Supplomontto
BUCKT.ING
PIATru
OT T1AT P1YWOOD
IN COMPRTSSION,
STITAR,
OR
COITtsTNTD
COITPRTSSION
AND SHTAR
Information Revieu.redand Reafflrmed
September 196l
LOAN COPY
No. l3l6-f
Please return to:
Wood Engineering Research
.Forest products Laboratory
Madison, Wisconsin
53705
EFFECTIVE I{IDTH OF THIN PLN.TOOD
PLATES IN COMPRESSION
I{ITH TIIE FACE GMIN AT OO AI'ID 9OO ro rcADI
By
C. B. NORRIS, Prlnctpal
Englneer
and
A. l{. VOSS, Aseoclate Englneer
Foreat Productg Laboratoryr2 Fo.""t
U. S. Department of Agrlculture
Servlce
Surmarv
Thle report presente the resulte of corrpreeelon teste of thin plywood plates
at 0" and 90" to the face grain directlon
to determlne ttie atrese dlstributlon
under load and the conpresslve etrength after buckllng.
Presented aleo are
curvea for determlnlng from the propertles
the rreffectLve
of the naterlal,
wldth ratlo'r of plyrood plates in conpress.lon when the edges are elnply
supported ln a plane, the rreffectlve width ratlorr being defined ae the ratlo
of the maxlnnrm load sustalned by a buckled plate to the maxinmm load it would
carry had tt been regtralned from buckllng.
Purpose
Fornulas for the calculatlon
buckllng atresses of plywood plates
of crltical
oubJected to coryreeeion,
shear, and comblned compreselon and shear are presented ln Foregt Producta Laboratory Report No. 1316, rrBuckltng of Flet
Plywood Plates ln Compreael.on, Shear, or Combl.nedConpreselon and Shear. rl
The compregelon formula was checked experlmentaLly for stresses at 0o and 90"
to the face graln and the data ere presented ln Forest Products Laboratory
Report No. 1316-D, [Buckllng of Flat Plyvood Platee ln Conpresglon wlth Face
Graln at 0" and 9Q" to Load. tt At stresoes below the critical
buckllng streae,
the uaual fornulal
may be ueed to coryute the strese from the load on any
te report ie one of a gerlee of progress reporta prepared by the Foreet
Producte Laboratory to further the Natlonr I war effort.
Results here
reported are prellminary
and nay be revised as addltlonal
data become
avallable.
Orlglnal report dared Ocrober 1943.
2
--M
alntained
3
--F
at Madleon, I{ls.,
in cooperatlon wlth
oreat Products Laboratory Report No. 1315.
Report No. 1316-E
the Univereity
of Wleconeln.
gLven plate,
After buckltng occuro, theae\formulae .t" ,,oa appllcable becauge
It was the purpose of
the etreeses vary over the crose secttone of the plate.
ln plywood platee aubJected
thle study to deter:nl.ne the etress dletrlbutlon
wldth ratlo curves for
to coryreeslon and to determlne emplrlcat effectlve
coryutlng the courpreeslve load that a plywood plate wlll carry after buckllng.
The effecttve
wldth ratlo le deflned ae the ratlo of the maxlmuurload the plate
Bustalned ln teet to the maxlmum loed the plate would have wlthstood had tt
from buckllng.
been regtralned
DescrlptLon of Materlal
wldth ratlo curvea were the
The epecimens uaed to deteruine the effective
For a deecrlptlon
buckllng fornula.
aame BpecLmeng used to check the crltlcaL
of the epeclnens, the
matching, and condltlonlng
of the rnaterlal, -arklng,
buckllng teet method and the coordlnatlon of teets, see Foregt Product8
Laboratory Report No. 1315-D.
Method of Test
The evaluatl.on of the effectlve
width ratto for thln flat plynood plates wae
based on coryresslon teste of plates eupported in a spectal frane and on
coryreselon tests of coupons cut fron the panela, using the so-called pack
teet apparatue.
The pllmood panel conpreselon tests were made on the game
epeclmens used for the plywood buckLtng study and wlthout removlng the plate
from the teat frame (Report Noo f316-D).
The speclal frame for plate teotg
Le shown tn flgures 83 and 84..:i The method of conducting the compresglon
tests of plywood coupons ls llluetrated
ln figure 81 of Report No. 1316:D.
