Methods of computing the strength and stiffness of plywood strips in bending

MISSING IMAGE

Material Information

Title:
Methods of computing the strength and stiffness of plywood strips in bending
Physical Description:
Book
Creator:
Freas, A. D.
Forest Products Laboratory (U.S.)
University of Wisconsin
Publisher:
United States Dept. of Agriculture, Forest Service, Forest Products Laboratory ( Madison, Wis )
Publication Date:

Record Information

Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
aleph - 29393300
oclc - 757397739
System ID:
AA00020674:00001

Table of Contents
    Front Cover
        Front Cover 1
        Front Cover 2
    Main body
        Page 1
        Page 2
        Page 3
        Page 4
        Page 5
        Page 6
        Page 7
        Page 8
        Page 9
        Page 10
        Page 11
        Page 12
        Page 13
        Page 14
    Back Cover
        Back Cover 1
        Back Cover 2
Full Text


FILE COPY OS
%iML & POW~~ OF-1
METEOUS Or COMIPUTINC TE[ STIrNfTII
ANU STIFFNESS Uf IPLYWODU
STRIPS IN IENUINC
lRvised Vecember 194 URI


TL A -\ T A, GEC.

ATLA.TA aGE,>











This IPeporl is One of a Series
Issued In Cooperation with the
AIMY-NAVY-CIVI l COMMITTEE
on
AIlVCCAFTI DESIGN CRITERIA
Under the Supervision of the
AIERONAUTICAL BOAIVD

No. 1304


UNITED STATES DEPARTMENT OF AGRICULTURE
FOREST SERVICE
FOREST PRODUCTS LABORATORY
Madison, Wisconsin
In Cooperation with the University of Wisconsin

















Digitized by the Internet Archive
in 2013






VETHT= OF UCrrrOTIiT'` T_

OF PLY'NCOD 'T'




ALANT D. F?


i IT''1I)DU


This report gives methods of comp
)lywood strips in bending. The methods
>f nearly 4,00O static bending tests, an
-ate. Further analysis of the data may,
he details.

The methods are limited in applic


1TE'GCTH ANTr -3TTFFT'

IF BEIr eeGrW




2rq- ineer


Ti UN


iting the strength and stiffness of
.ave been developed with a background
[ are believed to be reasonably accu-
however, result in changes in some of


perpendicular to the span. Tata are not yet available for other cases.


?TIFF7,^ OF PLYWOOD STRIPS IN BE1Th.:G


The deflection of the center of a simply supported plywood strip under
!enter loading will be given approximately by the equation


w = Pa-' (1)
-49 Ecl

where w = deflection of the center of the strip

P = load

a = span

E = apparent modulus of elasticity in bending


ne (i.e., I U-L, bh-!2)
ie (i.e. I = bh/12)


L
-This is one of a series of progress reports prepared by the Forest Products
T,hn+r.to)rv rplatinpr ten t+h ni nr w in. n, a- : r t1-.. bperp. re-nnrte3









: 2 defth of strip

:he a-p;arent modulus of elasticity in bending, c., may be -o ,.

i =- n


i n


here i mnodulus of elasticity of the ith pl iae esured parallel to th :,a

S mo::ent of inertia of the cross section of the ith ply about the
..eutral axis of the cross section

ind the other terms are as defined above.
"o x~o -0 symeri' '1 -1
or pywood colnstructcd smetricI, that is, with r ?.r; nf lies
)f eou-! Ghic'mu-ses at equal distances fro;., the center, the neutral axi>: of
the ,tri will be at the center of the plypood. This will usually be t:e case,
3t last; for carefully mcAde pl rwood; bu.t occasions uay arise when mo. rmxetrical
)lywood vwill be encountered. In such ern -vent, the location of the neJtral
ixis ma- oe fouled by
i=n
Ai AE Ei di

\7 AiE,-~
dna a(,


i :- 1
i2-l

,here d, = Jistancu from top of beam. to neutral axis

d 1 itance from top of beam to center of ith ply

Aj. = 'rss-sectional area of ith oly

o- -.id.,wood hevinp- all plies of equal thickness, for example,
lus o' wil. be given by use of eqLuation ('.), as:


