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!'lood Engineering Research
Forest Products Laboratory
Madison, Wisconsin 53705
BUCK1INGOTTIAT pl-ywooDpl-ATts tN
COMPRTSSTON,
SHTAA,OR COITBINTD
AND SHTAR
CO,|IPRTSSTON
Buchling Tosts of flat Dlyu.roodPlates in Compression With
faco Grain 45" to load -- l-oaded fdges Clampod,
Others Simply Supported
lrfe-m.tlon
,$arclrftl{ic
No. t3l6-J
Rcvlcure#leaff
lrmed
|NF0RMATl0f,{
REVIEVVID
ANDREAFFIHIVIED
1962
BUCKLING OF FLAT PLYWOOD PLATES IN COMPRESSION,
SHEAR, OR COMBINED COMPRESSION AND SHEAR1
Buckling
'l4rith
Tests of FIat Plywood Plates in Cornpression
Face Grain
Clarnped,
45' to Load -- Loaded Edges
Others
Sirnply Supported
By
Forest
Products Laboratoty,L
Forest
U. S. Departrnent of Agriculture
Surnrnary
Service
and Gonclusions
This investigation
was undertaken for the purpose of developing a curve
for the deterrnination
of the critical
buckling loads of. flat plywood plates
with the grain direction at an angle of. 45" to the edges and with the
plates subjected to edgewise cornpression with their loaded edges
clamped and the rernaining edges sirnply supported.
Frorn a plot of the buckling vp.lues of 50 such test plates, a curve waa
developed sirnilar to the curve in figure 103 of Forest Products Laboratory Report No. 1316-G applying to sirnilar plates tested with all edgee
sirnply supported.
Upon cornparison,
it is found that the curve developed in the present report has values for the abscissas 1.5 tirnes those of the previous curve.
I
{he
work here reported was done in cooperation with the u. s. Air
Force under order No. (33-038)45-3018. original report published
in L949.
Z
-Maintained
at Madison, Wis. , in cooperation with the university of
'Wisconsin.
R e p o r t N o . 1 3 1 5- J
-I-
Agriculture
-Madigon
Introduction
long plywood panels
in closely designed plywood structures,
Frequently,
with the face grain at an angle of. 45" to the edges are subjected to an
edgewise cornpressive stress applied in the direction of the width of the
panel.
The edges of the panel are rigidly fastened to the framework.
Such a panel, because of its size, has a low critical buckling load that
can be increased rnanyfold by the addition of a few stiffeners at regular
intervals along its length.
These srnaller panels, between stiffeners,
then have clarnped loaded edges and are sirnply supported by the stiffeners.
It was the purpose of this investigation to develop a rnethod for
cornputing the critical buckling loads of these srnaller panels.
It was desired to ernploy the critical buckling
Products Laboratory Report No. 1316,
p
'cr
and to deterrnine the proper
their loaded edges.
-k
c
E
forrnula
(6) of Forest
hz
L
( r)
z
a
value of k" for plywood
plates
clarnped
at
dirnenThe value of this coefficient is dependent upon the construction,
sions, and elastic properties of the plywood, as well as upon the edge
conditions and the direction of the face grain of the plate.
In particular,
it was desired to deterrnine a curve sirnilar to that shown in figure I03
(Forest Products Laboratory Report No. l316-G) for sirnply supported
plates of plywood having the direction of its face grain at 45" to its edges,
but which would apply to sirnilar plates having their loaded edges
clamped instead of sirnply supported.
Preparation
of Specirnens
The test plates consisted of three- and five-ply yellow birch and threeply yellow-poplar
plywood rnade at the Forest Products Laboratory to
AN-NN-P-Slla
specifications and were designed so that the ratios of
their estirnated critical buckling stresses to their proportional-limit
R e p o r t N o . f 3 1 6- J
-z-
stresses had values of 0.2, 0.4, or 0.6.
plywood panels.
They were cut from Z- by 5-foot
The mechanical and elastic properties of the plywood were deterrnined
frorn coupons cut frorn parts of the large panels adjacent to the test
plates and tested in accordance with tentative ASTM Method D805 -45T.
The coupons and the test plates were conditioned
75' I'. and 64 percent relative humidity.
Description
to constant weight at
of Test Apparatus
The testing apparatus is shown in figures 150 and l5l.
The plates were
tested in a hydraulic testing rnachine of 100,000-pound capacity with
their loaded edges clarnped and their other two edges sirnply supported.
