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FILE COPY OS %iML & POW~~ OF1 METEOUS Or COMIPUTINC TE[ STIrNfTII ANU STIFFNESS Uf IPLYWODU STRIPS IN IENUINC lRvised Vecember 194 URI TL A \ T A, GEC. ATLA.TA aGE,> This IPeporl is One of a Series Issued In Cooperation with the AIMYNAVYCIVI l COMMITTEE on AIlVCCAFTI DESIGN CRITERIA Under the Supervision of the AIERONAUTICAL BOAIVD No. 1304 UNITED STATES DEPARTMENT OF AGRICULTURE FOREST SERVICE FOREST PRODUCTS LABORATORY Madison, Wisconsin In Cooperation with the University of Wisconsin Digitized by the Internet Archive in 2013 VETHT= OF UCrrrOTIiT'` T_ OF PLY'NCOD 'T' ALANT D. F? i IT''1I)DU This report gives methods of comp )lywood strips in bending. The methods >f nearly 4,00O static bending tests, an ate. Further analysis of the data may, he details. The methods are limited in applic 1TE'GCTH ANTr 3TTFFT' IF BEIr eeGrW 2rq ineer Ti UN iting the strength and stiffness of .ave been developed with a background [ are believed to be reasonably accu however, result in changes in some of perpendicular to the span. Tata are not yet available for other cases. ?TIFF7,^ OF PLYWOOD STRIPS IN BE1Th.:G The deflection of the center of a simply supported plywood strip under !enter loading will be given approximately by the equation w = Pa' (1) 49 Ecl where w = deflection of the center of the strip P = load a = span E = apparent modulus of elasticity in bending ne (i.e., I UL, bh!2) ie (i.e. I = bh/12) L This is one of a series of progress reports prepared by the Forest Products T,hn+r.to)rv rplatinpr ten t+h ni nr w in. n, a : r t1.. bperp. rennrte3 : 2 defth of strip :he ap;arent modulus of elasticity in bending, c., may be o ,. i = n i n here i mnodulus of elasticity of the ith pl iae esured parallel to th :,a S mo::ent of inertia of the cross section of the ith ply about the ..eutral axis of the cross section ind the other terms are as defined above. "o x~o 0 symeri' '1 1 or pywood colnstructcd smetricI, that is, with r ?.r; nf lies )f eou! Ghic'muses at equal distances fro;., the center, the neutral axi>: of the ,tri will be at the center of the plypood. This will usually be t:e case, 3t last; for carefully mcAde pl rwood; bu.t occasions uay arise when mo. rmxetrical )lywood vwill be encountered. In such ern vent, the location of the neJtral ixis ma oe fouled by i=n Ai AE Ei di \7 AiE,~ dna a(, i : 1 i2l ,here d, = Jistancu from top of beam. to neutral axis d 1 itance from top of beam to center of ith ply Aj. = 'rsssectional area of ith oly o .id.,wood hevinp all plies of equal thickness, for example, lus o' wil. be given by use of eqLuation ('.), as: .r 1 ** l S= width of striiu **1 +_.I'T E?+ 28 1 + 26r ?27 E 27 L ." 1= 25rT + 99 26 + 99r7 L E 125 125 (4) 7 T; E! 99rT + 244 E9 9 + 244rT E 34 243 =2 343L ly; 1 8244rT + 485 E 244 + 485rT E 1 729 EL 729 L where Zl for plywood strips having the grain of the outer plies para1,el to the span E, = for plywood strips having the grain of the outer lies )er; n dicular to the span = o.O.lus of elasticity of wood in the longitudinal direction (parallel to the grain) rT= 'T/EL S = moxulus of elasticity' of wood in the tangential direction Equat ons (4) above an ,ply strictly only to plywood made of "'o;,r  cut veneer, since .the ratio r ha.s been used. For plywood made of quarter slice<. veiee', the ratio r = S/"L should be used, since the modulus of elasticity in .h radial direction would hobe involved. ,nhil equation (1) for a simply suported beam loaded in the center has been izse.l a an example, values of E as fouid from equation (2) !maz be used in the cm.7ropriate equation for deflection corresponding to the method of loz.di bJ, s'bstituting E for E in the usual equations. c f1' the effect of shear deformaation is to be taken into account, equation (1) (uid the corresponding equations for other loadinrs) would be modified b',,another term, as, for examr,ple, w = Ea3 (+ e (5) where e = a term involving the elastic constants of wood and the construction of the plywood h = depth of beam a = span of beam Published values of E, based on static bending tests maade '. ':lhe Forest Products Laboratory arc about 10 percent below the, true vale, ,. . for the matcri.&i because of the effect of shear deformatLon. I'fere no correction for shear deformation is to be made, A' , be calculated wiuh the Forest Products Laboratory published values of IT.. '"'A.i, values of 3c so calculated will ,ive values of deflect'.on correct for ,S: when the effect of shear deform;.tion amounts to about 10 percent. U' sunl these values of E will be sufficiently exact. Where, ho.,ever, a correction for shear deforr.ation is to be u' ,., the published values of E. should be increased 10 percent. J"IL S ,/.; valueoE for (e) are jivec, in table ]. A discuss on of their uses n r:ii nations will be found in the Oiscussion company ..... ]ce 1. COF PLY""OCD STIPS 17 5S 7I1T For Pl^/ood Hvin the Groin of the Outer Plie: iarallel to the Suoin The .trenmth of :'la,,eood stris of this trne bi ending; 