Plywood Properties

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U.S. DEPARTMENT OF AGRICULTURE FOREST SERVICE FOREST PRODUCTS LABORATORY MADISON, WI

U.S. FOREST SERVICE

RESEARCH NOTEF P L-05 9

September 1964

BENDING STRENGTH AND STIFFNESS OF PLYWOOD1

By

Forest P roducts Labora tory, Forest Service

U.S. Depart ment ofAgricultur e

Summary

Layers of a plywood beam in which t he grain direction is parallel to the span

have properties distinctly different from th ose of adjacent layers because of the

90 orienta tion of adjacent plies. Such differences in properties in adjacent plies

complicate the stress distribution a t various points in the cross section, as com-

pared to material with the same properties at all points in the cross section. The

properties of a plywood beam thus depend on th e properties in t he span directionof each ply and on t he construction of the plywood--that is, on the thickness and

number of plies.

This report presents data from tests of plywood of various ply thicknesses and

numbers . Methods are given for computing the s t rength and elas t ic proper t ies

from t he constr uction of the plywood and the properties of the individual plies.

Introduction

Wood is anisotropic in chara cter, having three mutua lly perpendicular axes of

symmetry-

-longitudinal , radia l , and tangent ia l. The proper t ies of wood in the

1This Note is a slight revision of Forest Products Laboratory Report No. 1304, originally written

in 1942 by Alan D. Freas under the title, "Method of Computing the Strength and St i ffn e ss of

Plywood Strips in Bending." It was first revised in 1946 an d then revised again in 1956 under

the present title.


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longitudina l d irect ion are found to be d is t inct ly d ifferent from corresponding

propert ies in the other two direct ions. Bending strength in the longitudinal direc-

t ion , for example , is found to be some 15 to 20 t imes as grea t as in the tangen-

t ial direct ion. Other propert ies also show differences.

P lywood , cons is t ing a s it does of a lt e rna t e laye r s with g r a in d ir ect ions a t

r ight angles, in t roduces fur ther complica t ions . The d irect ion of pr incipa l s t ress

in a p lywood beam is para llel to the span, Thus the pr incipa l s t resses a re a l ter-

nate ly para lle l to gra in and perpendicular to gra in from layer to layer . The d if -

fer en ces in s tr en gt h a n d m od ulu s of ela st icit y in t h e p ar a llel-to-grain an d

across-the-gra in d ir ect ions t hus complica t e t he s t r es s d is t r ibu tion a t va r ious

points in t he cross section of a plywood beam as compared t o a beam of ma terial

with the same proper t ies a t a l l poin ts in the cross sect ion .

The object ive of th is repor t i s to develop methods of ca lcula t ing the e las t ic

and s t rength proper t ies of p lywood beams from the proper t ies of t he component

plies and the construction.

Scope of Study

The bending tests included in th is invest iga t ion of p lywood covered var ious

species , th icknesses , and cons t ruct ions . Speci fica l ly , the var iables cons idered

were:

Three species--Douglas-fir , S it ka spruce , and ye llow-poplar. Five veneer or p ly th icknessess--1/24, 1/16, 1 /12, 1 /8 , and 3 /16 inch . Five combinations with respect to n umber of plies--1, 3, 5, 7 , a n d 9 . Five a r r angemen t s of p lie s--

2 (a) Single-ply veneer with gra in para llel to span.

(b) Laminated wood with grain of al l plies paral lel to span.

(c) Laminated wood with gra in of a l l p lies perpendicular to span.

(d) Plywood with grain of outer pl ies para l lel to span, grain of

adjacent pl ies at r ight angles.

(e) Plywood with grain of outer pl ies perpendicular to span,

grain of adjacent plies at r ight angles.

Related tests--s tandard specimens of sol id wood with gra in para lle l

to span.

Tes ts were made only on specimens in which a l l pl ies were of the same spe-

cies and the same nominal th ickness . S imi lar ly, no defects were permi t ted in the2

It is desira ble, for convenience, to employ a more concise, t hough less accura te, term inology for

the various ply arr angement s. The following term will, ther efore, be u sed in later portions of

the report: All-para llel will be used to mean ply arr angement described un der (b) above: all-

perpendicular, that under (c); outer-para llel, tha t u nder (d): and outer-perpendicular,that

under (e).

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specimens t es t ed . Defect s such a s knot s and spir a l gr a in t ha t . occu r r ed in a

shee t of veneer were e liminated from the mater ia l tha t was to form the speci-

men. Deviat ion of the grain from the plane of the veneer (diagonal grain) is to be

expect ed in rot a ry-cu t veneer a s a r esu lt of unavoidable eccent r icit y of t he

growth r ings. No a t tempt was made to el iminate th is defect nor to eva lua te it s

effect , because cons iderable var ia t ion i s poss ib le with in even a small a rea andbecause of the difficulty of measuring its magnitude. The effect of defects , there-

fore, has been effect ively eliminated in this s tudy.

Bending tests were made on 2- by 2- by 30-inch solid specimens cut from t he

cores of the pee ler b locks . Ten specimens were cut from each of two cores for

both Dougla s-fir and S itka spruce--a tota l of 20 specimens for each species.

Yellow-poplar cores were not ava ilable for these test s .

The following tests were made on veneer, plywood, and laminated specimens:

Sitka Spruce

Three-ply.--Four t es t s were made on each of fou r veneer s of each th icknes s

(1/24, 1/16, 1/12, 1/8, 3/16 inch) from each of two trees and of each of the five

basic constructions. The t otal number of tests was 800.

Five-ply.--The5-p ly t e st s er ies wa s t h e s am e a s t h e 3-ply series, except

t ha t two t es t s were made on pane ls from each of two shee ts from each of two

trees for each th ickness and cons t ruct ion . The to ta l number of tes t s was 200.

Seven-

ply.--

The 7-

p ly t es t s er ies wa s t h e s a me a s t h e 3-

ply series, excepttha t four test s were made on panels from each of two t rees for each th ickness

and construction. The total number of tests was 200.

Nine-ply.--The 9-p ly t es t s er ies wa s t h e s am e a s t h e 7-ply series, with the

same tota l of 200 tests .

In al l, 1,400 tests were made on Sitka spruce panels .

Douglas-fir

The ser ies of test s made on Sitka sprucepanels was a lso made on Douglas-fir

panels. The to ta l number of test s was a lso 1 ,400.

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Yellow-poplar

Three-ply.--Th e3-ply yellow-p op la r wa s given t h e s am e s er ies of t es ts a s

t h e 3-ply Sitka spruce. The total number of tests was 800.

Five-ply.--Th e5-ply t est ser ies wa s t he sa me as t he 3-ply series, except

that one test was made on panels from each of two sheets from one tree for eachthickness and construction. The total num ber of tests was 50.

Seven-ply.--Th e7-p ly t es t s er ies wa s t h e s am e a s t h e 5-ply series. The total

number of test s was a lso 50 .