The clarnps consisted of pairs of steel bars 2 by 2 inches in cross section and 30 inches long.
The bars were clarnped to the ptrate by rneans
of six 3/8-inch bolts spaced along the centerline of each pair of bars.
The upper clarnp was bolted to the head of the testing rnachine.
The
lower clarnp rested on a 1-inch-thick
steel plate 12 inches wide and 30
inches long.
This plate was centrally supported by a transverse
I/2inch-diarneter
hard-steel
roller resting on the bed of the testing
rnachine and was, therefore,
free to tilt tongitudinally.
The two clarnps
were alined in the same vertical plane.
This arrangement allowed good
alinement of the specirnen and distribution
of the load.
The sides of the plate or the edges that were not loaded were sirnply supported.
These supports were I- by L-llZ-inch
hardwood rails I/8 inch
shorter than the free length of the plate.
Dovetail grooves 3/16 inch
deep were cut along the centerline of one side of each of these two rails
as shown in figure 150. The throat of each groove fitted the edge of the
plate snugly to give it sirnple support.
Two dial indicators reading to 0.001 inch were placed so that they indicated the deflection norrnal to the surface of the plate.
The readings of
the indicator at the center of the plate were plotted for the deterrnination
of the critical
buckling load when the plate was of such proportions
that
it buckled into a single half wave.
The readings of the other dial indica.
tor at a point approximately
one -third the length of the plate gave a
better indication of the critical buckling load when the width of the plate
Report No. 1316-J
-3-
was reduced on the subsequent tests, and also when the plate becarne of
such proportions that it buckled into a full wave.
A sarnple plot of typical lateral-deflection
buckling loads is shown in figure 147.
Preparation
readings
and o f t h e i r c r i t i c a l
of Specimen for Test
The load-bearing edges of the plates were cut straight and parallel to
each other.
The plates were then inserted in the testing rnachine and
pretested for uniforrnity of bearing at a low initial load of about 100
pounds. A feeler gage was used to deterrnine the exactness of fit between the bearing surfaces of the testing apparatus and the edges of the
plate.
When a
If the fit was not satisfactory,
the plate was retrirnrned.
satisfactory fit was obtained, the plate was centered, rnarked, and
This
drilled for the clarnping bolts and slotted as shown in figure I50.
was done so that the plate could be inserted and rernoved frorn the
clarnps without cornpletely disrnantling thern each tirne. .The plate was
then clarnped in place ready for test as shown in figure l5l.
Test Procedure
The plate was loaded at a constant rate of total strain, and readings of
the lateral deflection of the plate were plotted at regular incrernents of
Ioad until the critical load was indicated.
The load incrernents chosen
were about one-fifteenth of the estirnated critical load, and the rate of
strain was adjusted so that readings were obtained about every 5 seconds.
The plate was then rernoved frorn the testing rnachine, and the width rratl
of the plate was symrnetrically
reduced by incrernents such that the original width was reduced to one-half in four or five operations.
After
each reduction the plate was again inserted in the testing rnachine and
its critical buckling load was deterrnined as before.
The critical loads were deterrnined from the points of inflection of the
load-lateral-deflection
curves as shown by figure 147. This rnethod is
degcribed in Forest Products Laboratory Report No. l5Z5-A.
R e p o r t N o . t 3 1 6- J
-4-
Explanation
of Tab1es and Figures
Table 30 contains the dirnensione, elastic properties,
and constants for
the plywood test plates according to species and construction.
Columns
l through 4 contain plate designation and dirnensions.
Colurnns 5 and 6
contain the effective modulus of elasticity
of the plywood in bendingr as
deterrnined frorn rnatched coupons, parallel and perpendicular,
respectively, to the direction of the grain of the face plies cornputed according to the formula
E"
IX
PL3
o r E " Iu| =
4wh3y
where P is the load, L is the span, w is the width, h is the thickness,
and y iFtne d.efLectioiln
the
L = 48h *tGn parallel to face
".rtu",-"nd
grain and 24h when perpendicular
to face!rain.Colurnn ? contains the
values of the-modulus
of elasticity
the
of wood in
direction parallel to
the grain
as cornputed
and 9 contain values
of figure 148.
by the equation
E1
for the particularfiywood
=
#
("r*
+ Efx).
iFtaittJF?"orir
Colurnns
8
the curves
Table 3l contains the data on the effect of the plate width on the buckling
loads, and the coordinates for figure 149. Colurnn I lists the widthe of
the plates tested.
