REG NACA-TM-604-1931 Flat Sheet Metal Girdes With Very Thin Metal Web.pdf

1、NOTICE THIS DOCUMENT HAS BEEN REPRODUCED FROM THE BEST COPY FURNISHED US BY THE SPONSORING AGENCY. ALTHOUGH IT IS RECOGNIZED THAT CER- TAIN PORTIONS ARE ILLEGIBLE, IT IS BEING RE- LEASED IN THE INTEREST OF MAKING AVAILABLE AS MUCH INFORMATION AS POSSIBLE. c Provided by IHSNot for ResaleNo reproducti

2、on or networking permitted without license from IHS-,-,-f I i t b 1 -_I- . Geaeral Theoiies and Assunptions . , . PZ e a mb 1 e 1 I This -treatise on sheet r1ieta.l girders 711ith very thin vfeb is the result of my activities with the Roiirbach Letal Airplzm C o rap any . I .i Icy object was to deve

3、lop the f;ltructural method .of sheet L metzl girdecs and shoxld for that reason be considered solely fron t:is s.txidpointe Tine ensuing iiiethods were based on the assuiqtion of the inficitely low. 3tiffness ia bendir-g of the v- nx - 1 iis. sii:plqf$es the basis of the calculations to metal -7eb.

4、 such ax extent that i?;Xkly ,questions of great practical importance I ca2 Se exaiiii:ied which othervise cannot be included in any analy- sis of the Se-ndi-ng stiffsess of the buckled plate. I refer here to such poiilts as the safety in uucxling of aprights to the ef- fect of Seilding flexibility

5、of spars, to spars not set parallel, etc . The assumption of infinitely lov resistance in bendi-ng of the plate produces eryars vhose inten8ity aild effect 02 the April 29, 1929, pp. 203-207; mid Tro1. 20, To. 9, Xay 14, 1929,. , no. 2-:7-2zl - A_- il *llZbem 3lechmmdtza.gcr ciit sclirift fdr Plutec

6、?niI: wid REPRODUCED BY NATIONAL TECHNICAL , INFORMATION SERVICE I U.S. DEPARTMENT OF COMMERCE SPRINGFIELD, Vk 22161 I Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-i f I 2 stress ii? tine plate vi11 be discussed iil Part 11. It becones a-?pae;zt t

7、hat the fornation of wrinkles iizduces local beilding stresses which axe pronounced eve:,2 iil very thin plates and which . also have a certain effect on the Gtress of the material. But primarily, i-t should be noted that the ultima.te load of a sheet %- ,iiLtal wall is lirays cokrectly interpreted

8、by the subsequeizt theory, because after exceedir,g the yield limit the bending re- sistaxe (almost) disagpeus in cor,iparntively thick netal plates. Oiiifssion of the Send-iizg resistance of the plate has practi- cally no effect 017- the calculation of the.ineen teasion stress iil the web aiid cons

9、equently on that of the spars and uprights. Eie caiculafion Ziethods in this report are confilled to flat sheet iiietal girders because their 2-erivation and zpplication re- quire no expe2inental data; the curved sheet netal girders Zre to be treatei? in a later report .-. . I I. We bkgiii kith tile

10、 kirfiple, so :.to say; every-day appli ed cal- l culatiohs ,. folibaing- vith explailatory considerations, aizd COII- cluding with .sevaral rough technical cokputations. *. F . . . . . . . +. For duralunia (there is no appreciakle difference for stecl or 1 wood), the tramition by KYiT values of abo

11、ilt 2 or 3 kg, is i i Let KIVJ = 2 correspond, for example, to a girder h = 50 cizl hi., and which is to be .subjected to a cross S$ZCGG 1 I- r t Q = 10,090 kg (ultinate load). The chect metal veb of such a i ! I girder io of about 1.2 xLi1Nal.,1 thickizecs; to make the web re- sistant to Suckling t

12、he spa.cing of the reinforcenents rrist not exceed forty times the wal.l tiiickness, that is, 50 ma. (The al- f l I I . This is the reason t1ia.t prsctical!ly all sheet imtal sirders used in airplane construction are fokixd md calculated as diag- o.sal -kilsion fields (unless coYrugatzd plates arc u

13、sed). over, bearing in xind that such a -kheet metal gizd-er is generally lighter and less e,wpelzsivc thaa a lattice girder, it is entirely justifiable to subject these problems to 8n exhaustive investi- gation. Row let; a tension CT be zpplied ct the uipcr xici lomr edge of tiie lobed shect (Fig.