Nine-ply.--Th e 9-p ly t es t s er ie s was t he s ame a s t he 7-ply series, except that

one test was made on panels from one sheet from one tree for each thickness and

construction. The total number of tests was 25.

The total number of tests on yellow-poplar panels was 925.

Total

In a ll , 3 ,725 tests were made on the panels of a ll three species. In addit ion ,

bending tests of 2- by 2- by 30-inch specimens were made by standard methods

on 20 Sitka spruce and 17 Douglas-fir specimens cut from the cores of t he peeler

blocks.

Mater ia l and Fabr ica t ion

Material

The exact region of growth of the material is not known. The Sitka spruce and

Douglas-fir venee r were cu t a t Tacoma , Wash., and the yellow-poplar veneer

was cut at Huntington, W. Va.

For each species , the veneer was cut by the rotary process from 8-foot bolts

of 2 logs in to 4-foot-wide sheets , except occasionally where defects made i t

necessary to cut smaller widths. Veneers of each th ickness were cut from each

log. The veneer shee ts of each th ickness were numbered success ively as they

were cut and were identified by log and sheet numbers.

The veneer was d r ied a t t he mills by usua l me thods. The cores r ema in ing

after the Sitka spruce and Douglas-fir veneer had been cut from t he peeler blocks

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were left intact and were shipped inthegreen condit ion to the Laboratory, where

t h ey wer e cu t in t o 3-1/2-inch-th ick p lanks tha t weresubsequent ly a ir dr ied. The

cores from the yellow-poplar were not obtained. The core diameters were: Sitka

spruce log 1 , 56 inches : S itka spruce log 2 , 45-1/2 inches; Douglas-fir log 1,

32 inches; Douglas-fir log 2, 34 inches.

The veneer was special ly cut for th is s tudy and was of h igh quality with only

very minor defects .

Matching and Marking of Specimens

The specimens were made up in ma tched set s of five specimens . Each se t

cons is ted of one specimen of s ingle-ply veneer and one specimen each of the

all-p ar a llel, a ll-perpendicular , outer-pa ra llel, a nd ou ter-perpendicular p ly

arrangements,2 a ll w ith t he s ame number of p lie s and made of p lies of t he s ame

thickness.

Since the chief function of the tests was to develop methods of computing the

strength and st iffness of plywood, i t was desirable to reduce, as far as possible,

the effect of variabil ity of material . For this reason, al l m aterial for a given set

of specimens was cut from a single sheet of veneer.

Tes ts were made genera lly on not less than four sets of specimens from each

t ree. Usually, each set was from a d ifferent shee t of veneer , but for the smaller

number of p lies and the th inner veneers i t was somet imes possible to ge t a ll the

material for four sets of tests from a single sheet of veneer. In such cases, more

than four sets of specimens were tested.

Gluing and Conditioning Specimens

The veneers were bonded with casein glue (Forest Products Labora tory for-

mula 4b) after they had been condit ioned to approximately constant weight in an

a tmosphere maintained a t 72 F . and 52 percent , re la t ive humidity (condit ions

tha t produce approximate ly 10 percent equi libr ium moisture content in wood).

After the specimens were glued, they were stored under the same condit ions unti l

their weight was about constant before they were tested. The gluing was done at

room tempera ture with a spread of about 0 .032 pound of g lue per square foot of

joint area.

The solid specimens were condit ioned at 72F. and 52 percent relat ive humidity

unti l their weight was approximately constant before they were tested.

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Methods of Tes t

Al l bending specimens were tested under center loading. The specimens were

2 inches wide and were made 2 inches longe r t han the span to provide a 1-inch

overhang at each end. The span used varied with the different constructions so as

to a fford a uni form effect of shear deformat ion . The span to be used for each

cons truct ion was compu ted from the span-dep th r a t ios based on the nomina l

d ep th of t h e s pecim en . F or t h e a ll-para llel, outer-parallel, and single-ply con-

s t ruct ions , t he span-d ept h r at io wa s 48. F or t he a ll-perpendicular and outer-

perpendicular constructions, the span-dep th r a t io was 24.

The radius of curva ture of the loading b lock was made 1 .5 t imes the nominal

depth of the specimen. The ra te of descent of the movable head was determined3

by the equation (1)

where N is the ra te of descent of the movable head in inches per minute , z the

ra te of outer fiber s t ra in (taken here to be 0 .0015 inch per inch per minute), L

the span in inches, and d the depth of the beam in inches.

The specimens were suppor ted on knife edges tha t were adjus table la tera l ly to

compensate, where necessary, for warp. Rol le r suppor ts were provided between

the knife edges and the specimen to e liminate end res t ra in t . F igure 1 shows de-

tai ls of the adjustable kn ife edges and the rol ler supports .

Simul taneous readings of load and deflect ion of the center with respect to the

ends were obta ined throughout each test . Deflect ions dur ing the ear ly por t ion of

the tes t were measured by means of a d ia l gage graduated to 0 .001 inch . For the

longer specimens, the d ia l gage was a t tached to a meta l yoke suppor ted on na i ls

driven into the specimen at the neutral plane immediately above t he supports . The

spindle of the dial gage was at tached to a nai l dr iven in to the neut ra l p lane a t the

center of the specimen, as il lus t ra ted in figure 1 .

With the shorter specimens, i t was necessary to at tach t he dial gage to th e base

of the suppor t , with the spindle of the d ia l gage suppor ted from a yoke a t tached

to the center of the specimen (figs. 2 and 3).

3Underlined numbers in parentheses refer to literature cited at the end of the text.

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For tes ts of s ingle-ply veneer , it was impract ica l to make any a t t achments to

the specimen it self and , in such te s t s, the d ia l gage was a t t ached to the base of

t h e s u pp or t a n d t h e s pin d le of t h e d ia l ga ge wa s a llowe d t o b ea r a ga in st t h e

bottom of t he specimen, directly below t he loading block (fig. 4).

For the longer specimens, where deflect ions in excess of the capaci ty of thed ia l gage were encoun te red , a s tee l sca le g radua ted to 0 .01 inch was suspended

fr om t he cen ter of the specimen and a fine wire was s t retched be tween na i ls

dr iven into the specimen direct ly above the supports . The deflect ion was meas-

ured by obse rving , th rough a t e lescope, the passage of the sca le past the wire .

The tes ts were discont inued when i t was cer ta inthat the maximum load h ad been

passed.

Where loads were small and the t e s t ing mach ine was no t sens it ive enough to

g ive sa t is factory resu lt s , a more accura te weigh ing sys tem, employ ing a p la t-

form sca le , was used . The p la t form sca le was suppor ted on the s ta t ionary p la t-

form of the t e st ing mach ine , and mot ion was impar ted to the load ing b lock bymeans of rods pass ing th rough holes in the sca le p la t form and connect ing the

movable head of the tes t ing machine with the loading block. The tes t ing machine

was thus used on ly as a means of ach ieving the des ired ra te of movement of the

loading block, while loads were measured with the pla tform scale to 0 .01 pound.

This device is i llustra ted in figure 3 .

