REG NACA-TR-748-1942 Normal Pressure tests of Rectangular Plates.pdf

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1、k. .#_x_ _7_f,/17_/t1, , . 7,YNATIONAL ADVISORY COMMITTEEFOR AERONAUTICSl. r _oT-:748Y i.NORMAL-PRESSURE.TESTS 0FRECTANGULAR PLATES r. , ,- -By_WALTER RAMBERG, ALBERT E. MePHERSON, and SAMUEL LEVYIiREPRODUCED BYNATIONAL TECHNICALINFORMATION SERVICE -iU,S. DEPARFMENT OF COMMERCE 1SPRINGFIELD VA 22161

2、 )-Provided by IHS Not for ResaleNo reproduction or networking permitted without license from IHS-,-,-AVqLDDoD_D,i_ “ Angle of setting of wings (relative to tIirustiine):_gi Angle of stabilizer setting (relative to thrust-line) -b Spanc ChordAspect ratio, _True air speed1 _.Dynamic pressure, _pVflLi

3、ft, absolute coefficient _._-_ “ - q “Dra ,a ,.o u,oooo o oo .“Resultant momentReSultant angular VelocityReynolds number, p-_ where 1is a linear dimen-sion (e.g./for an airfoil of 1.0 ft chord, 100 mph,standard pressure at 15 C, the correspondingReynolds number is 935_400; or for an airfoilof 1.0 m

4、_chord, 100 mps, the correspondingReynolds number is _,865_000)-Angle of attackAngle of downwashProfile drag, Doabsolute coefficient C_o-_ _Induced drag, absolute coefficient G_,_q_Parasite drag, absolute coefficient O_-q_. c “Cross-wind force, absolute oeflicmnt _-_2626 a0 Angle of attack, infinite

5、 aspect.ratioa_ Angle of attack, induceda_ Angle of attack, absolute (measured from zero-lift position)Flight-path angleProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-THISTHE BE STAGENCY.NOTICEDOCUMENT HAS BEEN REPRODUCED FROMCOPY FURNISHED US BY TH

6、E SPONSORINGALTHOUGH IT IS RECOGNIZED THAT CER-TAIN PORTIONS ARE ILLEGIBLE, IT ISLEASED IN THE INTEREST OF MAKINGAS MUCH INFORMATION AS POSSIBLE.BEING RE-AVAILABLEg/,tProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-REPORT No. 748NORMAL,PRESSURE TESTS

7、 OF RECTANGULAR PLATESBy WALTER RAMBERG, ALBERT E. McPHERSON, and SAMUEL LEVYNational Bureau of StandardsProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICSHEADQUARTERS, 1500 NEW HAMPSHIRE AVENUE NW., WASHINGTO

8、N, D. C.Cieated by act of Congress approved Ma_ch 3, 1915, for the supervision and direction of the scientific body of the problemsof flight (U. S. Code, title 50, sec. 151). Its membership was increased to 15 by act approved March 2, 1929. The members areappointed by the President, and serve as suc

9、h without compensation.JEROME C. HUNSAKER, SC. D., Chairman,Cambridge, Mass.GEORGE J. MEAD, SC. D., Vice Ctlairmon,Washington, D. C.CHARLES G. ABBOT, SC. D.,Secretary, Smithsonian Institution.HENRY H. ARNOLD, Lieut. General, United States Army,Commanding General, Army Air Forces, War Depart-ment.LYM

10、AN J. BRIGGS, Ph.D.,Director, Nagional Bureau of Standards.W. A. M. BURDEN,Special Assistant to the Secretary of Commerce.VANNEVAR BUSH, Sc. D., Director,Office Scientific Research and Development,Washington, D. C.WILLIAM F. DURAND, Ph. D.,Stanford University, Calif.O. P. ECHOLS, Major General, Unit

11、ed States Army, Com-manding General, The Mat6riel Command, Army AirForces, War Department.SYDNEY M. _HAUS, Captain, United States Navy, Bureau ofAeronautics, Navy Department.FRANCES W. I_EICHELDERFER_ Sc. D.,Chief, United States Weather Bureau.JOHN H. TOWERS, 1lear Admiral, United States Navy,Chief,