14、IC) while the distcncc of the edges A . .-.- L . -31.- . . .“,ci.- I . . . -.- I. . _:_,* _. z -.L - - . . . “. a P - =I . t if Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-i. )! I ! ! .Q i ! 1J .A. C .A. Technical Xe!normdvn No. 604 5 is to remai

15、n thesame as iri.Figure lb. The sheet will withstand considcrzble tension. stresses in this direction without ally appre- ciadble change in the shqe of the wrinkles. If we applied tension stresses obliquely to the wrinkles it would ne c e s0.i t atc the pre s oil0 e o 9 outside s t r o s s es p erp

16、cndi cul ar to the surface of the.sheet in. order to preserve. equilibrium of the stresscs and the s-brcss coixponcnts zcting on a metal strip perpendicular to %he; .sulrface qf the. sneet. I. But since we disal-low the presence of such stresses,. the . o (m = -transverse contractionfigure) rrr .* R

17、e itre alvays in a poeition to check.-Yngse conditions which de- pend on the type of consJcruction and an %he applied stresses. We aow shall suinarize the chief featur-es of our discussion thus far: If. a very thin pkte forme wrinkles durtng deformation, there is no norrial stress perpendicular to t

18、he run of the wrin- kles, no matter what value - Cq. my a;sswne (provided Incquat on (2) is cor:iplied with) ; consequently, elonga%ion. c falling in the direction of t3e wrinkles is affected.by 0 (eqvration 1) PJ f (a L.l 2 but unaffected by - cq. There is no shear stress in a sectior, perpendicula

19、r or parallel to the wrinkles; .O being a principal stress the direction of-the wrinkles is in that. of the greatest .-. posiSive elongation c. .-. Eefore proceeding to nore general. .ci?e infi:itely small (9 -)O) when the glatc becones infiilitely thiE (s-O) ; but ill the limiting case of s equally

20、 2procclles a zwo value. a “. /. 0 with dininishiag lobe depth, A cr Le-; us Lake n sqxare panel a a forcled of Tour perfectly , rigici ;“icibers bvt vit3 flexibly connected 3oziiezs (Fig. 3a). To make. this panel sxititble for taking up traiisverse stresses, ae reinforcesit with cross diazocals ant

21、i Dz. The stresses in 1 the diagonals (as ?Oi:g as D2 does not buckle) ak inversely , .I I Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-4 X.A.C.A. Technical Mcnorandum No. 604 9 z equivalent; Dz is stressed in compression ar-d D1 in tension, I3ut

22、if the diagonals consist of low bending resistant sections any further increse in cross stress P induces D2 to buckle -2 i ; long before stress in it re.aches the yield limit of the material. I i I3jT further increase-. in. . P,: _. we can assume, that the -stress in the . . _ . .- I . . . . buckled

23、 Dz remains constant; but that thereby the tension in D, D, transaits the principal portion of the cross stress. During raises twice as i“as.t, so that finally the tension diagonal this defornation the angle formed by the two diagonals rexains . i f I r e ct a2-l ar . Bqt instead of the cross diagoP

24、.als: we can use a solid .web !Fie. princi.pa1 stresses pl?*tte- tin. siiear. that 0, nay be disregarded relative to. o1 for very thin plates and conespondicgly high stress P. le say: the plate is under tension; it 4. forms a diagonal tension field D2 I. i i al); that id, the piate wrinkles in the d

25、irec- 1 (Fig. 3c). Under: continual. rise of only a1 becomes materially larger akd asumes, in the linit- This near-s -* 1 . F : 1 “ i It is easily shown that by the described deformation of the Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-10 I_ .:

26、 . . . . . , . . . , . . X .A .C .A . Technical Xecoraad“Xo. 604 plate edges all fibers running fa the direction of the wrinkles . undergo the saiae elongation E (the edge sections to be perfect- ly rigid, hence resistant to bending) so that 4 has a coilstant i .: *.-+alue in the whole field. The ve

27、rtical component of the stress - _._ -_ - - _, - -. N6w. we le the- plate, having formed a diagonal teasion field., . io- be cut into zunerous strips parallel to the wriiikles so as to formiiothing but iiidivihal diagonals. This does not c we find that this line also reriaKs a- s%raier the deforimti

28、on. ever,. ?l?ipli-es- %la%- a straigfrt rknber,. if flexibly attached. to - - - -. .- - -*_ . . - .L v. - . - . ._ - L -.c ,-.?- . .- -_ -. ._ -L-; in the strips parallel to axis i y are equal, NOV, if 1, ar?d Zy is the length of these strips, the elongation in the direction of axcs x and y 5e- com

29、es , . , Be further presum that the strips, due to theaction of the outside forces, are subjected to a-direction of change at aiigle Yx and Yy. - The mutual angle formed by both strips after the deformation differs by Y = Yx 4- Vy from 90. -In_addition, let us suppose that the strips remain straight

30、 by the deforma- *i tion. To calculate the direction oftne ensuhg wrinkles and the tension -stresses in the skin, we proceed as follows. . . Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-I c I j -. ! *: i ! ! 1 i ! 1. I ! ! t. I N. A. C .A. Technic

31、al I.:Zemorandum. “io 604 17 . Ve assune tilie plate is resistant to buckling; then we draw a circlew,ith radius X around. a po.int 0 while the plate is as y .irkierr .the. edge strips are deformed the plate does likewise, and- bers are not elongated or else have the sane elongation by a? - I. Provi

32、ded by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-i f i I -1 t 20 N .A. C .A. Technical liernorandum No . 604 angular chmge Y between these nembers. In case the vertical edge memoers are under a slTght tension or even compression the wrinkles run at a sligh