.r 1 ** l


S=- width of striiu


**1






+_.I'T E?+ 28 1 + 26r
?27 E 27 L


-.-" 1= 25rT + 99 26 + 99r7 L
E 125 125

(4)
7- T-; E! 99rT + 244 E9 9 + 244rT E
34 243 =2 343L


-ly; 1 8244rT + 485 E 244 + 485rT E
1 729 EL 729 L


where Zl for plywood strips having the grain of the outer plies para1,el
to the span

E, = for plywood strips having the grain of the outer lies )er-; n-
dicular to the span

= o-.O.lus of elasticity of wood in the longitudinal direction
(parallel to the grain)

rT= 'T/EL

S- = moxulus of elasticity'- of wood in the tangential direction

Equat -ons (4) above an ,ply strictly only to plywood made of "'o;,r -
cut veneer, since .the ratio r ha.s been used. For plywood made of quarter-
slice<. veiee', the ratio r- = S-/"L should be used, since the modulus of
elasticity in .h radial direction would hobe involved.

,nhil equation (1) for a simply sup-orted beam loaded in the center
has been izse.l a an example, values of E as fouid from equation (2) !maz be
used in the cm.7-ropriate equation for deflection corresponding to the method
of loz.di bJ, s'bstituting E for E in the usual equations.
c
f1' the effect of shear deformaation is to be taken into account,
equation (1) (-uid the corresponding equations for other loadinrs) would be
modified b',,another term, as, for examr,ple,


w = Ea3 (+ e (5)


where e =- a term involving the elastic constants of wood and the construction
of the -plywood






h = depth of beam

a = span of beam

Published values of E, based on static bending tests maade '. ':lhe
Forest Products Laboratory arc about 10 percent below the, true vale, ,-. -.
for the matcri.&i because of the effect of shear deformatLon.

I'fere no correction for shear deformation is to be made, A' -, be
calculated wiuh the Forest Products Laboratory published values of IT.. '"'-A.i,
values of 3c so calculated will ,ive values of deflect'.on correct for -,S:
when the effect of shear deform;.tion amounts to about 10 percent. U' sunl-
these values of E will be sufficiently exact.

Where, ho.,ever, a correction for shear deforr.ation is to be u' ,-.,
the published values of E. should be increased 10 percent.
J-"IL

S ,/.; valueoE for (e) are- jivec, in table ]. A discuss on of their
uses n r:ii nations will be found in the Oiscussion company ..... ]ce 1.


COF PLY""OCD STIPS 17 5S 7I1T


For Pl^/ood Hvin the Groin of the
Outer Plie: iarallel to the Suoin

The .trenmth of :'la,,eood stri-s of this t-rne bi ending; '-il >e
givei. by

I = Kr1 s (3)


where 1, = resisting raomynt of plywood strip

1c on .at

S = ;tress in outer fiber of outermost loni;itudinal -.ly

c : istance frol.. neutral axis to outer fiber of outermost o.n ;itAdiial
)ly

03 = tL






M = Kr ()
C

where rm = Em/EL

Em = E for a strip of plywood having the outer plies at right angles
to the span, but considering that the outer ply on the tension
side does not act.

The position of the neutral axis for this case may be found by use of
equation (3) except that there will be (n l) plies, the outer ply on the ten-
sion side being omitted from consideration in calculating Em. (The value of I
as before is based on the full cross section about its center line, including
all plies.)


PLY'1701D MADE OF MORE THAN ONE SPECIES


The formulas previously presented in this report have been checked by
tests of specimenr made with all plies of the same species. A form of plywood
comm-.only met in aircraft work is that made of two or more species. In the
absence of test data to serve as a check, and pending the development of more
accurate methods, the following procedure is suggested for calculating the bend-
ing strength and stiffness of plywood of mixed species;

In computing deflections, equation (2) for Ec may still be used,
except that in this case the values of Ei for the parallel plies will not be the
same for all plies, but will be those corresponding to the species. Similarly,
the values of Eifor the perpendicular plies will be those for the species under
consideration.

In computing strengths, equations (6) and (7) may still be used. The
values of r will be determined from E. as indicated above. The value of 5,
which for plywood made with all plies of the same species would be the same for
either face grain direction, may now be different for the two directions, but
in any case will correspond to the outermost ply whose grain direction is
parallel to the span.


