IBIJCIKLING Of
CUM, 'PLYWOOD PLATES
IN AXIAL COMPRESSION
Information Reviewed and Reaffirmed
January 1953
INFORMATION
AND
REVIEWEb
REAFFIRMED
1060
This Report is One of a Series
Issued in Cooperation with the
ARMY-NAVY-CIVIL COMMITTEE
on
AIRCRAFT DESIGN CRITERIA
Under the Supervision of the
AERONAUTICAL BOARD
No. lOtail
UNITED STATES DEPARTMENT OF AGRICULTURE
FOREST SERVICE
FOREST PRODUCTS LABORATORY
Madison 5, Wisconsin
In Cooperation with the University of Wisconsin
BUCKLIN' OF THIN CURVED PLYWOOD PLATES IN AXIAL COMPRESSION/
By EDWARD ':'3. KUENZI, Assistant Engineer
Summary
This report presents the results of tests made to determine the buckThe
ling stress of thin, curved, plywood plates under axial compression.
tests were made in an apparatus that was arranged to prevent change of curvature at the ends of the plates and to provide guides, not clamps, for the
edges. The plates can thus be thought of as being simply supported. While
it is apparent that a plate supported in this manner is not found in industrial or commercial products where the edges are usually fastened to stiffeners, this method of testing provides means of determining the effectiveness
of thin plates in carrying loads without the complicated analysis that would
be necessary if stiffeners were incorporated.
The conclusions are briefly that the buckling stresses of thin, curved
plywood plates in axial compression are approximately equal to those of thinwalled plywood cylinders provided the width and length of the plates are each
greater than their radius of curvature. It seems likely that the length
effect on the buckling stress of such curved plates is the same as for thinwalled cylinders in compression. Plates of smaller widths and lengths exhibit
higher buckling stresses.
Scope of the Work
The major portion of the testing was conducted on thin, curved, plywood panels of widths from 1/2 to 4. and len gths from 1 to 6 times the radius
of curvature of the specimen. Both axial and circumferential directions of
the face plies were used in the principal series of tests, and a few check
tests were made on specimens having, the grain direction of the plywood at an
angle of 45' with the vertical.
As a check on the effect of the edge guides a few tests made on
cylinders fitted with internal "spiders" to restrain buckling; were compared
with tests on curved panels of matched material.
1
–This mimeograph is one of a series of progress reports prepared by the Forest
Products Laboratory to further the Nation's war effort. Results here reported are preliminary and may be revised as additional data become available
Mimeo. No. 1508
-1-
Buckling stresses of restrained cylinders were also compared with
theoretical buckling stresses of unrestrained cylinders.
Description of Specimens
All specimens were made of yellow birch or yellow-poplar aircraft
grade veneers, rotary cut at the Forest Products Laboratory. The plywood
was glued into flat sheets in a hot press using Tego film glue. To form
these flat sheets to the proper radius af curvature they were wet and bent
t he ceiinder s
over a hot mandrel. Prior to forrdnge the / sheets *ere scarf cut. The
scarf gluing was accomplished on the hot mandrel.
Sheets of matched material were pressed flat and subsequently cut
into minor coupons for testing in bending, compression, and tension. The
matching was accomplished by using veneers obtained from the same portion
of the loc. as were the veneers in the curved plates and cylinders.
While none of the material was conditioned prior to testing, it was
allowed to remain in the testing laboratory for about a week and then tested.
The major portion of the plywood consisted of 3-ply material with
faces of 1/100-inch veneers and cores of 1/40-inch veneers. Some of the
plywood used in the restrained cylinder study was of 5-ply material with all
veneers 1/100-inch thick.
All specimens in this study, curved plates and cylinders, were formed
to a 5-1/4-inch radius of curvature.