Th e s olid 2- by 2- by 30-inch specimens were tes ted under center loading on

a 28-inch span at a head speed of 0 .10 inch per minute (2). The loading block had

a radius of 3 inches . Deflect ion of thecenter with respect to the ends was meas-

ured with a device s imilar to that shown in f igure 1 .

All t es t s w er e m a de in a n a t m os ph er e m a in t a in ed a t 72 F . a n d 5 2 p er ce nt

re la t ive humidity .

Mois tu re dete rmina t ions were made on p ieces tha t were cu t from each speci-

men immediate ly after i t was tes ted.

Discussion of Results

The ana lyses d iscussed in th is sect ion a re based on a compar ison of theore t-

i ca l va lues ca lcu lated from s t rength p roper t ie s dete rmined from test s on lami-

nated and plywood specimens. In each case , the laminated specimen considered

had the same number and t hickness of plies as the plywood specimen with which

compar isons were made. Th is p rocedure was adop ted to e l imina te any possib le

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effect from differences in depth of beam or from differences in the number of

g lue join ts. The resul t s from tests of veneer were not used in the analyses.

No cor rect ions of da ta were made for the large deflections encount ered during

test. These cor r ect ions r ep resen t a negligib le pa rt of r esu lt s , t hus were not

considered.

Modulus of Elast ici ty

Theore t ica l cons idera t ions show (7 , 11) tha t the deflect ion of poin ts on the

central l ine of a central ly loaded rectangular s tr ip of plywood is given by

(1)

where w is th e deflection; P t h e cent r a l load ; a t he span ; E the appa ren t modu-c

lus of elast ici ty in bending; I the moment of iner t ia , based on the fu l l c ross sec-

t ion of the specimen; LT

the Poissons ra t io associa ted with the tangent ia l d i-

rection and stress in the longitudinal direction; TL

the Poissons rat io associated

with cont ract ion in the longi tudina l d irect ion and s t ress in the tangent ia l d i rec-

tion; B and e factors involving elast ic constants of wood; and h the depth of the

specimen,

The factor (1 - LT

TL

) B accounts for the d ifference in deflect ion a t d if -

fe rent poin ts across the width of the specimenthat resul t s from ant iclass ic cur-

vature . The d ifference between th is factor and uni ty was found to be re la t ive ly

unimpor tant for the r a t ios of span to wid th used in t hese exper imen t s. I t was

about 0.99 for al l t ypes of specimens except those with the grain of al l plies per-

pendicular to the span, for which i t was found to be 1.00.

h2

Th e fa ct or (1 + e2

) accounts for the deflect ions resul t ing from shear de-

a

formations. This factor var ied in i t s e ffect with d ifferent cons t ruct ions from

about 1.01 to about 1.13.

The modulus of elast ici ty is different at different points in a cross section of

a p lywood s t r ip , s ince the t ransverse p lies have a modulus of e las t ici ty para l le l

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t o t h e s p a n t h a t i s on l y a bou t 3 t o 5 percent of th at of th e longitu dinal plies. The

t e r m a p p a r en t m od u lu s of e la s t i ci t y i n b en d in g i s t h e r e for e u s ed t o m e a n a

com posite or overall m odulus such as m ight be obtained by the use of the u sual

equations with tension or compression data or withstatic bending data corrected

for shear deform at ion. The a pparent m odulus ofelasticityin bending, E , has thegeneral equation C

(2)

where EC

and I are as pr eviously defined, Ei

is the modulus of elasticity of the

ith ply parallel to the span, I the m om ent of inertia of the ith ply about the cen-i

t r a l l in e of t h e fu l l cr os s s ect i on , a n d n t h e n u m b e r o f p li es . Wh e r e r is e qu a l

t o ET

/EL, E

1i s t h e a p p a r en t m od u lu s for a s t r i p w it h t h e gr a i n of t h e ou t e r

plies parallel to the length of the specim en, and E2

is the apparent modulus for

a strip with th e grain of the outer plies perpendicular t o the length of the speci-

m en, and it is assum ed that all plies are of the sam e thickness, as was the case

in the tests m ade in this stu dy, E m ay be shown to have the following values:c

N u m ber E qu a t ion for Ec

of

plies Ou t er-pa r a llel Ou t er-perpendicular

r + 2 6 1 + 2 6 r3 E1

=27

EL

E2

=27

EL

2 6 r + 9 9 26 + 99r=5 E1 125

EL

E2

=12 5

EL

(3)

99r + 244 99 + 244r7 E

1=

34 3E

LE

2=

34 3E

L

244r + 485 244 + 485r=9 E1 729

EL

E2=

72 9E

L

EL

is th e modulus of elasticity of wood in th e longitudina l direction, an d ET

is

th e modulus of elasticity of wood in th e tan gential direction. It may be n oted th at,

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in equation (1). Ec

= EL

for specimens with the grain of al l pl ies paral lel to th e

length of t he specimens, and E = ET

for specimens with the grain of al l pl iesper pen dicu la r t o t he len gt h. c

Values of E

L

a n d E

T

were obtained by use of equation (1) from tests on al l-

pa ra llel a nd a ll-perpendicular specimens, respect ive ly , and were used with

equ a tion s (3) t o ca lcu la t e v alu es of E a n d E Va lu es of E a n d E a n d ca lcu-1 2 L T

la ted va lues of E and E are shown in tables 1 , 2 , and 3 in columns 5 , 7 , 8 , and

9, respectively.1 2

Values of E1

and E2

were obtained by use of equation (1) from tests on outer-

p ar a llel a n d ou t er-perpendicular specimens, respect ively, and are shown in

tables 1, 2, and 3 in columns 11 and 13 as E1

(obs) and E2

(obs).

Throughout the repor t , the te rm ca lcula ted va lue i s used to mean a va lue

pertaining to plywood derived from theoretical considerat ions based on the con-

struction of t he plywood and from values computed from tests of al l-parallel and

all-perpendicular specimens. The term observed value is used to mean a value

computed from tests on p lywood. The observed va lues may then be compared

with the calculated values to check the validi ty of the theoret ical considerat ions

involved in set t ing up the formulas for the strength and st iffness of plywood.

The rat ios of observed values of E1

a n d E2

to calculated values are shown in

columns 14 and 15 of tab les 1 , 2 , and 3. The p lywood specimens that gave the

observed values were matched with the laminated wood specimens that gave t he

results used in obtaining the calculated values.

All values except speci fic gravi ty in tab les 1 , 2 , and 3 have been adjus ted to

a uniform moisture content basis of 10 percent on the assumpt ion tha t moisture

adjustments for plywood and laminated wood maybe made in th e same manner as

for solid wood (12). Other work (5) has confirmed the validity of th is assumption.

From a considerat ion of tables 1, 2, and 3, it may be seen tha t there i s appar-

ently no uniform variat ion of th e rat io of observed to calculated values of E1

and

E2

, e ither with p ly th ickness for a given number of plies , with number of p lies

for a given th ickness , or between t ree 1 and t ree 2 . I t seems proper , therefore ,t o cons ider a ll of t hese r a t ios t oge ther for each specie s. Table 4 pr esen t s

s ta t is t ics summarizing the compar ison between observed and ca lculated va lues

given in detai l in tables 1, 2, and 3.