Colurnn 2 contains the critical
Loads obtained frorn
;corresponding
the tests.
Golurnn 3 contains the
critical stresses.
Colurnn 4 shows the values of k" that are obtained frorn
P""
k"=
EL
h
z
7
which is a variation of equation l. Gol.urnns 5 and 6 contain the valuee
of the coordinates for the plot in figure 149. Colurnn 5 contains the
values for the ratio k"/(k.)-,
which was obtained by dividing each of the
ratios in colurnn 4, table 31, by the appropriate value in colurnn 9, table
30. Golurnn 6 contains values obtained by dividing each of those in
Report No. f 316-J
-5-
colurnn 5, table 31, by the product
4 and 8 of table 30.
of the appropriate
In figure 148 the values of the constants k" and
Ef*
tions of the ratio
E"
Ilfi'
lal
are plotted as func -
i
The curve for k.-
+E.
values in colurnns
i" reproduced
frorn
I)<
figure
35, Porest Products Laboratory Report No. 1316-8, and the
br
values for the c'u r v e ;
are frorn the results of calculations made in connection with the sarnileport.
Figure I49 cornpares the plot of the test values for the buckling of 45"
face-grain plywood in cornpression,
tested with the loaded edges clarnped
and the others simply supported, to the curve f.or 45 " face -grain plywood
tested in cornpression with all edges simply supported.
This curve is
obtained frorn that of figure 103, Forest Products Laboratory Report No.
l316-G by multiplying the values of the abscissas by 1.5.
Figure 147 shows the plots of the lateral-deflection
cal platee and indicates the rnethod of deterrnining
load.
readings of two typithe critical
buckling
Figures 150 and t 5 l are photographs of the test set-up, showing the
rnethod of fitting the test plate into the apparatus and the supported plate
ready for test.
Analysie
The coefficient
buckling
of Results
k" for each test plate u/as cornputed
data obFained in the investigation
Pcr = k" Et
thus
Report No. 1316-J
frorn
the critical
by the use of forrnula
hz
7
l,
i.e.
in which a is the width
the observed
wood parallel
The ratios
critical
stress,
of this observed
149.
h the thickness
of the plywood,
the rnodulus of elasticity
and E"
pcr
of the
to the grain.
rnined coefficient
in figure
of the. plate,
k"-
coefficient
for an infinitely
Thil.lues
for (O"J
k. to the rnathernatically
ilng
plate are plotted
are obtained
deter-
as ordinates
frorn the upper
curve
in
figure 148. This curve was detGrined
by the energy method and is presented in figure 35 of Forest Products Laboratory Report No. l316-8.
b
The abscissas in figure I49 are *,
which is the ratio of the lengths of
br
the plates tested to the lengths o?Ttre half wave of sirnilar infinitely
long
plates.
The values for bt were obtained frorn the lower curve in figure
148, in which a is the *IE-ttt of the test plate.
It was desired to develop a
curve for the Gaded edges clarnped sirnilar to that developed for the sirnply supported edges, as shown in the upper curve in figure 103, Forest
Products Laboratory Report No. 1316-G. Such a curve is drawn in figure 149 to fit the plotted points.
Frorn a corrrparison of these curves it
was found that the values of the abscissas for the clarnped condition are
about I.5 tirnes those for the sirnply s.upported condition.
The curve in
figure 149 was drawn according to this assurnption.
The plot of the test points confornrs approxirnately
to the contour of the
curve within the range of the data. Sorne scatter is to be expected due to
the nonuniforrnity
of the rnaterial and to inaccuracies
in the experirnental
deterrninations of the critical stresses.
Notation
The rnajor
symbols
used in this report
are:
= the length of the loaded sides of a plywood plate,
loads.
for compressive
= the length of the unloaded sides of a plywood plate,
loads, with all edges sirnply supported.
for cornpressive
= the length of the unloaded sides of a plywood plate,
loads, with loaded edges clarnped.
for compressive
R e p o r t N o . f 3 1 6- J
-7-
br
= the half -wave length of a buckled
Iong plate.
h
= the thickness
Ef*
= effective rnod.ulus of elastic ity of.the plywood in bending rneasured
perpendicular
to the grain direction of the face plies.
