SIATE &PRIATE FUNKSh
MAtTIA) 0C CAICIATINC- Tilt1 STIP1tNC;TE
ANI) MOIVIUS 0Cf ELASTICITY 011
P4ywcul) IN CCAIPEISSICN
lIevised December 19443
This reportt Is On. of a Series
Issued In Cooperation with the
AlRM V-NAVY-Cl VI t COMAITIM
AIICVAf I)LMIN Cg?#TtA
Under the Supervision of fhm
UNITED STATES DEPARTMENT OF AGRICULTURE
FOREST PRODUCTS LABORATORY
in Coopwamio with the University of Wi~tonfin
IMT 0D$ P? CALCTMIATINTG THE 'STRY,'ITGT- .AIM
11ODTUU7 OF ELAIT!C!TY OF PLYWOOD IY COMPRPWE3--lON1
J. A. LIGKA, 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 (1) 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 (3) plywood in which all
plies are of the same species. The tests are being continued to amplify the
data and to cover aditional plywomod constructions. The methods indicated are,
hence, subject to modification as 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 n 'ot applicable to ply'o od colums 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
'S a E L 1 + -Z/ AL M L A--- I + r Tk (2)
Ak E ,,i
A, is the total area.
AL, is the area of the plies whose grain is parallel to the direction of
the applied forces.
1-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
AT, is the area of the plies whose rain is perpendicular to the direction
of the applied forces (AT = A- AL).
k A AL AT
3, is the avera-e unit stress over the total area (either the unit maxi-
mum crushing stress or the unit fiber stress at proportional limit,
Depending on whether SL is the maximum crushing stress or propor-
tional limit value).
SL, is the unit compressive stress parallel to the grain (longitudinal).
Ea, is the modulus of elasticity of plywood in compression.
qT, is the modulus of elasticity of wood in compression perpendicular to
EL, is the modulus of elasticity of wood in compression parallel to grain
The value of the ratios = r and = r, where R is the
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 1529 and supplements thereto. For
species on which no data are available, the use of average values of rT = 0.05
and rR = 0.10 is succested, w',ich will Vive a rood approximation of results.
It Tay be noted that the strength and moduli of elasticity of plywood
are largely dependent on the relative :rea of the. pywood whose grain is
parallel to the direction of test. Since rm is small, the value of the term,
r Tk, 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 been found satisfactory for plywood
made from rotary-cut veneer. No tests on plywood from quarter sliced veneer
hnve thus far been made. Presumably the formulas will prove applicable to this
latter case if rR i substituted for rT in formulas (1) and (2) and k = E.
report No. 1315
One of the common plywood constructions met in practice is that in which
all plies are not of the same species. The strength and molull of elasticity
of this type 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 in believed that the
following formulas can be used for calculating the compressive strength and
moduli of elasticity of multi-species plwyood:
12 AL2 L2
Ll AL1 1 ASL2 A2 r 2 A (3)
E AL L T2A
L E 1 +2EL1 L + L2 E 12 +2
Ea = A
L1 A +1 r AT 1 ) + j 2 \ AL2 + rT2 AT2 *** (4)
where the terms have the meanings previously indicated and the subscripts 1,
2, etc. refer to the different species,
The unit stress and moduli of 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 Nvo. 479, "Strength and Related 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 found. 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 fcr
structural timbers may be obtained from U. S. department of Agriculture
Miscellaneous Publication No. 185, "Guide to the Grading of Strlctural Timbers
and the Determination of "Corking Stresses." ANC Bulletin 18, "Tesign of Iood
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
(1) .IY-4VY-CIVIL COrI!MITT-7 0CT AIRCRAFT IrESIGN CRIT I.A
19~4T. sign of wcod aircraft structures, A C Bulletin 19, 247 PP.,
(2) 'CTp. v., TrFP-vr, J. T., and McHURfNEY, R. S.
19~5.Elastic properties of wood, Forest Products Laboratory Report
NO. 1529 and supplements.
(3) MA-RT ;kFDT, L. J. and '1LSI7N, T. R. C.
19Y35. Strength and Related Properties of Woods Grown in the United
States. U. S. Pept. Agr. Tech. Bul. No. 479, 90/ pp., illus,
(4) WILSONT, T. It. C.
1934. Guiide to the grading of structural timbers and the determination
of working stresses. U. S. Dept. A, r. Misc. Pub. 19F, (16 pp.,
-(rort No. 1315
WIVERhiry OF FLORIDA
3 1262 08866 6036