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From table 4 i t may be seen tha t , in genera l, the ra t io between observed and

calculated values is approximately unity. Considering the ma gnitude of the stand-

ard devia t ion i t may be seen a t once tha t none of the m ean va lues of the ra t io is

significantly different from unity.

From th is i t may be concluded tha t equat ion (1) represents, with in the l imi tsof var iabili ty of the mater ia l , the re la t ion between load and deflect ion of a cen-

t r a lly loaded r ect angu la r s t r ip of p lywood for s t re sses up to t he p ropor t iona l

l imit , with the values of apparent m odulus of elast ici ty for the plywood defined by

equation (2).

Fiber St ress a t Propor t ional Limi t

Theoretical ly, the stress at a point z distant from the neut ra l ax is of the cross

sect ion of a s t rip of p lywood subject ed to a bend ing momen t M is g iven by

(4)

where f is the unit s tress at a point z distant from the neutral axis , M the bending

moment , z the d is tance from the neut ra l ax is to the poin t being cons idered, E

the modulus of elast ici ty of the material in the direct ion of the stress at the point

being cons idered, E the apparent modulus of elast ici ty in bending for the s t r ipc

of p lywood, and I the moment of iner t ia based on the fu ll c ross sect ion of the

specimen.

Equation (4) applies, of course, only when stresses are below the proport ional

limit a t a l l poin ts in the cross sect ion . The analys is leading to equat ion (4) i s

based on the assumpt ion of l inear var ia t ion of s t ra in across the cross sect ion ,

and i s applicable only where the shear deformat ions are not grea t enough to in-

val ida te th is assumpt ion , as in beams of re la t ive ly la rge span-depth ra t io or in

regions of low shear, such as the centralport ion of a uniformly loaded beam.

The r e sis t ing moment of a p lywood beam for a s t r es s f in the ext reme fiber

is given by

(5)

where c is the d is tance from neut ra l ax is to ext reme fiber in inches.

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fEC

IfE

is replaced by fa

, wh ich m ay b e called an ap p aren t stress, eq u ation (5 )

x

may be replaced by

(6)

wh ere

(7)

If th e ap p aren t stress at p ro p o rtio n al l im it is d en o ted by FL

FT

, a n d F1

for

a ll-p arallel , all-p erp en d icu lar, an d ou ter-p arallel specim en s, resp ectively , i t

may be seen th at , based on equation (7),

(8)

I t m a y be n ot e d t h a t , f or a l l-parallel and all-perpendicular specimens, the ratio

E /E b ecom es u n ity , an d eq u ation (4 ) red u ces to th e u su al eq u ation for stressc x

in a bent beam.

Valu es of FL

a n d FT

were ob tain ed , b y th e u se of equation (6), from data on

a ll-p a r a lle l a n d a ll-p erp en d icu lar sp ecim en s, resp ectively , an d v alu es of FL

were used with equation (8) to calculat e values of F1

. Values of FL

a n d FT

a n d

F1 (calc.) a re shown in t ables 5, 6, and 7 in columns 5, 10, and 7, respectively.

Valu es of F1

were obtained by use of equation (6) from data on outer-parallel

sp ecim en s, an d ar e sh own in tab les 5 , 6 , an d 7 in colu m n 1 5 a s F1

(obs).

T h e ob serv ed an d calcu lated v alu es were t h en com p ared . T h e ratios o f ob-

served to calculated values are shown in column 20 of tables 5, 6, and 7 a n d a r e

su m m ar ized in tab le 8 . T h e calcu lation s were m ad e for g rou p s of sp ecim en s a s

described in the discussion of modulus of elasticity.

It may be noted that the observed values were approximately 90 percent of the

calculated values; ranging from 0.72 to 1.09 times the calculated values. This is

F P L-05 9 -12 -


13/55

because the p ropor t iona l. l imit in the bend ing te st i s r eached fir s t a t on ly one

loca t ion in the beam. Th is loca t ion i s d irect ly under the load in the ex treme

compression fibe r . As t h e t es t p r ocee ds , a d ja cen t m a t er ia l a ls o r e ach es t h e

propor t iona l l imit . A cons iderab le amount of ma te r ia l mus t be a ffected be fore

the load deflect ion curve is su fficien t ly in fluenced to ind ica te a p ropor t iona l

limi t (3 ). Thus the p ropor t iona l l imit s ob ta ined from bend ing te st s a re a lways

greater than those obtained from compression tes ts .

The tensile and compressive s t rengths of wood perpend icu la r to the g ra in a re

very low, Ca lcu la t ions ind ica te tha t the t ensi le s t r ength of the ou te r t r ansverse

tension ply of a plywood s tr ip that has i ts face grain direct ion perpendicular to

the span i s exceeded by the t ime the ou te rmos t longitud ina l p ly has reached i t s

p ropor t iona l limi t. When the t ensi le s t r ength of the t ension t ransverse p ly has

been exceeded, i t can no longer contr ibute to the bending s t rength of the plywood

s t r ip . There fore , the p ropor t iona l limi t bend ing s t rength of a p lywood s t r ip i s

controlled by that of the outermost longitudinal ply, and the outer t ransverse ply

may be neglected in computing th e proport ional l imit s t rength of the s t r ip.

There are indicat ions that the proport ional l imit in compression perpendicular

to gra in i s r eached a t a deformat ion abou t 2-1 / 2 t o 3 t i m e s a s g r e a t a s t h a t a t

p ropor t iona l limi t in compression pa ra llel to g ra in . Th is means , then, tha t the

outer t ransverse compression ply of a 3-ply plywood s tr ip with a l l p lies the same

t h ick n es s r ea ch es it s p r op or t ion a l lim it a t a bou t t h e s a me t im e a s d oes t h e

longi tud ina l p ly. The same wil l be t rue of plywood with more than th ree p lie s.

Therefore , the outermost longitudinal ply wil l be th e controll ing factor , and the

propor t iona l l imit of the p lywood s t r ip wil l be reached when the s t ress in th is

ply reaches i ts proport ional l imit value.