33、tly saall.er arrgle to the horizontal. If the compression; for example, in the vertical edge members is lotiier than inthe horizontal, the wrinkles are in more of a verL tical direction. Equations (4b) ai?d (dc) zre out of the discussion inasrmch as they are not used, at least for the conventional c

34、alculations of sheet netal girders. Aster defining a:?,gle a the tension stress . is moTe easily determined from the outside stresses of a girder. Now we must prove that - 3 - 5 =- 0, otherwise our comid- II erations have no real meaning. Adding(4b) and (4c) yre obtain: - + 9 = x + y For - - - 70 it

35、 folloim from the last equation that cl rfl this condition can also be expressed by Since in sheet metl girders it is exclusively the case of c 0, and cx + cy 0 f mi Wrknklingachiallp occurs in all these cases . The conditioiis existing dter the: yield lfrnit h;: ,*. . . . . . . Sheet . idetd . Gird

36、er with Spars. Resistant in E3e:iding - . Stress Czlculation I .Figure 9 sham a sheet metal girder pin-ended et the right side. , .We assuie its spas to be .contiiiuous and .very .(infinitely) . .- ._ - . . _. . . rigid in bending, and ail upFights pin-joir-ted to the spars. le use the followiil sym

37、bols: . i I* 6 = wall thickness of web plate. h = girder h.eigi1-b from C.G. to C.G. of spar. . A. . . S . i L . = cross-sectio1ia.i area ofug6er spar. cross-sectidnal area of loner qxn. *HO FH.= . t = spzcing of tuouprights. Fv, Jv, i, = cross-$ectional area of BT upright and inertia . :, noncilt m

38、d radius of this area. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-24 e B x Q CT 01 IT .A. C .A Techilical Mernorandux Xo . 604 = distance 02 the C.G. frorn thecross sectioin of the upright to the aeb. plate. . . . = aEgle of upright aiid spax. .

39、 _. . = distance of a point Oil tie plate wall from the line of action of stress P. ._ -. = cro6s stress to be transmitted by the plate wall. = principal web tension. -1 = angle of directi,on of this tensioii with the spars. - , c =g= principal elongation in the plate web. Ho, HU = longitudinal stre

40、sses in upper and lower spars. Qxo, Q:m = (local) cross stress in spar. Msa, XT = (!-oeaI-) -bending mouents in spar. , 3 .* - ha - EU . 2C-u , . cxu = b.pu loigitu- Oxo - YT; E , *xu - - cxo = - 3 clinal stresses and elongations in the spars (spars parallel). , %u ix = 3 (Cxo -k cxu) meen elongatio

41、n of both spars, - V = compression in upright. av - - v. , cv - *v - stress and elongation is an upright. i“V cy = elongation perpendi.cular to spars (in uprights y = cv). - OW ve subject the girder on the left side to cross shear Q, assume the diaensions of the sheet metal gireer to be such that th

42、e direction of the tension stresses CJ is constant in the whole range of the web plate so thzt the :.reb plate forms a diagonal tension field. We (a = coilstant) . Then inre .coiqpute. (3 . !l%e tension ntresses 0 of the web plate act at angle a on Provided by IHSNot for ResaleNo reproduction or net

43、working permitted without license from IHS-,-,-!. N .A. C .A. Technical Memorandum Bo. 604 25 i: tne spars, anc! t5e easuing stress p per unit spar length is (Conpare Fig. ,9) p=lsinusa Now we divide this stress illto horizontal and vertical compo- t. I i . e. nents. It is px =. p c06.a = o s sin a

44、cos CL 3.f = p sin a. = s sin2 a pY -.: i* Stress px actiilg in the spas direction efTects, for example, i I I. an increase in it Q =, px = a s sin a*cos a, d xo .* .: consequently, i. pullc bot; spars 6okd ?ne web; the uprights PY The ctreaa prevent both from approach, but in doir, coy mst take up

45、a COLI- t Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-26 r! .A C .A. Techi1ica.l Memorandun Bo. 604 i pression of the order - V = py t = cr a t sin2u. .I . Comp,?,red with equation (9), we have . 1 t - V = Q tan u (10) and the compressior, stress

46、 in the upright is I- me stress. p produces local cross stresses Qo and Y - QI aad local bending moments NHO and idm in upper aiid lower The spars being continuous, the bending monents are high- I spars. est at the point of attachment to the uprights, and this zpplies to both upper and lower spar *

47、! ! (11) Now let us ima,gine at point x a cut parallel to the up- i i I I the outside stress Q into balance with the imide stresses : rights (parallel to Q) through the sheet metal girder and bri2.g , transmitted at the intersection. included in Figure 9, The tension Tge latter stresses have been .I

48、 Z6 = h COS a s 0 t .j trsnsnitted by the web in the directioa of ct is now divided into i *I i two components X8 = h COS a 0 s COS a T QB = h COS 01 0 6 sin z *i T i 1 I Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-11, A. C .A . Technical h!lemora:?dw,! Xo 604 27 -. . * . .I. .* ). , I. r i Xoting that .the cross stresses Qo,. QYJ, a:ic2