Apparatus and Testing Methods
The apparatus used to test the curved plates was arranged to simply
support the vertical edges of the plate (fig. 1). The top of the specimen
was allowed to bear on the edge guide support plate fastened to the upper
head of the testing machine, and the bottom rested on a flat plate mounted
on a spherical bearing on the lower head of the machine. The bottom plate
was adjusted to assure uniform bearing, and screw jacks were placed to prevent tilting. A strap of we'ebiag was passed around the ends of the cylinder
to hold the ends tightly to the end plates. The separation of the edge
guides to receive the specimen was adjusted by means of feeler gages to
Provide a uniform clearance of about 0.002 inch along the entire length of
the specimen. The edge guides were such as to restrain the curved dates inthe radial direction only and afforded no restraint in the circumferential
direction. The load was applied at a slow uniform rate until failure occurred.
The cylinders that were fitted with internal restraining spiders were
loaded in the same manner as the curved plates. The internal spider was
arranged to prevent the cylinder from buckling in certain places by holding
6 or 12 equally spaced radial vanes against the inner wall of the cylinder.
Mimeo. No. 1508
-2-
These vanes were not glued to the specimen. The vanes were made about 1/4
inch shorter than the length of the specimen so that they would carry no load.
Methods of testing minor coupons in bending, compression, and tension
are described in the appendix.
Results of Tests
All specimens (curved plates, cylinders, or restrained cylinders)
failed by buckling of the plywood. 1Tnile this was usually a sudden failure.
all buc'eles appearing instantly, it was occasionally of a progressive nature,
that t6, an initial buckle would develop, then a second, third, and so on
until maximum load was reached. The progressive buckling occurred rapidly,
and the difference between the load at the initial buckle and the maximum
load was usually indiscernible.
In general, the shape of the buckles (figs. 2, 3, 4, and 5) was
,essentially the same as those found in cylinders under compression, although
the size and the aspect ratio changed when the width of the plate was decreased below the radius of curvature of the specimen. The size of the buckle
appearing in the narrower plates was smaller than in cylinders, and the aspect
ratio approached unity.
Long specimens, 1/2 radian wide, of plywood with the face grain direction axial, flattened when the load was applied because of the small stiffness of the panel in its circumferential direction.
Cylinders fitted with restraining spiders failed by buckling. The
shape of the buckles was the same as that of the curved panels of comparable
widths. It was difficult to adjust the vanes on the spider to fit the exact
inside of the cylinder. Evidence substantiating this was seen occasionally
when the width of the buckle was greater than the spacing of the vanes.
This also ma ny have been due to the fact that buckles in adjacent bays caused
some increase in diameter of the specimen thus allowing the buckle to increase in width.
Computation of Results
The buckling stresses were computed ie the usual manner, by dividing
the buckling load b y the loaded area. Prom previous work the buckling
stress for thin-walled plywood cylinders in axial compression was found to
be expressed by the formula:
p e kE
r
...YAmeo. 7o. 1322, "Buckling of Long, Thin, Plywood : Cylinders in Axial Compression."
Mieo. No. 1508
-3-
where:
p = buckling stress
E
1
and defined in Mimeo.1322
E l + E2
k = a constant depending on the ratio = modulus of elasticity of the veneers measured parallel to the grain
h = thickness of the plywood
r = radius of curvature of the plywood
Values of E
were determined from bending, tension, and compression
L
tests on minor specimens of the plywoods. The method is discussed in the
follbwing:
For any plywood construction having the grain of the face plies either
parallel or perpendicular to the span, the modulus of elasticity (E 1 or E )
2
in bending is related to E by the formula:
L
i=n
\
E.
7.