From the above cons idera t ions , ca lcu la t ions of F2

h a ve b ee n m a de on t h e

b as is t h a t t h e com pr es sive t r a n sver s e p ly is effe ct ive , b ut t h a t t h e ten s ile

t ransverse ply is completely ineffect ive . Under this assumption and neglect ing

t h e e ffect of ch a n ge of n eu t r a l a xis wh en t h e ou t er t r a n sve rs e t en sion p ly is

neglected, equation (5) becomes

(9)

where E ' is t he apparent modulus of e las t ici ty about the centroidal axis with the2 outer t ransverse tension ply neglected and c' is the dis tance from the centroidal

FPL-059 -13-


14/55

axis to the outer longitudinal ply. I f a l l p lies are of equal th ickness , then

(10)

wh er e n is the number of plies . Making this subst i tu t ion into equat ion (9), equa-

t ion (5) becomes

(11)

Based on this equat ion the apparent s t ress a t proport ional l imit for plywood with

outer-perpend icu la r p lie s is

(12)

a n d for d iffer en t n um ber of p lies , F2

can be calculated from the fol lowing

equations:

Number Equat ion for E2' Equa t ion for F

2of

plies

1 +3 E

2' =

27

13rE

LF =

1 + 1 3 rFL2 9

26 +5 E2

' =125

50rE

LF =

2 6 + 5 0 rFL2 75

+7 E ' =

99 + 135rE

LF2

=99

245

135rFL2 343

9 E2' =

244 + 292rE

LF =

244 + 292rFL72 9 2 567

Values of F2

calculated on the basisofthese equat ions are shown in column 17

of tables 5 , 6 , and 7 . Values of F2 were obtained by use of equation (6) from data

on outer-perpendicular specimens and are shown in column 18 of the same tables

FPL-059 -14-


15/55

as F2

(obs), The r a t ios of obse rved to ca lcu la t ed va lues of F2

are shown in

column 22 of tab les 5 , 6 , and 7 and are summarized in tab le 9 . While cons ider -

able va r iabilit y is found, t he ave rage va lue of t he r a t io is found to be abou t

93 percent .

F rom the foregoing, it may be concluded tha t t he load-carrying capacity (fors t resses a t the propor t ional l imit ) of a s t r ip of p lywood may be predicted by the

equation

(13)

where K i s an empir ica l factor , I i s the moment of iner t ia of the whole crosssect ion , c is the d is tance f rom the cent roida l ax is to the ext reme fiber , and F

a

may be found from the fol lowing tabulat ion forplywood with al l pl ies of the same

thickness and species .

Number Equat ion for Fof

a

pliesOuter-para llel Outer-perpendicular

r + 2 6 1 3 r + 13 F

1= F

L 27 F 2 =FL

9

50r + 265 F 1 = F L

26 + 99

125F

2= F

L 75

799r + 244

F =F135r + 99

F 1 = F L343 2 L 245

244r + 405 292r + 2449 F1 = F L 729

F2

=FL 567

A method i s given e lsewhere in th is repor t for set t ing up s imi lar formulas for

any construction.

Modulus of Rupture

Obviously, any theories based upon assumptions of elast ic behavior are invalid

for applica t ion a t fa i lure . However , it i s not unreasonable to assume tha t va lues

FPL-059 -15-


16/55

of apparent modulus of ruptur e for plywood, based upon the theory outlined in the

preceding sect ion, would differ from the observed values by some approximately

constant factor .

Upon th is p remise, there fore , va lues of apparent modulus of ruptu re based

u pon m od uli d et er m in ed fr om t es t s of a ll-para lle l and a ll-perpendicular speci-

mens were calculated on the same basis as that employed in calculat ing values

of apparent fiber s t ress a t proport ional l imit . These calculated values were com-

pared with observed values of apparent modulus of rupture from tes ts of outer-

p ar a llel a n d ou t er-perpendicular specimens,

M od uli of r u pt u r e fr om t es t s of a l l-para lle l and a ll-perpendicular specimens

are shown in tables 5 , 6 , and 7 in columns 6 and 11 as SL a n d S T , respectively.

Va lues of S and S calculated from these moduli a re shown in columns 8 and 13,1 2

respectively. Values of S2

were calculated assuming outer tension ply ineffective

as was explained for the calculation of F2

. Observed values of S1

and S2

as found

fr om d at a of ou t er-para lle l specimens and ou ter-perpendicular specimens are

shown in columns 16 and 19, respect ively . The ra t ios of observed t o calculated

values are shown in columns 21 and 23 of tables 5 , 6 , and 7 .

I t may be concluded tha t the u lt ima te s t rength of a s t r ip of p lywood may be

predicted by the equat ion

(14) where S may be found from t he followingtabulation for plywood with all plies of

a

the same th ickness and species , and the other t e rms have the mean ings given in

connection with equation (13)

Number Equa t ion for S

ofa

plies Outer-para llel Outer-perpendicular

1 3 r + 13

S1

= SL

27S

2= S

L 9

r + 2 6

5 7

9

26 r + 99S

1= S

L 125

50 r + 2 6S

2= S

L 75

99r + 244 135r + 99S

2= S

L 245S

1

= S

L

343 244r + 485 292r + 244

S1

= SL

729S

2= S

L 567

FPL-059 -16-


17/55

A later portion of this report will give a method of setting up similar equations

for any construction.

Tables 8 and 9 p resen t summar ies of the compar isons between obse rved and

ca lcu la ted va lues given in deta il in t ab les 5 , 6 , and 7 . In t ab le 8 , the va lues of

S1 rat ios for a l l numbers of pl ies are considered t ogether . The average ra t io of

S1

(obs) to S1

(calc.) is 0.86. In ta ble 9, however, the value of S2

ra t ios for the 5-,

7-, a nd 9-ply construct ions are considered together in one group and those for

t he 3-ply a re cons idered separa tely, s ince the average ra t io for 3-ply construc-

t ions is 1 .15, and for the 5-, 7-, a n d 9-ply is approximat ely 1.0.

Effect of Neglect ing Transverse Pl ies

Considerat ion of tables 1 , 2 , and 3 and 5, 6 , and 7 indicates that the t ra nsverseplies may be expected to contr ibute , ingeneral , but l it t le t o the s t rength or s t iff -

ness of a plywood s tr ip . A comparison of values of modulus of e las t ici ty from

t es ts of a ll-perpendicular specimens with those from tes ts of a l l-parallel speci-

mens shows tha t ET

is only about 3 to 5 percent of EL

. Similar ly, a comparison

of moduli of rupture indicates that the ult imate s t rength in tangent ia l d irect ion is

only about 4 t o 6 percent of that in th e longitudinal direction.

F r om t h is i t would appear that a good approximation could be obtained by

neglect ing the effect of the t ransverse pl ies and by consider ing that the plywood

consis ted only of the longitudinal plies , with the t ransverse pl ies act ing only to

space the longitudinal plies . Computat ions of modulus of e las t ici ty, fiber s t ressa t p ropor t iona l l imit , and modulus of rup ture were made on th i s bas is by con-

s ider ing only t hose plies with the grain direct ion parallel to t he span.

Modulus of Elast ici ty

In the case of modulus of e las t ici ty, neglect ing the e ffect of the t r ansverse

plies amounts , essent ia l ly , to neglect ing th e terms involving r (r = ET

/EL

) in

equa t ions (3 ). The e r ror s to be expected from th is approximat ion may be est i-

m a t ed . As su m in g r = 0.04 for t h e 3-ply outer-para llel constr uction, for instan ce,

the ra t io of exact to approximate value would be 26.04/26 = 1 .0015. The error is

only a small fract ion of 1 percent . Other values of the ra t io of exact to approxi-

mate values of E1

and E2

are tabulated below for r = 0 .04.