'il >e givei. by I = Kr1 s (3) where 1, = resisting raomynt of plywood strip 1c on .at S = ;tress in outer fiber of outermost loni;itudinal .ly c : istance frol.. neutral axis to outer fiber of outermost o.n ;itAdiial )ly 03 = tL M = Kr () C where rm = Em/EL Em = E for a strip of plywood having the outer plies at right angles to the span, but considering that the outer ply on the tension side does not act. The position of the neutral axis for this case may be found by use of equation (3) except that there will be (n l) plies, the outer ply on the ten sion side being omitted from consideration in calculating Em. (The value of I as before is based on the full cross section about its center line, including all plies.) PLY'1701D MADE OF MORE THAN ONE SPECIES The formulas previously presented in this report have been checked by tests of specimenr made with all plies of the same species. A form of plywood comm.only met in aircraft work is that made of two or more species. In the absence of test data to serve as a check, and pending the development of more accurate methods, the following procedure is suggested for calculating the bend ing strength and stiffness of plywood of mixed species; In computing deflections, equation (2) for Ec may still be used, except that in this case the values of Ei for the parallel plies will not be the same for all plies, but will be those corresponding to the species. Similarly, the values of Eifor the perpendicular plies will be those for the species under consideration. In computing strengths, equations (6) and (7) may still be used. The values of r will be determined from E. as indicated above. The value of 5, which for plywood made with all plies of the same species would be the same for either face grain direction, may now be different for the two directions, but in any case will correspond to the outermost ply whose grain direction is parallel to the span. VALUES OF TE RATIOS rT = ET/EL and rR = ER/EL Values of ET and ER from which to compute the ratios rT and rR are available for a few species. The data are, however, incomplete in that only a few species have been tested and that little is known about the variation of IT. I Z n) I 'a as are available are presented in "Elastic from these publications should be used when applicable. For cases in which no data are available, the use of values of rT = 0.05 and rR = 0.10 is suggested. As pointed out later, even approximate values of these ratios will generally give results only slightly in error, so that lack of exact values is not a serious deterrent to the use of the proposed methods. PTI EPROR INTRODUCED BY YTGLECTING TRANSVERSE PLIES The transverse plies may, in general, be neglected with relatively small error except in the case of 3ply plywood having the grain of the outer plies perpendicular to the span. For plywood having the grain of the outer plies parallel to the span, such neglect will generally result in small errors. ?or plywood having the grain of the outer plies perpendicular to the span, however, the error is somewhat larger, and for 3ply plywood of this type the error may be consider able. Figures 1 to 4 show the error that may be expected from neglect of the transverse plies for 3, 5, 7, and 9ply plywood of two types for various values of r. While certain approximations were used in calculating the values for these figures, they will be useful as a guide in determining whether or not neglect of the transverse plies will be a serious matter. It will be recog nized that interpolation in the curves of figures to 4 is not possible. The connection of the plotted points by straight lines has been done only to emphasize the trend, as the number of plies is varied, of the ratios concerned. The foregoing discussion also permits the conclusion that, for most cases, reasonably accurate results may be obtained even with assumed values of r. Therefore, reasonable results may be obtained for species for which no values of rT and rR are available by using the approximate values previously given as a guide in estimating values for other species. VALUES FOR (e) FOR USE IN EQUATION (5) The factor (e) for use in correcting deflections for the deformations due to shear has been evaluated for 3, 5, 7, and 9ply Douglasfir and Sitka spruce plywood having all plies the same thickness for the case of a simply UO* 13(A1 Corresponding val er load, but no exact values are available. It should be noted, however, that reasonable corrections for shear onn may be made even with values of (e) considerably in error. Assu Le, that the proper shear correction was (1 + 0.10O) and that the val sed was 20 percent low. The computed correction would then be (1 + ich is only about 2 percent in error, so that the corrected deflect only about 2 percent in error. From this it appears that the values of (e) given in table 1 may be approximations of the correct values for other types of plywood and f other species, and may also be used to estimate approximately the reactions for such cases. It is