12、 Bureau of Aeronautics, Navy Department.EDWARD WARNER, So. D.,Civil Aeronautics Board,Washington, D. C.ORVILLE WRIGIIT, Sc. D.,Dayton, Ohio.THEO1)ORE P. WRIGHT, So. D.,Asst. Chief, Aircraft Branch,War Production Board.GEORGE W. LEWIS, Director of Aeronautical Research JOHN F. VICTORY, SecretaryHENRY

13、 J. E. REID, Engineer-in-Charge, Langley Memorial Aeronautical Laboratory, Langley Field, Va.SMITH J. DEFRANCE, Engineer-in-Charge, Ames Aeronautical Laboratory, Moffel Field, Calif.ED_rABD R. SHARP, Administrative O_cer, Aircraft Engine Research Laboratory, Cleveland Airport, Cleveland, OhioTECHNIC

14、AL COMMITTEESAERODYNAMICS AIRCRAFT MATERIALS INVENTIONS of the sheet relative to the plane of tile networkmust be zero from symmetry wherever the sheet passesover the center line of each supporting beam. Eachrectangular field will therefore behave as a rectangularplate clamped along its foul edges o

15、n supports thatare rigid enough in tile plane of the sheet to preventtheir displacement in that plane. At the same timethese supports must have _ rigidity normal to theplane of the sheet equal to that of tile actual supportsin the seaplane bottom. The rigidity of the supportswill lie somewhere betwe

16、en tile unattainable extremesof zero rigidity and infinite rigidity. The extremeof infinite rigidity normal to the plane of tile sheet isone that may be approximated in actual designs and,furthermore, it is a ease that can be experimentallyinvestigated by clamping rectangular plates in a rigidframew

17、ork and subjecting them to normal pressure.It is probable that tile stress distribution in such afixed-edge plate will, in most cases, be less favorablethan the stress distribution in the elastic-edge plate.The strength of plates obtained from the tests willtherefore be on the safe side if applied i

18、n seaplanedesign. Reference might be made in this connection5Oto “_ paper by Mesnager (reference 4) in which it isshown that a rectangular plate with elastic edges of acertain flexibility will be less highly stressed than aclamped-edge plate.Considerations of this nature led to the decision totest r

19、ectangular plates of various materials, thick-nesses, and ratios of length to width by holding theiredges clamped in a :rigid frame and subjecting themto hydrostatic pressure. It was decided also to sub-jeer to normal pressure some plates with freely sup-ported edges. It was felt that this type of d

20、eformationwould approximate thedeformation in a rectangultrpanel of the bottom plating resisting a higher impactpressure thttn the surrounding panels and supportedon beams of torsional stiffness insufficient to developlarge moments along the edges. The high bendingstresses at the edges characteristi

21、c of rigidly clampedplates would then be absent.SPECIMENSDimensions and tensile properties for the plates_ested with damped edges are given in table 1 and forplates with freely supported edges in table 2. Testswith clamped edges were made on 39 plates of 17S-Taluminum alloy ranging in tlfickness fro

22、m 0.0104 to0.1000 inch and in size from 2.5 by 2.5 to 7.5 by 17.5inches; on 12 plates of 18:8 stainless steel ranging inthickness from 0.0127 to 0.0601 inch and in size from2.5 by 2.5 to 5 by 5 inches; on 3 plates of 17S-RTaluminum alloy ranging in thickness from 0.0208 to0.0384 inch and 2.5 by 7.5

23、inches in size; and on 2 platesof 24S-RT alunfinum alloy 0.0204 and 0.0250 inchin thickness and 2.5 by 7.5 inches in size. The testsof plates with freely supported edges were confinedto five 5- by 5-inch 17S-T aluminum-alloy plates0.0292 to 0.0641 inch in thickness.o/“ x/ ? lJ - /fl z)_reci/on of co

24、il, rigfX l-r-orTNv_r_se/,FIGURE l.-Tensile stress-strain curves for 17S-T ahlmim_in alloy.0,/ | / t Ib,=latcs 9, 10, 11, and 12. (d) Plates 13, 14, and 15.(c) l)latcs 16, 17, and 19. (f) Plates 22, 23, and 25.FIGURE 1 l.-Deflection and s_t at center of 17S-I? atlllllUln-alloy plates with clamped ed