VALUES OF TE RATIOS rT = ET/EL and rR = ER/EL


Values of ET and ER from which to compute the ratios rT and rR are
available for a few species. The data are, however, incomplete in that only a
few species have been tested and that little is known about the variation of


IT. -I -Z n) I





'a as are available are presented in "Elastic


from these publications should be used when applicable. For cases in which no
data are available, the use of values of rT = 0.05 and rR = 0.10 is suggested.

As pointed out later, even approximate values of these ratios will
generally give results only slightly in error, so that lack of exact values is
not a serious deterrent to the use of the proposed methods.


PTI
EPROR INTRODUCED BY YTGLECTING TRANSVERSE PLIES


The transverse plies may, in general, be neglected with relatively
small error except in the case of 3-ply plywood having the grain of the outer
plies perpendicular to the span.

For plywood having the grain of the outer plies parallel to the
span, such neglect will generally result in small errors. ?or plywood having
the grain of the outer plies perpendicular to the span, however, the error is
somewhat larger, and for 3-ply plywood of this type the error may be consider-
able. Figures 1 to 4 show the error that may be expected from neglect of the
transverse plies for 3, 5, 7, and 9-ply plywood of two types for various values
of r. While certain approximations were used in calculating the values for
these figures, they will be useful as a guide in determining whether or not
neglect of the transverse plies will be a serious matter. It will be recog-
nized that interpolation in the curves of figures to 4 is not possible. The
connection of the plotted points by straight lines has been done only to
emphasize the trend, as the number of plies is varied, of the ratios concerned.

The foregoing discussion also permits the conclusion that, for most
cases, reasonably accurate results may be obtained even with assumed values of
r. Therefore, reasonable results may be obtained for species for which no
values of rT and rR are available by using the approximate values previously
given as a guide in estimating values for other species.


VALUES FOR (e) FOR USE IN EQUATION (5)


The factor (e) for use in correcting deflections for the deformations
due to shear has been evaluated for 3, 5, 7, and 9-ply Douglas-fir and Sitka
spruce plywood having all plies the same thickness for the case of a simply


UO* 13(A1





Corresponding val


er load, but no exact values are available.

It should be noted, however, that reasonable corrections for shear
onn may be made even with values of (e) considerably in error. Assu
Le, that the proper shear correction was (1 + 0.10O) and that the val
sed was 20 percent low. The computed correction would then be (1 +
ich is only about 2 percent in error, so that the corrected deflect
only about 2 percent in error.

From this it appears that the values of (e) given in table 1 may be
approximations of the correct values for other types of plywood and
f other species, and may also be used to estimate approximately the
reactions for such cases. It is expected that these values, for the
plywood specified in table 1, will give corrections somewhat too lar
or the case of a uniformly loaded, simply supported beam.

Calculations based on the values in table 1 indicate that the corre
shear deformation will be less than 10 percent in practically all ca
o of span to beam depth greater than 48 to 1 is maintained for plywo
vring the grain of the outer plies parallel to the span, and greater
o 1 for plywood strips having the grain of the outer plies perpendi-
bhe span.


-Values of (e) for plywood having all plies the same thickness and
used as a simply supported beam with center load


(e)

Lies : Sitka spruce Douglas-fir

: Outer plies : Outer plies : Outer plies : Outer plies
parallel to : perpendicular parallel to : perpendicula
span to span span to span


I84. : g.6 141.7 9.9

160.8 46.3 llg.4 36.5

147.1 63.5 108.5 4g.g

138.S 73.3 102.5 55.7


D. 130o4


r_






VALUES O :


The values of K suggested for use in equations (6) and (7) are:

Stresses at or below proportional limit --
Outer plies parallel to span, K = O.95
Outer plies perpendicular to span, K = 0.90

Stresses at or near modulus of rupture -
Outer plies parallel to span, K = 0.85
Outer plies perpendicular to span,
3-ply, K = 1.10
Others, K = 0.95

If the approximate method, neglecting the effect of the transverse
plies, is used, the values of K for the outer perpendicular plywood will have
to be increased somewhat, since this approximation results in values of momen
lower than the true values. The difference will, of course, depend upon the
construction of the plywood, but an approximation of the correct factor may b
obtained by dividing the appropriate factor above by the appropriate ratio
given in figure 2 or 4.

For outer-parallel strips the approximate method gives results, in
general, close enough to those of the exact method so that no modification of
the factor is necessary.