In the plate coryreeslon te6ta, the exact procedure varled somewhat ln relatlon
to the buckllng teots on the snme plateer and depended on the ratlo of che
streas.
erltical
buckllng stress to the proportlonaL linlt
buckllng atreas less than 75 percent of
For thln plywood havlng a crltical
llmlt
the proportlonal
stress, the plate coryreesLon test was made lumedlately
buckllng load.
after the teet for critLcal
After removal of the load ln the
and
buckllng test, the apeclmen waa agaln l.lned up with the edgee etralght
parallel.
Gompreeslon gages were attached 3/8 lnch from the edges of the
apecinen on both facee and a gage was mounted wlth the splndl-e ln contact wlth
Flguree 83 and 84
defl.ectlone.
the center of the plate to meaaure lateral
show the two facee of a speclmen ready for test.
4
The
flgures and tableg ln thls supp'lement are numbered consecutlvely wlth
those of Foreet Products Laboratory Report No. 1316 and supplementa A' B'
C, and D.
Report No. 1316-E
-2-
For thicker plywood, having a buckllng stress greater than 75 Percent of the
proportlonal
stress, each plate tras tesLed slrmrltaneously for plate comllnit
The load was applled
presslve strength and for crltical
buckllng load.
A11 gages were
ln equaL lncrements untl1 fallure occurred.
lntermlttently
was approached, at \ilhlch tlme the
fallure
reed after each increment untll
gages were rernoved. Another series of tests was made on nlne plates to
before and after buckling occurred, uslng
determLne the straln dlstrlbutlon
the same loadlng condttlons as for the plate compresslon tests made to evatuate
as the load were meaaured,
effective wldth.
Stralns in the same dlrectlon
uslng 1-lnch metalectrLc etrain gages on both faces of the plates at Polntg
31 4-112, and 6 inches from the edgee on the transverse centerU2, l-U2r
llne.
A1so, 4-lnch coupression gages lrere mounted on gage llnes 3/8 inch
fron the edgee and a dlal gage rilaa nounted wlth lts spindle ln contact with
the center of the plate to measure lateral deflectlons.
Data Presentation
Strain
Distrlbutlon
Across Plate
etudy on plyuood plates ln coryresTypl-cal data from the straln dletrlbutLon
slon are presented ln table 12. Readlngs of the slx metalectrlc gages on the
In colunns 9 to 14, the
north facl of the plate are llsted ln coLumrs 3 to 8.
'
The 4-lnch
readlngs of the correspondlng gages on the south face are glven.
gage length conpfesslon gage readlngs are tabulated in columns 15 to 18 and
are deslgnated by the number of the nearest metalectrlc gage. The lateral
at the center ls presented ln coluur 2.
or buckllng deflectlon
The rnetalectrlc gages read straln dlrectl"y, but the readings of the 4-lnch
gage length cornpiesslon gages should be dlvided by four to convert to strain.
These data are plotted ln flgure 85 wtth the compr6sslve etral.ns ag ordlnates
The sketch above the curves
axls.
and the gage numbers al-ong the horlzontal
Each
shows the gage posltlons along the transverse center llne of the plate.
plotted polnt was determined by averaglng the readlngs of the two netal"ectrlc
straln gages mounted upon the same gage Line but upon opposite faces of the
plate.
The currre of average etralns acrose the wldth of the plate ls glven
Numbers on the curves rePresent
for each load at whlch the gages were read.
pounds.
loads ln hundreds of
These data are replotted ln flgure 86 wlth the load as an ordlnate and the
average compreesive straln of each group of four gages the same dlstance from
elther edge as an abecLssa. Curves for gages 1/2 tnch from the edges are
labeled (in-fS-On-6S);
rhose L-Ll2 lnches from the edges (2N-2S-5N-5S); and
those 3 lnches from the edges, (3N-3S-4N-4S). The curve for the 4-lnch gage
length coupresalon gages at 3/8 inch from the edges is aLso sholtn ln this
flgure.
Flgure 87 ehows how the lateral
wlth the Load.
Report No. 1316-E
deflectlon
-3-
at the center of the plate
varied
Effectlve
Wldth Ratlos
Effectlve width ratlos obtalned ln thls eerles of tests are preeented in
table 13 together wlth teet data and cornputed loads.
To determine the effectlve wldth ratlos at proportlonal
lfunit, column 2 or 4, the data obtalned
durlng the plate compreeelon test were plotted as a load-etraln curve as
ahown ln flgure 88. The stralne used were those meagured at 3/8 lnch from
the edges of the plates.