E l or E2 =
I
i=1
1
E = KE L
L
where:
I = moment of inertia of the entire cross section about its
bh3
centerline (I - Tr-)
I i = moment of inertia of the i
th
ply about the neutral axis of
the cross section
Ei = modulus of elasticity of the i th ply, measured parallel to
the span (for plies having the face grain parallel to the
span Ei = EL ; for plies having face grain perpendicular
E.=0.045EL
for yellow birch and E. = 0.037E L for yellow'
poplar)
The values of E l and E2 ware determined from the test data on a plywood beam simply supported at the ends and loaded at the center, by using
the formula E -
F13
. The values of E were then computed by use of the
L
11-.8 A I
3
values of K given in table 1. —
3 Table 1 is the same as Table 7 of Forest Products Laboratory Mimeo. 1322-B.
Mimeo. No. 1508
-4-
For any plywood construction having the grain of the face plies
either parallel or perpendicular. to the direction of the applied load the
modulus of elasticity (E a or Eb ) in tension or compression is related to
EL by the formula:
i=n
Tr-Ai
E _ i=1 uL
A
EL = CEL
where:
A P area of the entire cross section (A=bd)
. th
A.=area of the
ply
Values of E l. and Eb were obtained from compression and tension test
PI
data by using the formula E =
The values of E L were then computed by
Ae
use of the values of C given in table 1.
Values of EL as, found from several tests of each kind (bending, tension, and compression) and in each direction on coupons from the matched
flat plates of plywood were averaged to get the value applicable to a particular curved plate or cylinder. The values of E 2 as found from the bending
tests of the plywood were erratic, and many were for this reason omitted
from the averages. Furthermore, the valid values were too few to be used as
E1
for use in finding the value of k to
a basis for computing the ratio E + E2
K
1
1
be used in the buckling formula. Consequently, the equivalent ratio
K 1 K2
was in each instance computed from the data of table 1 which have been
derived from more adequate tests and are hence considered more appropriate
fOr the purpose. Using these computed values of , 1
1
-
ni
+
n2
+
K2
1
values
of k for use in the buckling formula were read from the graph in figure
6.
Discussion of Results
Experimental values 'of k as computed from the results of tests on
curved plates using the relation k = a- with values of p as found in these
E h
L
tests and values of E L as derived from coupons taken from matched plywood
panels are listed in column 7 of tables 2 and 3. Column 8 lists for comparison theoretical values of k as found by the use of figures 6 from the ratio
Mimeo. No. 1508
K
1
The actual buckling stress as found in test is shown in column 4
K1 + K2.
and the theoretical value in column 9. The theoretical value was found from
the buckling formula (p = kEL 17) using the theoretical values of k and the
values-of EL derived from tests on the coupons from matched panels.
Curved Plates -- Face Grain Axial
and Circumferential
The effect of length of specimen as shown in figure 7 is greater for
specimens with face grain direction axial than for specimens with face grain
direction circumferential. In both instances the length effeot is not
significant until the length is shorter than twice the radius of curvature
of the specimen. A decrease in length from two radii to one radius increases the k about 20 percent.
The effect of width of specimen as shown in figure 8 is not apparent
until the width is less than one radian. A decrease in width from one
radian to one-half radian increases the k about 10 percent.
a
The points plotted in figure 9 show about the same scatter as p ints
in a similar plot for thin plywood cylinders in compression (fig. 10)•—
Curved Plates -- Face Grain at 45 Degrees
Figure 11 presents a comparison between curved panels of plywood with
the grain directions of the veneers at 45° to the axis of the plate and
cylinders of matched material. Experimentally determined values of k are
plotted. The points representing specimens of lengths greater than the
radius of curvature agree closely with theoretical values inasmuch as k is
essentially the same for plates and cylinders. The points representing
shorter specimens show an increase in the buckling stress of the curved
plate as compared to that of the long cylinder. This increase is about 20
percent, or about the same as for specimens having face grain directions
'axially or circumferentially.
Restrained Cylinders Face Grain
Axial and Circumferential
Table 4 presents the data obtained from tests of restrained cylinders.
The experimental results agree fairly well with theoretical values.
-F igure 3 from Mimeo. 1322, "Buckling of Long, Thin Plywood Cylinders in
Axial Compression."
1508
Curved Plates Compared with Restrained Cylinders
-- Face Grain Axial and Circumferential
Table 5 and figure 12 present the results of tests on curved plates
compared with restrained cylinders in compression. Due to the difference
in edge conditions, the restrained cylinders exhibit buckling stresses about
20 percent greater than the curved panels. The curved plate edge is free to
hinge and free to move circumferentially, while in a cylinder the continuation of material over a restraining vane provides more of a fixed edge con.
dition.