STRESS VALUES TO BE USED IM CALCULATIONS


The stress values or modulus of elasticity values to be used in the
calculations will depend upon the use for which the plywood is intended.

U. S, Department of Agriculture Technical Bulletin 479, "Strength a;
Related Properties of 'foods Grown in the United States," gives average strong
and modulus of elasticity values for the more common species as found from
tests on small clear specimens.

U. S. De-Dartment of Aoriculture Miscellaneous Publication 15, "Guil


INo. 130


-g-











= cross-sectional area of ith ply

= width of beam

= distance from neutral axis to outer fiber of outer
longitudinal ply

= distance from top of beam to neutral axis

= distance from top of beam to center of ith ply

= a term dependent upon the elastic constants of wood
construction of the plywood

= apparent modulus of elasticity in bending

= B for plywood strips having the grain of the oute3
parallel to the span

= E for plywood strips having the grain of the oute]
perpendicular to the span

= modulus of elasticity of wood in the longitudinal
(parallel to the grain)

= modulus of elasticity of wood in the tangential dil

= modulus of elasticity of wood in the radial direct-

= modulus of elasticity of the ith ply measured para]
the span

= E for a strip of plywood having the grain of the c
at right angles to the span, but considering thai
ply on the tension side does not exist

= depth of beam

= moment of inertia of the whole cross section of thE
about its central line (i.e., I = bh3/12)

= moment of inertia of the cross section of the i th I
the neutral axis of the cros section

= constant

= resisting moment of plywood strip































LRMY-
19L



)OYLE


-ties of wood, Forest Products Laboral
i supplements.


4. n 'I r 1 T .3 M 4- -.1 M 4-


/ J c'JV'- ^ M^'t -~/ -L ^ U iV
D. Dept. Agr. Tech. Bul. 479, 99


fading of structural timbe.rs and t'
;resses, U. S. Dept. Agr. Misc.


L ,;.
































































1..= = _L --j -_-.. ..... -

5 7
PLIES (NUMBER)



FIG. /


4


' T K ---- -\















^ Q^ ^ /^ TORPR-O.Or6O.O
K./ / rT ORPR =0.0
rTTO~r =0.03

0=0.04
00 X a- rT OR r- = 0.05
kj OR r0 = 00. 6



% 0j/70/ L E6END
/ /(ALL PLIES SAME THICKNESS)
.... / o- o OUTER PLIES PERPENDICULAR
// o--...-o OUTER PLIES PARALLEL


0 000

3J 5 7 r
PLIES (A'UAIBER)


F16.2
RTOOE PI/ES P-5D CALdCULATED
B NE6LECIN& UTRANVERISE PLIES TO LOAEETS
CALCULATED BY CONSIDERING TRANSVERSE PLIEI.





1.50 LEGEND
(OUTER PLIES ONE-HALF AS THICK AS OTHER PLIES)
OUTER PLIES PERPENDICULAR
.o----o OUTER PLIES PARALLEL
1.4 .^ --------------_..............................----.__......... ----------



LA 1.30\ rORr0.06
Z; \ -rTORrR=O.05
| rT ORrR =0.04

| / <\o rT orp-0.03

^ 1 .10N < V ^ ^ / = o o
CL

'^~~r ^/ V rOR rf 0.06
00 \rT OOR rR = O.O

-" .o -------- ---- -- -


/.Q--"----------------------I----------------
3 5 7 9
PLI ES (NUMBER)


FIG. 3
RATIOS OF DEFLECTIONS CALCULATED
BY NEGLECT/ING TRANSVERSE PLIES TO DEFLECTIONS
CALCULATED BY CONSIDERING TRANSVERSE PLIES.





4 10 --rTO _o---?00-
r. R~

5 ^ /.90 O rp --.02 LEGEND ......
S^ 7^ ^^'K rjOr-03 (OUTER PLIES ONE-HALF AS THICK
r T OR r. =0.04 AS OTHER PLIES)
P rTORrR -0.5 o--o OUTER PLIES PERPENDICULAR
SrOR rR -0.06 o---o OUTER PLIES PARALLEL
S0.80 -----1-
S 3 5 7 9
PLIES(NUMBER)


FI6. 4
RATIOS OF MOMENTS CALCULATED
BY NEGLECTING TRANSVERSE PLIES TO MOMENTS
CALCULATED BY CONSIDERING TRANSVERSE PLIES.
Z m 41128 F