MAJI & PRIVATE FOREST** 
 
 METHODS Of CALCULATING THE STRENGTH 
 
 AND MODULUS OE ELASTICITY OF 
 
 PLYWOOD IN COMPRESSION 
 
 Revised December 1946 
 
 -IF 
 
 ^ 
 
 '■ $ ' Vff, **T»t NTm 
 
 This Report is One of a Scries 
 Issued In Cooperation with the 
 ARMy-NAVy-CIVIl COMMITTEE 
 
 on 
 
 AIRCRAFT DESIGN CRITERIA 
 
 Under the Supervision of the 
 
 AERONAUTICAL BOARD 
 
 No. 1315 
 
 UNITED STATES DEPARTMENT OF AGRICULTURE 
 
 FOREST SERVICE 
 
 FOREST PRODUCTS LABORATORY 
 
 Madison, Wisconsin 
 
 In Cooperation with the Unhrenitjr of Wisconsin 
 
METHODS OF CALCULATING THE STRENGTH AND 
 MODULUS OF ELASTICITY 0^ PLYWOOD IF COMPRESSION^ 
 
 By 
 
 J. A. LISKA, Engineer 
 
 This report presents a .method developed at the Forest Products Laboratory 
 for calculating the compressive strength and moduli of elasticity of plywood. 
 This method is based on tests which to date have been limited to (l_) plywood in 
 which the grain of the alternate plies is at right angles, (2) loading condi- 
 tions in which the compressive stress is either parallel or perpendicular to 
 the direction of the grain of the face plies, and (j$) plywood in which all 
 plies are of the same species. The tests are being continued to amplify the 
 data and to cover additional plywood constructions. The methods indicated are, 
 hence, subject to modification a3 additional data become available. The for- 
 mulas and discussion relate to members or specimens of such size and supporting 
 conditions that the compressive stress is the controlling factor; accordingly, 
 the data here presented are not applicable to plyvo od columns or plates where 
 buckling is the controlling factor. 
 
 The following formulas, which mathematically are only approximate, have 
 been found by test to be satisfactory for computing the compressive strength and 
 modulus of elasticity of plywood, when the stress is parallel or perpendicular 
 to the direction of the face grain and the grain of alternate plies is at right 
 angl es : 
 
 S = 
 
 J L 
 
 '-#M 
 
 A L / 
 
 A v 
 
 + r,jk 
 
 (i) 
 
 / 
 
 E = 
 a 
 
 where: 
 
 ^r 
 
 1 
 
 J 
 
 Em 
 
 
 \ 
 
 *L 
 
 'A - 1 
 
 *L 
 
 *L 
 
 E^ — 
 "^ A 
 
 (2) 
 
 A, 
 
 is the total area. 
 
 At , is the area of the plies whose grain is parallel to the direction of 
 the applied forces, 
 
 —This is one of a series of progress reports prepared by the Forest products 
 Laboratory relating to the use of wood in aircraft. Results here reported 
 are preliminary and may be revised as additional data become available. 
 
 Report No. 1315 
 
 -1- 
 
Ap, is the area of the plies whose grain is perpendicular to the direction 
 of the applied forces (Ap = A - At ) . 
 
 k = 
 
 A - A^ Ap 
 
 3, is the average unit stress over the total area (either the unit maxi- 
 mum crushing stress or the unit fiber stress at proportional limit, 
 depending on whether S^ is the maximum crushing stress or propor- 
 tional limit value). 
 
 S_ , is the unit compressive stress parallel to the grain (longitudinal). 
 
 B_i is the modulus of elasticity of plywood in compression. 
 
 S n , is the modulus of elasticity of wood in compression perpendicular to 
 grain (tangential)* 
 
 E , is the modulus of elasticity of wood in compression parallel to grain 
 (longitudinal) . 
 
 ^ = E L 
 
 3m E 
 
 R 
 
 The value of the ratios — - = r_ and -= = r^, where 3_ is the 
 
 Bj, * E L E "R 
 
 modulus of elasticity of wood in compression perpendicular to the grain 
 (radial), are available for a few species, although the data are incomplete in 
 that little is known about the variation of these ratios with changes in speci- 
 fic gravity and moisture content. These data are reported in "Elastic Properties 
 of Wood," Forest Products Laboratory Report 1528 and supplements thereto. For 
 species on which no data are available, the use of average values of r^ = 0.0^ 
 
 and r_ = 0.10 is suggested, which will give a good aprroximation of results. 
 