In general, much of the variation in test results is accredited to
the fact that small initial imperfections may cause buckling. This variation may also be due to differences in the dimensions of the specimen and
in the mechanical properties of the materials. Factors affecting thicknesses
may be due to difficulties encountered in manufacture, such as the cutting
of the veneer, shrinkage during drying, pressing the plywood, and many others.
Because of the variation of the mechanical properties of the material it is
conceivable that even though a minor specimen was cut from a portion of the
.log adjacent to the major specimen and had a similar specific gravity and
moisture content, the mechanical properties might differ to some degree.a
Figure 13 presents a design curve for long, thin-walled plywood
cylinders and can be used for designing curved plates.
Conclusions
The buckling stresses of thin, curved, plywood plates simply supported
at the edges and loaded in axial compression are approximately equal to those
of thin-walled plywood cylinders provided that the width and length are each
greater than the radius of curvature of the specimen. A decrease in width
from one radian to one-half radian increases the k about 10 percent. A
decrease in length of specimen from two radians to one radian increases the
k about 20 percent.
APPEND IX
Tests of Minor Specimens
Flat plates of plywood that matched the material of the cylinders
and curved plates furnished specimens for minor tests in bending, tension,
and compression.
2See points on curves for strength-moisture and strength-specific gravity
relations for mod as given in Technical Bulletin 479, "Strength and
Related Properties of Woods Grown in the United States."
Mimeo. No. 1508
-7-
Bending specimens were 1 inch wide and were tested on a span length
48 or :More times the thickness of the specimen for face grain direction
parallel to the span and 24 or more times the thickness for face grain
direction perpendicular to the span, thus eliminating the necessity of
correcting for shear deformation. Specimens were cut so that the face
grain direction was parallel to the span and perpendicular to the span.
Specimens rested on end supports rounded to about 1/16-inch radius. The
load was applied at the center with a bar of about 1/8-inch radius. The
stiffer specimens were tested on an apparatus that measured the load by
means of a platform scale reading to 1/100' pound. The rate of loading and
the driving force was obtained from a testing machine on which the scale
was mounted (fig. 14). Specimens not stiff enough to test on the platform
scale apparatus were tested on an apparatus which used water as a load.
The load increments could be read to 10 grams, and the rate of loading was
controlled by the size of nozzle (fig. 15). Lmaediately after testing, a
sample was cut from the specimen for moisture content determination. The
specific gravity was obtained from measurements, and weights were taken before testing and subsequently corrected for moisture content. During the
test, load-deflection curves were plotted. Properties computed from the
test data were the modulus of elasticity, the fiber stress on the most
remote fiber at the proportional-limit load, the modulus of rupture, the
moisture content, and the specific gravity. The modulus of rupture could
not always be computed because the specimen sometimes was pulled down between the supports and wood failure did not occur.
The tension specimens were 1 inch wide and 11 inches long with face
grain directions parallel and perpendicular to the direction of the load.
The ends of the specimens were gripped in Templin grips fastened to the
testing machine by bolts passed through spherical bearings. The strain
over a 2-inch gage length was measured at the center of the specimen with a
Tripolitis extensometer reading to 0.0001 of an inch (fig. 16). The rate of
loading was 0.05 inch par minute. During the test, load-deformation curves
were plotted. Properties computed from the test data were the modulus of
elasticity, the tensile stress at the proportional-limit load, the tensile
strength, the moisture content, and the specific gravity. Moisture content
and specific gravity were determined in the same manner as theywere for the
bending specimens.
The compression specimens were 1 inch wide and 4 inches long with face
grain directions parallel and perpendicular to the direction of the load.