Entering the curve at the straln et proportional
llnlt
determlned by che compresslon tests of the coupons (polnt A, flg.88),
column 13 or 16, the load on the speclmen at thle strain was obtalned (polnt B,
fig. 88) colunrn 5 or 8. The streee et proportlonal
llmit determlned by test6
of coupone, coLumn L2 ot 15, was used to
the load at proportional
llurlt that the speclmen would have carried "orprrt"
if buckllng had not occurred
(polnt C, fig, 88).
Thle load ls entered ln col.urnn10 or 1.1. The ratlo of
the load on the plate at thle etrain (B) to the load at thls straln that the
epeclmen would carry tf lt lrere restralned
from buckl.{ng (C) ls the effectlve
wldth ratlo at proportlonal
ltmit and la entered ln colunn 2 or 4. .If the
plate' fatled before the proportlonal
llnlt
straln lndicated by the coupon
teets waa reached, the maximum load was used ln computatlng the effectlve
wldth ratlo.
The effective
wldth ratlo at maximum atreao, columr 3 or 5, le the ratlo of
the naxluttn averege compreselve streaa acroas the plate, column 7 ot 9, to
the maxtuum streso that the plate would carry lf tt lras reatralned from
buckllng,
columr 14 or 17. The latter
maxlmum stresa was couputed from Ehe
testg on coupong.
In columrs 18 and 19 are entered the equare roota of the ratios of the computed
proportlonal
1funlt atresses to the couputed critical
buckllng streaaes taken
from columr 2 or 8 of table 11. of the report on buckllng tests of these Bame
epecl.mene (Report No. 1315-D).
The effectlve wldth ratloe at proportlonal
lfuntt are plotted as ordlnatee ln
flgure 89 wtth the aquare roota of the ratlos of computed proportlonal
llnlt
streases to couputed crltlcal
buckllng stresses plotted as abeciseas.
The
effectlve
wtdth ratLos at maxlmun load are plotted ln a similar manner ln
flgure 90.
. Analysle of Resulte
The study of straln dietrlbutl.on
acroes the wldrh of the pLatee lndlcated
that the strain le uniformly dietrlbuted
buckllng
untll the computed crltical
load la attalned.
Figure 85 ehows that the compressive straln remained
practlcally
unlforn across the wldth of the pLate for loads up to 400 pounds.
At 400 pounde one edge was stralned a greater amount than the center or the
other edge. At 500 pounds the strain at the edgee lraa at leagt twice the
etrain at the center.
The buckling, or lateral,
deflection of the center of
the plate etarted at about 75 pounds and increaeed to 0.1 inch bt a load of
470 pounde with no lndlcatlon
buckLtng load.
The computed
of a critical
crltlcal
buckllng load f,or thls speclmen wag 350 pounds. ThIs agreemeng
Report No. 1316-E
-4-
buckLlng load and the toad at whlch the straln
between the computed critical
becones concentrated at the edgee and relleved at, the center of a platerwaa
observed tn all nine specLmens studied.
buckllng load, the eEraln became
As the load was lncreased above the crltlcaL
concentrated at the edges as ehown by flgures 85 and 86. The average comvanlshed aa fallure ltes aPProached.
preestve etrain at the center practlcally
Flgure 86 showe that, after buckllng occure, the average stralne comPuted from
the readlngs of the 4-lnch gages mounted 3/g lnch from the edges of the plate
gagee mounted 1/2 lnch
are greater than the stralna measured by therl-lnch
Much of the
from the edgea of the plate on the same transveree centerllne.
to the rapid Lncrease ln straln as the edge of
dlfference can be attrlbuted
the plate ie approached. Extrapolatlon on flgure 85 to the 3/8-inch gagellne
accounts for 40 to 60 percent df the dlf,ference.
ite vertlcal
edges pull ln more at the center than at
Ae the plate deflecte,
the top and bottom and therefore the A-lnch gages measured the change ln
The l-lnch gages were of
length of the chord rather than that of the arc.
the metalectrLc type and therefore meaeured the change In length of the arc.
Computatlons show that tt accounts
however, ie negllglble.
The dtfference,
for only 5-Ll2 percent of the difference between the two gageg.
direction
ln a veftlcal
It ls evident, therefore, that the atraln dletrlbution
near the edge of the plate ls not unlform but ls ma>rimumat the top and botton
cornerg of the plate and mlnlmtrm at the center.
Durlng the tests, it was noted that the greatest curvature occurred near the
cornera of the piates.