FPL-059 -17-


18/55

Number Ratio of exact to approximate

of modulus of elasticity

plies

Outer-parallel

(E1)

3 1.0015

5 1.0105

7 1.0162

9 1.0201

Outer-perpendicular

(E 2)

2.0400

1.1523

1.0986

1.0795

F or t h e ou t e r-parallel specimens, the error is negligible in comparison with

the natural variability of the m aterial. For the outer -perpendicular specimens,

on the oth er han d, the errors, particularly for the 3-ply, are of significan t size.

Tables 10, 11, a nd 12 present values of EL

, FL

, a n d SL

calculated from th e

results of tests of plywood specimens by considering only th e para llel plies. In

col u m n s 6 a n d 7 a r e s h ow n r a t i os of t h e v a lu e s of E fr om su ch ca l cu l a t ion sL

com p a re d w it h r e su lt s fr om t e st s of a ll-parallel specim ens. The rat ios are

genera lly n ear u nit y except for t hose for the 3-ply out er-perpendicular specimens.

As previously pointed out, approxim ate values of E m ay be calculated byc

neglecting t he terms involving r in equa tions (3). The rat ios of values calculat ed

from equations (3) considering th e terms involving r to those calculat ed by n eg-lecting such term s are shown in table 13 for var ious values of r. The values ofr

chosen are average values ( table 16) for the various groups of specim ens. The

ratios should correspond with those given in colum ns 6 and 7 of tables 10, 11,

and 12. The compar ison, shown in table 14, indicates good a greement .

Figures 5 (left) and 6 (top) show the variation in error to be expected from

neglecting t he tran sverse plies for various values of r an d for 3-, 5-, 7-, a n d

9-ply plywood. Figure 5 sh ows th is r elation for plywood with all plies the sa me

thickness, and figure 6 for plywood with th e face plies one-h a l f a s t h i ck a s t h e

others.

F P L-05 9 -18 -


19/55

F ibe r S t res s a t P r op or t ion a l L im it ;

Modulus of Rupture

Consider equation (5):

(5)

F o r a 3-ply s t r ip with the grain of outer plies paral le l to th e span, th is equat ion

reduces to

(15)

for s t r ess in the ext reme fibe r .

Neglect ing the effect of the t ransverse plies here again amounts essent ia l ly t o

neglect ing r in equat ion (15) and in the re la ted equat ions for other construct ions .

The e r ror s int roduced by th is approximat ion a re ind ica ted in figures 5 (r igh t )

and 6 (bot tom) and by the ra t ios shown incolumns 11, 12, 16, and 17 of tables 10,

11, and 12.

F or ou t er-para lle l specimens, the e r ror r e su lt ing from neglect ing the t r ans-

verse plies in computing modulus of e las t ici ty, fiber s t ress a t proport ional l imit ,

or modulus of rup tu re i s so small a s to be negligible, even for p lywood wi th a

la r ge n u m be r of p lie s. F or ou t er-perpendicular specimens, on the other hand,

the error is considerable , especially for 3-ply and 5-ply plywood. For such con-s truct ions , the approximation may be too great ly in error to be useful .

Rela tion Between the Proper t ie s of

Laminated Wood and Sol id Wood

In the p receding sect ions , ce r ta in re la t ionsh ips between the p roper t ie s of

laminated wood and plywood have been developed with the taci t assumption that

the proper t ies of laminated wood and sol id wood were ident ical . Some consider-

at ion must be given to the validi ty of th is assumption.

FPL-059 -19-


20/55

In genera l , there appeared to be no var ia t ion in the s t rength proper t ies of the

laminated wood with var ia t ions in p ly th ickness or in number of plies , except

tha t t he r esult s from t es t s of s ingle venee rs were gene ra lly somewha t lower

than those from specimens withmore thanoneply. The reason for th is d iffe rence

is not known, but it is pos sib le t ha t t he glue join t s i n t he mu lt i-ply specimens

may have had some effect in increasing the strength,

Bending tests of sol id wood have indica ted a decrease in both fiber s t ress a t

proport ional l imit and modulus of rupture with increasing depth of beam (10). I t

might have been expected, then, that a tendency toward decreasing strength would

be found for lamina t ed ma ter ia l w ith increas ing numbers of p lies of a given

veneer th ickness, or with increasing p ly th ickness for specimens of a given

number of p l ies. Such a t rend was not found in e ither case. The var iabili ty of

resul ts was cons iderable , and apparent ly was sufficient ly la rge to obscure a

trend if any were present . The comparisonof specimens of a given veneer thick-

ness for various numbers of pl ies would be expected to give the better compari-

son, s ince such specimens would have come more nearly from t he same port ion

of the tree than would th ose with the same number of plies but of different veneerthicknesses.

Obviously, any exact matching of material in laminated a n d solid specimens is

impossible. I t was considered, however, that some semblance of matching might

be obtained by test ing solid specimens from the cores of the peeler blocks from

which the veneer had been cut . The result s of s tandard bending tests on speci-

mens from peeler b lock cores a re summarized in tab le 15. The result s , ad jus ted

to a moisture content basis of 10 percent , a re a l so shown to facil ita te compar i-

son with the results of the tests of laminated specimens. Specific gravity values

were not adjusted to the 10 percent moisture content basis .

Because of the l imitat ions of s ize of available material, bending tests on speci-

mens of solid wood with t he grain perpendicular to th e span could not be made.

The result s from the test s of solid specimens bore no cons tant re la t ion to the

result s from the test s of laminated specimens, a lthough the averages were gen-

era lly with in the range of result s from laminated specimens. I t i s probable tha t

the matching was inadequate, because the solid specimens came f rom near the

center of the tree and the laminated specimens came from varying posit ions near

the outs ide. The genera l agreement of result s , however , indica tes tha t there i s

no serious difference in propert ies between solid and laminated specimens, and

tha t the ca lcula t ion of p lywood proper t ies us ing the methods d iscussed herein,together with strength propert ies from tests of solid wood, is valid.

FPL-059 -20-


21/55

Conclusions and Recommendations

The preceding por t ion of the repor t has presented methods of comput ing the

strength and st iffness of plywood str ips subjected to bending, with a discussion

of the re la t ionships exist ing between the methods . A summary of these methods

wil l now be presented, together with the factors to be used in applying them.These factors apply to plywood having al l equal thickness plies.

Deflect ion of Plywood Str ips

Exact method.--The deflection of a plywood strip may be determined (exclusive

of deflect ions result ing from shear deformations) by use of the usual equations,

s imply by replacing modulus of e las t ici ty in bending by an apparent modulus .

This apparent modulus of e las t ici ty in bending is a funct ion of the number and

th ickness of the p lies in the s t r ip , and of the longitudina l and t ransverse moduli

of elasticity of the wood.

The apparent modulus of e las t ici ty, E , may be ca lcula ted fromc

where I is the moment of iner t ia of the fu ll cross sect ion about it s cent ra l l ine ,

E.i

the modulus of e las t ici ty of the i th p ly para lle l to the span, Ii

the moment of

iner t ia of the ith p ly about the cent ra l l ine of the fu ll cross sect ion , and n thenumber of plies.