 It may be noted that the strength and moduli of elasticity of plywood 
 are largely dependent on the relative area of the plywood whose grain is 
 "oarallel to the direction of test. Since r n is small, the value of the term, 
 
 r^k, is small compared to unity so that a good approximation of the property 
 
 desired can be obtained even if this term is omitted. 
 
 The formulas presented herein have beon found satisfactory for plywood 
 made from rotary-cut veneer. Ho tests on plywood from quarter sliced veneer 
 -e thus far been made. Presumably the formulas will prove applicable to this 
 
 latter case if r-p is substituted for r m in formulas (l) and (2) and k = _£. 
 
 Report No. 1315 -2- 
 
One of the common plywood constructions met in practice is that in which 
 all plies arc not of the same species. The strength and moiuli cf elasticity 
 of this tjrpe of plywood cannot be calculated "by means of equations 1 and 2 , 
 although the basic formulas are in general believed to be applicable. While 
 subsequent tests need to be made to check this theory, it is believed that the 
 following formulas can be used for calculating the compressive strength and 
 moduli cf elasticity of multi-species plywood: 
 
 <3 = 
 
 
 h l \ "1 + *1 *1 
 
 f A T . Tm A T ) ,, 
 
 (3) 
 
 E u = 
 
 ( S \ ( ^ \ 
 
 A 
 
 St ! At , rm Asp ) , Et I At -j. rm Am ! , 
 
 L l \ ~u + -1 i l I + ^2 \ L 2 + 1 2 L 2 I + 
 
 (*0 
 
 vrhere the terms have the meanings previously indicated and the subscripts 1, 
 2, etc. refer to the different species. 
 
 The unit stress and moduli cf elasticity values to be used in the formu- 
 las can be obtained from previously published data. To give a more correct 
 result, these values should be adjusted to the specific gravity of the plywood 
 and to the expected moisture content when in service, ■ U. S. Department of 
 Agriculture Technical Bulletin lv T o. U79 , "Strength and F.elated Properties of 
 Woods Grown in the United States," will probably furnish most of the desired 
 values for obtaining maximum stresses. While no values for the moduli of 
 elasticity in compression will be foun' 3 therein, they may be obtained by increas- 
 ing the bending moduli values by 10 percent to correct for shear deformation. 
 Basic stress values and methods for determining working or design stresses for 
 structural timbers may be obtained from U. S. lepartment of Agriculture 
 Miscellaneous Publication Ho. 185, "Guide to the Grading of Structural Timbers 
 and the Determination of Working Stresses." AN'C Bulletin 18, Tesign of Wood 
 Aircraft Structures," provides information for a number of aircraft woods. The 
 appropriate values to be substituted in the formulas will depend upon the infor- 
 mation desired or upon the manner in which the plywood is to' be used. 
 
 Report No. 1315 
 
 ■3- 
 
LITERATTvE CITES 
 
 (1) ARMY-rAVY-CIVIL COMMITTEE OF AIRCRAFT TESIG-N CRITERIA 
 
 19UU. resign of wood aircraft structures, ANC Bulletin IS, 2kf pp., 
 illus. 
 
 {2) DOYLE, r. V., DH0W, J. T. , and McBURNEY, R. 8. 
 
 19^5« Elastic properties of wood, Forest Products Laboratory Report 
 l*o. 1528 and supplements. 
 
 (3) MARKVARDT, L. J. and VILSON, T. R. C. 
 
 1935* Strength and Related "Properties of Woods Grown in the United 
 States*. U. S. Dept. Agr. Tech. Bui. No. U79, 99 pp., illus. 
 
 (U) VIL3CII, T. R. C. 
 
 193^» Guide to the grading of structural timbers and the determination 
 of working stresses. U. 5. Dept. Agr. Misc. Pub. 185. 26 pp., 
 illus. 
 
 Report No. 1315 -U_ 
 

 
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