25、ges.478263 42-2Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-8 REPORTNO.748.-NATIONALADVISORYCOMMITTEEFOIAERONAUTICS36 .0634 “37 0668 0 40 80 120 160P_essure, /O/sq ,7.(g) Plates 27, 28, and 29.(i) Plates 18, 20, 21, and 24.m.(k)280(h) Plates 31, 3

26、2, 34, 35, and 38.(j) Plates 26 and 30. “(k) Plates 33, 36, and 37.FIGURE 11 Concluded.-I)eflection and set at center of 17S-T aluminum-alloy plates with clamped edgeaProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NORMAL-PRESSURE TESTS OF RECTANGULA

27、R PLATESincreasing rate with increase in pressure and, in mostplates, it approached a straight line having approxi-mately the same slope as the asymptote to tile deflec-tion curve. In this respect the rectangular platesshowed the same behavior as the circular plates)lotted in figures 14 to 20 of ref

28、erence 5.6.5,4.3.2./o.5.44:5,9o.2./o.5.4.3.2./ ._r _i I I I I I I I I IC, Cenfe/- def/ecf/bn. S, 2tel“of ceni-ez-.Ii I t t _-ISymbol Plate h,/. 2a, in.-x 39 0.0127 2.5- F_ 1 _a-o 40 , 5.0- + 4z .0281 -2.5 .,111 -_, 43 .0-283 5. 0f- o _“ a, “%A_ _, _. _: “. I . j:+_, , -_ , , , - -(a)t 1 II i_ymbol P

29、lote- x 45o 46- + 48a 49h,/n. -2a,/b.0.0338 Z.J.0342 5.0.0587 -2.50530 5.0iC, ooi 0 _) 0o ( ,o0 .,lrOoforthe other half.A/c/ I I I IGc/ge l/be LJD“ecion z y ,x _. I.SE 0/3 _ .8S 0 T t_, 2.00 0+ 6 _= 0 0x _ tv 0 0o _ t i -I.80 0I,/3/-6TIi2 4 6 844Pressure, /b/sq ,.FIQURE 17.-_ediunl-fiber tensile str

30、ain andextreme-fiber bending strain (averageover l-in. gage length) for square 178-T Munlinum-alloy )|ate 0a with clampededges,STRAINSurface strains for plates 10a and 34 _-ere measuredwith 1-inch Tuekerman strain gages placed directlyon the surface of the plate. (See fig. 21 of reference 5.)“15I le

31、 strain readings were corrected for the apparentstrain due to bo_ing of the plate between gage pointsby adding a terln 24r) (see reference 10, p. 6) where1= 1 inch is the gage length and r is the average radiusof curvature of the plate between gage points (obtainedfrom the measured contour of the pl

32、ate).The results for the 5- by 5- by 0.0202-inch aluminum-alloy pbte 10a with clamped edges are given in figuresProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NORMAL-PRESSURE TESTS OF RECTANGULAR PLATES 1116, 17, and 18. Figure 16 shows surface stra

33、ins at sixgage lines for pressures from 1 to 6 pounds per squareinch; these pressures were below the washboarding pres-sures of the plate (31 to 58 lb/sq in.). Unfortunately,the gage length of 1 inch was too great to show thereversal in extreme-fiber bending strain and its increaseto a maximum value

34、 of opposite sign at the clampededges. Measurements over smM1 gage lengths or witha number of overlapping gage lines, such as those madeon circular plates (reference 5) would be required for anadequate description of the spanwise strain distribu-2Oi IS_t_Olr7 overclge lover (_Jone-ibch-goge /engehxI

35、O-4 _-5“-4Exfreme-flT_erh: 0 0202 in.Cl_mped edqes l / Novy Jneld/ I Iores ure/ rl.ro,n./ I J“/ / /X/- - Obser red/ III,2 / / ,ens,e from_0 / / curvoCur-e mee/sut-emeilfs/ L_3I-1- III!/ _ / _-ExfFeme-fJ_er bendzbgIWeshboord/_lg pressures from p/ere/OI I I I _ I0 2o 40 60Pressure, Ib/sq in,8OFIGURE 1