Ef*
= effective rnodulus of elasticity
of the plywood in bending meaeured
parallel to the grain direction of the face plies.
Er
= rnodulus of elasticity
rJ
kc
surface
of the plywood.
of wood in the direction
c@
= coeffici.;
p"" = n"
rJrrt",
= value of the coefficient
load at *h;
P"t
= cornpressive
stress
P
= load in static -bending tests.
L
= span in static-bending
v
= deflection
w
= width in static -bending tests.
cr
to the grain
a
buckling
long plate.
occurs.
at which buckling
occurs.
tests.
in static-bending
R e p o r t N o . 1 3t 6 - J
{
k" for an infinitely
= cornpressive
P
parallel
zo/zt (Er* + Efx)
""
k
in the case of an infinitely
tests.
-8-
.6 -t6
Table 30. --Description
Plate
No.
( 1)
and pertinent
:Thick-: Length
b
: negs:
:h,"
(2)
:
(3)
lx
"f*
(4):
Et
E-
width
a
of the Platee tested
proPerties
a
(5)
(5):
bl
(7)
(8) : (e)
-:------Inch
:
Inches : Inches : 1 , 0 0 0 : I , 0 0 0 : 1 , 0 0 0
:p. s.i. :p. s. i. :p. s.i.
Yellow Birch
3xJl
3xJ2
3xJZa
: 0. I 7 5 : 1 6
:
.178 : 28.O6 :
. 178 : 12.94 :
-- Three
l0
22
10
.
.
.
.
t78
178
178
178
25,5
13,25
25.59
r2.96
Yellow
13xJl
13 x Jla
13xJZ
13 x JZa
. 110
. 110
.108
. 108
R e p o r t N o . 1 3 1 6- J
Birch
3r.62
14.4
3L.62
15.06
i2, 17?t I87.4:2,248
i2, 173: 187.42 2,248
i2, l73z 187.4:2,248
-- Three
Yellow-Poplar
6xl
6xIa
6xZ
6 xZa
1/15-Inch Plies
zz
1l
zz
1t
l , 7 9 0 tz0
1 , 7 9 0 rz0
1 , 7 9 O IZO
l , 7 g o IZO
-- Five
2Z
t0
z2
II
l/16-Inch
l/48-Inch
l, 5go
l, 690
l,5go
l, 6go
525
525
525
525
0.848
.848
.848
o.872
.872
.872
.BZL
.82t
.8Zl
.821
.786
.786
.786
.786
. 968
.968
.968
.968
t.444
Plies
l, gl9
1,819
1,819
1,819
Plies
z, ro9
2, LOg
z, Lo9
z,lo9
r.444
L.444
t.444
Table
effcct
11.--&e
of vartoug
Ylaltbs
oD tJre crltlca.l
buckllng
losdg
of plFrootl
pLatee.
wliltb:crlttcal:crltlcal:
: }"
: b" ::Iltttth :crltlcar:crltlcal.:
.=--.'i:!
a
lctl
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aIoad : Etregs
:
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pcr
t
:
;(k"b;b';;
;
,.,,p",
:i k "
i",
%
r
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(r)
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(2)
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a
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DEFLECTlON
z lrl 81561. F
( INCH)
Flgure 147.--Plot
of lateral
defleetions
of typlcal test plates
6 x 2 -- 22 inches wide and 6 x pa -- Z inches wide, indicating
critical
buckllng Ioad at point of irrflection.
alb
3
a
I
o
s
ot?
o.n
ott
'o.3
Ef,
Eft+ Efr
Figure
constants k " o , a n d b ' / a e
Ef*
. Buckllng
of the ratlo. of
+ Ef*
Ef*
z U 81560 t
148.--The
bot't'r plotted
lnfinitely
of
symmetr ical cons truc t lon, h a v l n g t h e d l r e c t i o n
the face plies 45o to the d l r e c t l o n
of the applied
pressive stress.
as
long
functions
pl&tes
of
of
the grain
comunlform
.H
E
LL
b0 b0 oJ
d
.doo
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Figure
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in
150.--Test
plate in position
bearing,
both top anrl oottom,
plate for clamoing bolts.
zr1 7903?F
before clarnping.
Note
groove in side support,
unifornity
and slots
Figure
< r YT g o J r F
151.--P-tate
claups,
side-raiI
clamped. in
clearance,
position
ready
and transverse
for test.
roller.
Note