The deflected surface in thdse areas approximated a
portlon of a cone wlth the apex at the corner.
Thls same concentratton of
In the
bendlng wag observed ln teots of Longer plates not reported here.
longer platee, slmilar conellke deflections were noted in the corners formed
by nodee and the gulded edges of the platee.
The platee generally fall.ed neer the cornera where the compresslve and bendlng
gtresaes were concentrated.
Slnce thie occurred outside of the range of the
4-lnch gage length, the meaeured strains were lesa than the maxlmum stralne
that
ln the pf"t".
6ccaetonally fallures occurred before these gages lndiiated
llnit
the proportlonal
etraLn, calculated from the compreesion tests of the
was observed ln 8 percent
coupons, had been reached.
Thls premature failure
to the face graln, and
of the tests ln whlch the load was applled parallel
to
tn 30 percent of the tests ln whlch the load was applied perpendicular
straln lta8
llnlt
the fate graln.
When the specimen fail.ed before the elastlc
llmlt
etrain
obaerved, the maximum load was used as the load at the elasttc
wldth ratio at the ProPortional- Llmit'
ln the computation of the effective
The stralns measured by the 4-inch gages were, then, less than the maximum
buckLing stresses were
stralns ln the plywood plates when the critical
88)
exceeded. The observed load at the elastlc Limit strain (poi'nt'B of ftg'
strain'
llmlt
ls, therefore, greater than the toad at the true proportional
Report No. 1315-E
It follor{s that the method of computing effective width ratios
proportlonal
llrntt glves values whlch are too great.
at the
The effectlve width ratlo at maximum stress was obtaLned as previously
explalned on page 3. This ratio was based on accuraLe measuremenLsof Load
and area wlthout lntroducing the strain readings.
The effectlve width ratlo
curve ls glven in flgure 9.
The effectlve wldth ratios were plotted as ordinates in figure 89 and 90 with
the square roots of the ratlos of proportlonal
limlt stresses to crltical
computed buckllng stresses as abscissas.
The abscissas are, therefore, ratlos
except for
of the wldths of the plates to the widths of plates, identical
wldth, which would buckle at the proportlonal- limit stress.
These abscl.ssas
were chosen because it seemed logical that they would lead to an effective
wtdth ratlo curve which would apply equalLy well to plywood plates of alL
constructlons.
There are probably, other factors which influence the value
of the effective width ratlo.
The existence of such factors ls indicated
bj the dlvergence of the points for t,ests with compresslon parallel
to face
graln from the polnts for tests with compresslon perpendicular to face grain
as the abeclssas increased.
The effective width ratios may not be exact due
to varlatlons between the minor test specimen and the buckling test specimen.
Also, the buckllng test specLmenswere of such proportions as would glve a
minlmum crltical
buckllng load.
However, the curves are belleved dependable
for the range covered; and the effective
wldth ratio may be determined for
plates from the properties of the materlal and the plate dimensions.
Conclus-tons
The straln dlstribution
ln a plywood plate simply supported at the four edges
and subJected to compresslon parallel
to the face grain or to compression
perpendicular to the face grain remains relatively'unchanged
until the
computed critical
buckllng load is exceeded. After buckling occurs the strain
dlstrlbutton
changes rapldly with strains becoming concentrated at the edges
of the plate
The comton compresslon formulas.are appllcable for computlng loads, stresses,
or stralns before buckling occurs.
After buckling occurs, a portion of the
plate may be consLdered to carry the load.
Ihe width of this portlon
(effectlve
width) at maximum load can be determLned, if the stresses are at
0" or 90" to the face grain, bY the use of figure 90 in connectlon wlth the
plate
elastlc and strength properties and the dimensions of the particular
consldered.
From the nature of the evaluation,
it ls evldent that the effective width
ratlos
for maximum loads are lnherently
more accurate than for the proPortlonal. llrnlt loads, which are indicated as being somewhat htgh.
Further
study Ls necessary to establish more accurateLy the effective wi-dth ratios
at the proportional
limit,
and to determine the ratLos at other loads between
the crltical
buckllng loads and the maximum loads.
Report No. 1316-E
are lnvolved becauee of the compllcated etreae dletrlbusuch determlnatlons
buckllng load has been exceeded. Further
tlon ln the plate after the crltlcal
behavlor
Btudy r'ould involve also the mathematlcal analyslg of the elastlc
comPllcated
mctte
of the plate lrr thle range and the {evelopment of new and
teetl.ng technlques.
Report No. 1316-E
-7-
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