For p lywood with a l l p lies of the same species , E may be found fromc

where I is the moment of iner t ia of the fu l l cross sect ion about i t s cent ra l l ine ,

I and I a r e t he momen t s of iner t ia l of t he t ransve rse and longitudina l plie s,x w

r espect ive ly, abou t t he cent r a l line of t he fu ll cros s s ect ion , r is t he r a t i o of

the t ransverse to longitudina l modulus of e las t ici ty of the wood, and EL

is the

FPL-059 -21-


22/55

longitudinal modulus of elast ici ty of the wood (9 ). A table of values of E forc

plywood with al l pl ies of the same species an d the same thickness has been given,

equat ion (3).

Approximat e method. --The deflect ion may be computed approximately, using

a moment of inert ia based upon only the paral lel pl ies; th at is,

where the summation is made only for those plies with the grain direct ion paral lel

to the span. For plywood with al l pl ies of the same species,

For plywood with the face grain paral lel to the span, this approximation wil l, formost cases, be only slightly in error . For plywood with the face grain perpendic-

ular to the span, however , the e r ror may be cons iderable and in many cases will

be so large as to render the approximation unu sable. The magnitude of the errors

to be expected from the approximation has been shown, for cer ta in cases , in

figures 5 (left) and 6 (top).

Values of E (modulus of elast ici ty in the tangentialdirect ion of the wood) andT

E (modulus of e las t icity in the radia l d irect ion of the wood) for comput ing theR

ra t ios r = E /E are avai lable for some species . The da taT T L

and rR

= ER

/EL

are incomple te, however , in tha t only a few species have been tes ted , and l it t leis known about the variat ion of these rat ios with variat ions in specific gravity or

with changes in moisture content .

The pr incipa l ava i lable da ta a re presented in Elas t ic Proper t ies of Wood,

Forest Products Laboratory Report No. 1528, and supplements thereto (4). Some

data are available also in references (6) and (8). For cases in which no da ta a re

ava ilable , t he u se of va lues of r = 0.10 is suggested. Approxi-= 0.05 and rT R

mate va lues of these ra t ios may g ive resul t s only s light ly in e r ror .

The correction for an t icla s tic cu rva tu re is u sua lly so small t ha t it may be

neglect ed . F rom t able I I of Marchs paper (7), i t may be seen to be less than

2 p er cen t for 3-ply a n d 5-ply str ips of spruce plywood, even for str ips with a

rat io of span to width as low as 4.

FPL-059 -22-


23/55

The correct ion for shear deformation, on the other hand, may be considerable .

This correct ion is made (see equat ion (1)) by mult iplying by a factor involving

the constant e , which depends upon Poisson 's ra t ios and moduli of r ig idity . Data

on these proper t ies are available (4 , 6) for a few species , and may be used with

equat ions presented by March to calculate values of e . Some values of th is con-

s tant have a lready been calculated and are presented in table 18.

These values of e ma y be used as a basis for est imating values of e for other

species . Reasonable correct ions for shear deformations may be made even with

va lues of e cons iderably in e r ror . Assume, for example , tha t the p roper shea r

corrrect ion is (1 + 0 .10) and tha t the value of e is 20 percent low. The computed

correction would then be (1 + 0.08), which is only 2 percent in e r ror , so tha t the

corrected deflect ion would be only about 2 percent in error .

Load-Carrying. Capaci ty of Plywood Str ips

(For s t resses a t p ropor t iona l limit )

Exact method .--The load-carrying capaci ty of a plywood s tr ip for s t resses a t

the proport ional l imit may be determined by

where K is an empir ica l factor , F is found as ind ica ted be low, I i s the momenta

of iner t ia of the whole cross sect ion about i ts centra l l ine , and c is the dis tance

from the centrodial axis to the extreme fiber of the outermost longitudinal ply .

Th e t er m F for ou t er-para llel s t r ips i s given bya

where F is an apparent s t ress in bending, FL

is the des ired s t ress in the ou ter-a

most longitudinal ply, and the other terms are as previously defined.

For outer-para lle l s t r ips with a ll p li es of the same species , F may be founda

from

FPL-059 -23-


24/55

wh er e r , I , a n d I a r e a s p reviou sly defin ed , a n d F is t h e des ir ed st r es s inx w L

the outermost longitudinal ply.

For ou ter-perpend icu la r s t rip s, F is given by a s im ila r p rocedu re, excepta

t ha t t he ou t er t r an sve r se p ly on t he t en s ion s ide will be neglect ed . H e re, Fa

will be given by

where E equals E for a s t r ip ofp lywood with the outer p lies a t r igh t angles tom c

the span, and the outer ply on the tension side i s considered ineffect ive. The othert e rms are as previous ly defined.

For ou ter-perpendicu lar s t r ips with a ll p l ies of the same species, F will bea

given by

where I ' is t he moment of iner t ia about the cent ra l l ine of the fu ll cross sect ionx

of al l t ransverse pl ies except the one on the tension side, and al l other symbols

have the meanings previously given.

Omiss ion of the outer t ransverse p ly on the t ension s ide will resu lt in a sh ift

in the neut ra l axis from the center of the depth toward the compress ion face of

the beam. The effect of this shift i s general ly smal l enough to be neglected, and

the neut ra l ax is may be assumed to be a t t he center of the depth of the beam.

The factor K has been determined experimental ly and the fol lowing values wil l,

in gene ral, give r e su lt s on t he s a fe s ide: ou t er-para llel plywood, 0.85; outer-

perpendicular plywood, 0.90.

Approximate method. --The load-carry ing capacity may be computed approxi-

mate ly by

FPL-059 -24-


25/55

where the t e rms are as previous ly defined. The same va lues of the factor K may

be used, except for the 3-ply outer-perpendicular plywood, where a value of 1.20

should be used,

For plywood with the face grain paral lel to the span, this approximat ion, which

involves neglect ing the t ransverse plies, wil l, for most cases, be only slight ly in

er ror . For p lywood with the face gra in perpendicu lar to the span, however , t he

er ror may be cons iderab le and in many cases will be so la rge as to render the

approximat ion unusable, The magnitude of the errors to be expected from the ap-

proximation has been shown, for certain cases, in figures 5 (right) and 6 (bottom).

Ult imate Load-Carrying Capaci ty

of Plywood Strips

Exact method.--The ult imate load-carrying capaci ty of a plywood st r ip may be

computed by the method given for st resses at the proport ional l imi t by subst i tu-

t ing modulus of rup ture in p lace of the lower s t ress and by using appropr ia t e

values of K, which are somewhat different for ul t imate load than for the lower

stresses.

Va lues of K a re: outer-paral lel plywood, 0.85; outer-perpendicular plywood,

3-ply, 1.15; outer-perpendicular plywood, 5 plies or more, 1.00.