Because of the thinness of the specimen an apparatus consisting of thin spring
fingers was used to give lateral support (fig. 17). . The strain was measured
over a 2-inch gage length with a Marten's mirror apparatus. Load-deformation
curves were plotted as the test proceeded. Properties computed from the test
data were the modulus of elasticity, the compressive stress at the proportional-limit load, the compressive strength, the moisture content, and the
specific gravity. The moisture content and specific gravity were determined in the same manner as for the bending specimens.
Yimeo. No. 1508
Table 1.--Values of K and C used for computing EL
:
Plywood
construction
Bendinp,
parallel
: Tension or : Tension or
Bending
:
: perpendicular: compression : compression
:perpendicular
parallel
:
:Yellow:Yellow-:Yellow:Yellow-:Yellaw:Yellow-:Yellow:Yellaw: birch: poplar: birch: poplar: birch: poplar: birch: poplar
C
:TC•K:K•K:C:C:C:
K2
2 '
1
K1 '
:0.965 : 0.965 :0.080. 0.072 :0.682 : 0.679 :0.363 : 0.358
3-ply (1:1:1)
.944 : .100 : .093 : .632. .629 : .413 :
.408
.562 : .479.
.475
.8 34 : .209 : .203 : .470. .465 : .575 •
.572
3-ply (1:1.25:1)
.945.
3-ply (1:1.67:1)
: .912.
.910 : .133.
3-ply (1:2.5.1)
: .836 :
(1:1:1:1:1)
.800
.127 : .566.
.800 : .245. .237 : .618. .614 : .427 : .423
5-ply
(1:1.25:1.25:1.25:1): .744.
.742 : .301 : .295 : .584 : .582 : .461 : .456
5-ply
(1:1.67:1.67:1.67:1): .664 :
.661 : .381 :
5-ply
(1:2.5:2.5:2.5:1)
.544 : .498 : .493 : .498 : .493 : .547 : .544
: .547 :
.276. .545. .541 : .500. .496
1.25:1.67:1.25:1) ` .724 :
r-(1: 1.25:1.67:1.25:1)
.722 : .321 :
.315 : .613 :
.610 : .432 :
.427
7-ply (1:1:1:1:1:1:1) : .724 :
.722 : .321 :
.315 : .590 : .5 8 8 : .45 5 :
.449
.600 : .441.
.437
.538 :
.534 : .507 :
.503
.465
7-ply
(1:1.67:1.67...:1)
: .604 :
.
9-ply (1:1 .
•1)
9-ply (1:1.25:...:1)
Mimeo. No. 1508
:
: .681 :
.678 : .364:
.359 • •575
.57 2.47 0
: .632 :
.629 : .413.
.408 : .556 :
.552 : .489. .485
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can be removed and the bottom head blocked so that short specimens can be tested.
Width adjustment is obtained by fastening the edge guide supports at different positions in the upper plate.
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M 54173 F
Figure 2.--Buckling failure of a curved plywood plate in axial compression. The plywood is 3-ply yellow birch. The faces are of
0.010-inch veneers, and the core is of 0.025-inch veneers. The
face grain direction is axial. The specimen is formed to a 5-1/4inch radius and is 2 radians wide and 30 inches long.
Z M 54174 F
Figure 3.--Buckling failure of a curved plywood plate in axial compression. The plywood is 3-ply yellow birch. The faces are of
0.010-inch veneers, and the core is of 0.025-inch veneers. The
face grain direction is axial. The specimen is formed to a 5-1/4inch radius and is one radian wide and 30 inches long.
Z 14 54175 F
Figure 4.--Buckling failure of a curved plywood plate in axial compression. The plywood is 3-ply yellow birch. The faces are of
0.010-inch veneers, and the core is of 0.025-inch veneers. The
face grain direction is circumferential. The specimen is formed
to a 5-1/4-inch radius and is 2 radians wide and 30 inches long.
Z /4 54176 F
Figure 5.--Buckling failure of a curved plywood plate in axial compression. The plywood is 3-ply yellow birch. The faces are of
0.010-inch veneers, and the core is of 0.025-inch veneers. The
face grain direction is axial. The specimen is formed to a 5-1/g
inch radius and is one radian wide and 30 inches long.
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