36、8.-Strain at center of square 17S-T aluminum-alloy plate 10a (averageover 1-in. gage length).tion. Curves from references 7 and 11 are included infigure 16. The strain-agMnst-pressure curves are sim-ilar to the deflection-against-pressure curves in so far asthe slope decreases with increasing pressu

37、re. The ex-planation, in both eases, is the same. At very lowpressures the entire load was carried in bending but, asthe deflection increased, eatenary tension developed andan increasing proportion of the load was carried bycatenary action.This action is brought out quantitatively in figure 17by the

38、 separation of the surface strain into median-fibertensile strain and extreme-fiber bending strain. The526120-43-3extreme-fiber bending strain was calculated for this pur-pose from the measured contour of the plate as the ratioof distance of extreme fiber flom the neutral plane ofthe plate to averag

39、e radius of curvature Mong the gageline. The median-fiber strain was calculated as thesurface strain minus the bending strain. The ratio ofbending strain to median-fiber strain decreased with in-I I rkeo/e/bal exme_e-f,Der s/)-Q,_ot_eniec._7,_,-I20 L 2_ _ _ Way (reference II) F = 0.3 _ _1_I-Levy( “

40、73 I s. = 0.316 s “_D/aaDDI_ o 2.00 o“,/.,_:,:y,-,_.P“_of + _+-+-+n-+ / 9., _+-: _ _- ._; -20 40 60 b :! 5-liAr. “_.oo ,L.D;,2_I0 120PFessure, /b lsq /,7.I?IQUIE 20.-Strain at center and edge of 17S-T almninum-alloy plate 34 (averageever l-in. gage length).Strains for the 5- by 5- by 0.0653-inch 17S

41、-T alumi-num-alloy plate 34 with clamped edges are given infigures 19 and 20. Figure 19 shows extreme-fiberstrains for eight g_ge lines at pressures from 1 to 25pounds per square inch; these pressures were below thewashboarding pressures of 62 to 84 pounds per squareProvided by IHSNot for ResaleNo r

42、eproduction or networking permitted without license from IHS-,-,-12REPORT NO. 748-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICSported edges, was therefore probably due to the forma-tion of diagonal folds at the corners. This fact isbrought out further by a comparison of the bendingstrains shown in fig

43、ure 22, which were derived from thechange in contour of phte 54 having freely supportededges corresponding to an increase in pressure from 1 to15 pounds per square inch. The bending strains acrossthe diagonals near the corner were considerably largerthan the str,t.ins elsewhere in the plate.Washboar

44、ding of the plates with clamped edges wasascribed to yielding along the edges due to the clampingstresses. In order to verify tills result experimentally,slots parallel to the edges were cut ill plate 31 after ithad washboarded severely as a result of a nomml-pressure test. The slots relieved the re

45、sidud stressesdue to bending along the edges and caused the inner por-tion of the plate to flatten so that the permanent setinch obtained for this plate. Measurements above 25pounds per square inch were made only on a centergage line and an edge gage line. The results are givenin figure 20 for press

46、ures up to 130 pounds per squareinch. The curve fox strain at the center of the plateresembles that fox“ plate 10a in so far as it shows adecrease in slope with increasing pressure.Curvature measurements were made on three of thefive 5- by 5-inch 17S-T alulnimlm-alloy plates with freelysupported edg

47、es. Normal-pressure tests of the firsttwo plates with freely supported edges had indicatedttmt yielding might be due to the development of adiagonal fold at each one of the four corners, which, inturn, seemed to be caused by pulling out of the platefrom the supports near tile corners. Curvatme was_.

48、ccordingly measured at both the center of the plate andacross the diagonal near one, or two of the corners. Theextreme-fiber strains for these gage lines are plottedbe 8vm/_ol fVce 2os/f/om h.in.I00! - o 57 /3 00370. 57 c_ , I a 58 fa 0.0483 _o ,_ 58 tx “ “ I80 faO_ u 59 B o.o53ooo20 _ - -DrJ 0_! _ll-oID at cen/er0 20 40 _0 80 I00 120 1410Pf-essure, Ib/s._1_ /6 7“/o4 B ;- _-CI l0 I0 20 80 40 50Pressure rohb, pa4,“Yh “_FIaURE 26.-Stress in a square plate with clamped edges.; C, D,strip instead of being