Approximate method.--The approximate method, as given for use with st resses

a t t he p ropor t iona l lim it , m ay be u sed a lso for com pu t ing t he u lt im a t e load-

carrying capaci ty by subst i tut ing modulus of rupture in place of the lower st ress

and by us ing appropr ia t e va lues of K . Values of K given for use with the exact

m et h od m a y be u sed wit h t h e a pp roxim a te m et h od excep t for 3-ply outer-

perpendicular plywood, where a value of 1.50 should be used.

Lit e ra ture Cit ed

1. American Society for Test ing Materials .

1946. S tanda rd m et hods of s t at ic t es t s of t i m ber in s t ruct u ra l size s.ASTM Designation D198-27.

2. .

1946. S tanda rd m et hods of t es t ing sma ll clear specim ens of t im be r.

ASTM Designation D143-27.

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3 . Bech tel, S . C ., and Nor r is , C . B.

1952, St rength of wood beams of rectangular cross sect ion as a ffected

by span-depth rat io. Forest Products Lab. Rpt . 1910.

4 . Doyle, D. V,, Drow, J . T ., and McBurney, R. S .

1945-46. E la s t ic p roper t ie s of wood . Fores t P roduct s Lab. Rpt . 1528

and Supplements A, B, C, D, F, G, H.

5. Dr ow, J . T.

1945. E ffect of m ois tu r e on t h e com pr es sive, ben din g, a n d s hea rs t rengths, and on the t oughness of p lywood . Fores t P roduct s

Lab. Rpt. 1519.

6. Jenkin , C. F .1920. Repor t on mater ia ls of cons t ruct ion used in a ircraft and a i rcraft

engines. (Gt. Brit . ) Min. Munit ions, Aircraft Production Dept.,

Aeronautical Research Com.

7. Ma r ch , H . W.

1936. Ben din g of a cen tr ally-loaded rectangular s t r ip of p lywood.Physics 7(1):32-41.

8. Ma r kwa r dt , L. J .

1938. Form factors and methods of calculat ing the strength of a woodenbeam, Forest Products Lab. Rpt . 1184.

9. , and Wilson, T. R. C.

1935. St rength and r ela t ed p roper t ie s of woods grown in t he Un it edStates. U.S. Dept. Agr. Tech. Bul. 479.

10 . Newlin, J . A. , and Trayer, G. W.

1924. The influence of the form of a wooden beam on i t s s t iffness ands t rength , I I. Form factor s of beams subject ed to t r ansve rse

loading only. Natl . Advisory Comm. for Aeronautics Rpt. 181.

11 . Norr is , C. B.1942. The technique of p lywood. I . F . Laucks , Inc., Sea t t le.

12. Wils on , T. R C .

1932. Strength-mois tu re r ela t ions for wood . U .S . Dep t . Agr . Tech .Bul. 282.

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T a b le 1 .--Comparison of observed and calculated values of E 1 a nd E 2 for Sitka spruce. (All

v a lu e s e xce p t s p e cific g r a vity a d ju s te d to 1 0 p e r c en t mois tu r e co n ten t b a s is . )

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T a b le 1 . -- C omp a r is on o f ob s er v e d a n d c a lc u la te d v a lu e s of E 1 a n d E 2 for Sitka sprucde. (All values

e xc ep t s p ec if ic e g r a v ity a d ju s te d to 1 0 p e r c en t mo is tu r e c on te n t b a s is . ) ( co n tin u e d )

(Sheet 2 of 2

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T a b le 2 .- - C omp a r i s on o f o bs e r ve d a n d c a lcu l a t e d v a l u es o f E 1 a n d E 2 f or D ou g l a s- fi r . ( Al l

v a lu e s e xce p t s p eci fi c g r a vi t y a d ju s t ed t o 1 0 p er ce n t m oi st u r e con t e n t b a si s. )

: 1 ,5 39 :: 1 ,1 15 :: 1 ,3 27 :

: 1,4 89 :: 1 ,121 :: 1 ,305 :

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Ta ble 2.--C omp a r is on o f o b se r v ed a n d c a lc u la te d v a lu e s o f E 1 a n d E 2 for Douglas-fir. (All values

e xc ep t s p ec if ic g r a v ity a d ju s te d t o 1 0 p e r ce n t mo is tu r e co n ten t b a s is . ) ( con tin u e d )

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Table 3.--Comparison of observed and calculated values of E 1 a nd E 2 for yellow-poplar. (All

values except specific gravity adjusted t o 1 0 p e r ce n t m oi st u r e con t e nt b a si s. )

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T able 4 ,--S u m m a r y of r a t i os of ob se r ve d t o ca l cu l a t ed v a lu e s fr om table 1


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Table 5.--Comparison of observed and calculated values of F1

, S1

, F2, a n d S

2for Sitka spruce.

(All values except specific gravity adjusted to 10 percent moisture content basis.)

(Sheet 1 of 2)


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Table 5.--Comparison of observed a nd calculated values of F1

, S1

, F2, a n d S

2for Sitka spruce. (All

e xc ep t g r av it y a d ju s t ed t o p e rce n t m oi st u r e c on t e n t b a si s. ) (c on t i nu e d)

2 Of 2)


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Table 6.--Comparison of observed and calculated values of F 1, S 1, F 2 a n d S 2 for Douglas-fir.

(All values except specifice gravity adjusted t o 10 percent moisture content basis.)

(Sheet 1 of 2)


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Table 6.--Comparison of observed and calculated valu es of F1, S1, F2, and S2 for Douglas-fir. (

values except specific gravity adjust ed to 10 percent moisture content basis.) (contin

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Table 7.--Comparison of observed and calculated values of F1, S1, F2, and S2 forf yellow-poplar.

(Al l value except speci fic gravi ty a djusted to 10 percent mois ture content basis. )

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Ta ble 8.-- S u m m a r y of ra t ios of observed to ca lcula ted va lues of F1

a nd S1

from tables 5, 6, a nd 7

Ta ble 9.-- Summary of ra t ios of observed to ca lcula ted va lues of F2 and S2 from tables 5, 6, a nd 7

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T ab le 1 0.--C om pa r is on of va lu es of m od ulu s of el as tici ty, fib er s tr es s a t I D r t ion al l im it a nd

modulus of r u pt ur e fr om t ests of a ll-p a r a ll el , ou t e r-p ar all el, a nd ou t er-perpenmar

s pe ci me ns , n eg le ct in g e ffe ct of t r a ns ve rs e p li es (S it k a s pr u ce ) ( con t in u ed )

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F igu r e 2 .--Details of apparat us for bending tests of plywood, showing method of atta chment of

dial gage to specimens too short to permit use of supporting yoke a s shown in figure 1.


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Fi gu re 3 .--Details of appara tus for bending tests of plywood, showing the u se of a platform scale

for measuring sm all loads.

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F igure 4.--D etails of apparat us for bending t es ts of s ingle-ply veneer.


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F i gu r e 6 .--Ratios of deflections (top) and m om ents (bottom ) calculated by neglecting tran s vers e

plies to deflections calculated by cons idering tran s vers e plies w hen the outer plies are one-

half as thick as the other plies .

Plywood Properties

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