!ICOMMrPI_E FOR AERONAUTICSwhich surrounds the anvil. Such provisionsare neces-sary to measure the thickness of thin material accu-rately. The sheetmust alsobe very clean,as p_rticlesofdust or filmsofdir
43、tcausesappreciable errors;itwasfound advisable to wet the sheet with alcohol duringthe measuring. In spite of such precautions, theerrorsin the measurement of tand in the variation inthe thickness at differentparts of the sheet undoubt-edly cause a largepart ofthe scatterin the finalresults.The vari
44、ation in thickness over a tube was usuallyLood/“Ca) 1.45 should buckle in two waves; and for1.45J0.35 it should buckle in three waves, etc.It will be noted that test results are quite consistentwith the theory in this respect.The relation between nSBJ and nSJ can be re Tnearly expressed, for the ran
45、ge of values of actu_dsignificance, by the formulas: nSBJ is equal to0.385 (nJ_) t + .94 (ttsJ:) | + 18. 3 (clamped edges)0.385 (nsJ_)t+(naJ_)t+6.5 (hinged edges_ 1_27)The values obtained from these expressions are shownin table II, in the column next to nSBJ. These rela-tions can be simplified to-|
46、 0.94 18.3B-0.385 n,. +n-_ij_+ a-_j (clamped edges)B-0.385 nJi+n_t+_6.5 (hinged edges) /) (2S)These are the equations of the individual curves infigure 2. For very large values of J, n = 2 and onlythe first terms of (28) are important, _ving us equa-tion (2). This is the equation of the line eef in
47、figure2, which the curves for n-2 approach asymptotically.By equating the right-hand side of (28) to the sameexpression with n replaced by a+ I, we obtain anequation for determining the value of J for which thenumber of circumferential waves changes from n ton+l.It will be noticed that the part of t
48、he jagged linesin figure 2 corresponding to larger values of n approachcloser and closer to the envelopes of all the curves,shown by the broken lines de. For values of J below-!Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-206 or 7 this envelope can be used instead of the jaggedline without serious error. We can obtain the equa-tion of this envelope very simply-merely by treatingI_ as though it coldd have any value, fractional as wellas integral. In the last column of table II, values ofns.P have been raised t