expected that these values, for the plywood specified in table 1, will give corrections somewhat too lar or the case of a uniformly loaded, simply supported beam. Calculations based on the values in table 1 indicate that the corre shear deformation will be less than 10 percent in practically all ca o of span to beam depth greater than 48 to 1 is maintained for plywo vring the grain of the outer plies parallel to the span, and greater o 1 for plywood strips having the grain of the outer plies perpendi bhe span. Values of (e) for plywood having all plies the same thickness and used as a simply supported beam with center load (e) Lies : Sitka spruce Douglasfir : Outer plies : Outer plies : Outer plies : Outer plies parallel to : perpendicular parallel to : perpendicula span to span span to span I84. : g.6 141.7 9.9 160.8 46.3 llg.4 36.5 147.1 63.5 108.5 4g.g 138.S 73.3 102.5 55.7 D. 130o4 r_ VALUES O : The values of K suggested for use in equations (6) and (7) are: Stresses at or below proportional limit  Outer plies parallel to span, K = O.95 Outer plies perpendicular to span, K = 0.90 Stresses at or near modulus of rupture  Outer plies parallel to span, K = 0.85 Outer plies perpendicular to span, 3ply, K = 1.10 Others, K = 0.95 If the approximate method, neglecting the effect of the transverse plies, is used, the values of K for the outer perpendicular plywood will have to be increased somewhat, since this approximation results in values of momen lower than the true values. The difference will, of course, depend upon the construction of the plywood, but an approximation of the correct factor may b obtained by dividing the appropriate factor above by the appropriate ratio given in figure 2 or 4. For outerparallel strips the approximate method gives results, in general, close enough to those of the exact method so that no modification of the factor is necessary. STRESS VALUES TO BE USED IM CALCULATIONS The stress values or modulus of elasticity values to be used in the calculations will depend upon the use for which the plywood is intended. U. S, Department of Agriculture Technical Bulletin 479, "Strength a; Related Properties of 'foods Grown in the United States," gives average strong and modulus of elasticity values for the more common species as found from tests on small clear specimens. U. S. DeDartment of Aoriculture Miscellaneous Publication 15, "Guil INo. 130 g = crosssectional area of ith ply = width of beam = distance from neutral axis to outer fiber of outer longitudinal ply = distance from top of beam to neutral axis = distance from top of beam to center of ith ply = a term dependent upon the elastic constants of wood construction of the plywood = apparent modulus of elasticity in bending = B for plywood strips having the grain of the oute3 parallel to the span = E for plywood strips having the grain of the oute] perpendicular to the span = modulus of elasticity of wood in the longitudinal (parallel to the grain) = modulus of elasticity of wood in the tangential dil = modulus of elasticity of wood in the radial direct = modulus of elasticity of the ith ply measured para] the span = E for a strip of plywood having the grain of the c at right angles to the span, but considering thai ply on the tension side does not exist = depth of beam = moment of inertia of the whole cross section of thE about its central line (i.e., I = bh3/12) = moment of inertia of the cross section of the i th I the neutral axis of the cros section = constant = resisting moment of plywood strip LRMY 19L )OYLE ties of wood, Forest Products Laboral i supplements. 4. n 'I r 1 T .3 M 4 .1 M 4 / J c'JV' ^ M^'t ~/ L ^ U iV D. Dept. Agr. Tech. Bul. 479, 99 fading of structural timbe.rs and t' ;resses, U. S. Dept. Agr. Misc. L ,;. 1..= = _L j _.. .....  5 7 PLIES (NUMBER) FIG. / 4 ' T K  \ ^ Q^ ^ /^ TORPRO.Or6O.O K./ / rT ORPR =0.0 rTTO~r =0.03 0=0.04 00 X a rT OR r = 0.05 kj OR r0 = 00. 6 % 0j/70/ L E6END / /(ALL PLIES SAME THICKNESS) .... / o o OUTER PLIES PERPENDICULAR // o...o OUTER PLIES PARALLEL 0 000 3J 5 7 r PLIES (A'UAIBER) F16.2 RTOOE PI/ES P5D CALdCULATED B NE6LECIN& UTRANVERISE PLIES TO LOAEETS CALCULATED BY CONSIDERING TRANSVERSE PLIEI. 1.50 LEGEND (OUTER PLIES ONEHALF AS THICK AS OTHER PLIES) OUTER PLIES PERPENDICULAR .oo OUTER PLIES PARALLEL 1.4 .^ _...............................__.........  LA 1.30\ rORr0.06 Z; \ rTORrR=O.05  rT ORrR =0.04  / <\o rT orp0.03 ^ 1 .10N < V ^ ^ / = o o CL '^~~r ^/ V rOR rf 0.06 00 \rT OOR rR = O.O " .o     /.Q"I 3 5 7 9 PLI ES (NUMBER) FIG. 3 RATIOS OF DEFLECTIONS CALCULATED BY NEGLECT/ING TRANSVERSE PLIES TO DEFLECTIONS CALCULATED BY CONSIDERING TRANSVERSE PLIES. 4 10 rTO _o?00 r. R~ 5 ^ /.90 O rp .02 LEGEND ...... S^ 7^ ^^'K rjOr03 (OUTER PLIES ONEHALF AS THICK r T OR r. =0.04 AS OTHER PLIES) P rTORrR 0.5 oo OUTER PLIES PERPENDICULAR SrOR rR 0.06 oo OUTER PLIES PARALLEL S0.80 1 S 3 5 7 9 PLIES(NUMBER) FI6. 4 RATIOS OF MOMENTS CALCULATED BY NEGLECTING TRANSVERSE PLIES TO MOMENTS CALCULATED BY CONSIDERING TRANSVERSE PLIES. Z m 41128 F 