;
.,
BUCKLING .OF STIFFENED HAT
PLYWOOD MATE S
IN COMPRESSIO N
A Single Stiffener parallel to . Stress
Original report dated 194 7
Information Reviewed and Reaffirmed 196 0
No. 1353-13
Please return t o
4'e d Ert . Res .
Forest Prod . Lab .
Madison, Uls .
FOREST PRODUCTS
MADISON
LABORATOR Y
5, WISCONSIN
UNITED STATES DEPARTMENI OF AGRICULTUR E
FOREST SERVIC E
In Coop eration with the L.ini ersity of Wisconsin
BUCKLING OF STIFFENED FLAT PLYWOOD PLATES IN COMPRESSION !
2
A Single Stiffener Parallel to StressBy
C . B . SMITH, Mathematician
L . A . RINGELSTETTER, Enginee r
an d
C . B . NORRIS, Enginee r
Summary and Conclusion s
This report presents a mathematical analysis of the critical stress of a plywood plate _
in edge compression stiffened by means of a single stiffener glued to the plate in a
direction parallel to the stress . The analysis yielded an approximate formula for th e
minimum stiffness of the stiffener required to cause the stiffener to remain straigh t
when the panel buckles . The data from 532 tests performed at the Forest Product s
Laboratory on 58 panels suggested a modification of the formula by an empirica l
factor to allow for a probable lack of original flatness of the panels .
Introductio n
The strength of structures including flat ply-wood panels subjected to edgewise com pression may be limited by elastic buckling of the plywood . The load at which suc h
buckling occurs can be increased by means-of a stiffening member fastened to th e
plywood . The effect of a single stiffening member fastened to a plywood panel at it s
centerline perpendicular to the direction of the edgewise compressive stress wa s
discussed in a previous report . 2 The present report deals with the effect of a singl e
stiffening member glued to a panel at its centerline parallel to the direction of the
edgewise compressive stress . The stiffening member, in this position, has two
functions, that of stiffening the panel and that of carrying part of the load .
!This is one of a series - of progress reports prepared by the Forest Product s
Laboratory relating to the use of wood in aircraft . Results here reported ar e
preliminary and may be revised as additional data become available . Origina l
report dated May 1947 .
This report is the third of a series of reports presenting the results of studies o f
the buckling of stiffened flat plywood plates in compression . Previous reports hav e
included "Buckling of Stiffened Flat Plywood Plates in Compression : A singl e
stiffener perpendicular to stress, " Forest Products Laboratory Report No . 1553 ,
and "Buckling of Stiffened Flat Plywood Plates in Compression : A single stiffene r
perpendicular to stress . Face grain of plywood at 45 ° to its edges," Fores t
Products Laboratory Report No . 1553-A .
Report No . 1553-B
If the stiffening member is sufficiently stiff, it will force the panel to act as two panels ,
one on -each side of the stiffener, and thus increase the critical load of the panel . Also ,
the stiffener will remain straight and function as a compression member . The minlmun1
stiffness of the stiffening member that is sufficient to cause it and the panel to function '
in these ways is discussed in this report . The effect of stiffening members having' stiffness values less than this minimum is also discussed .
An energy method is used, in a mathematical analysis of the effect of the stiffenin g
member, in which the lack of original flatness of the panel and the energy due to th e
twisting of the member were neglected . .This analysis is verified by test, of
stiffened panels clamped at their two loaded edges and simply supported at the othe r
two edges . It is found necessary to introduce an empirical factor in the mathernatitaal
formula for the minimum stiffness of the stiffening member in order to allow for tire
lack of original flatness of the panel and for other approximations made in the• atialyrsis ,
For the reader who does not wish to follow the mathematical details of this report, the
two important formulas derived in the mathematical analysis and an explanation of tht ~
constants involved are given for easier reference in the appendix .
Mathematical Analysi s
Notation
The choice of axes is shown in figure 20 . 3
Ex
= Young' s modulus in a direction parallel to the x axis in a given plyy . .o f
the plywood .
.r
= Young' s modulus in a direction parallel to the y axis in a given ply o f
the plywood .
xy
= modulus of rigidity associated with a shearing strain corresponding t o
x and y in a given ply of the plywood .
v yx
= the Poisson' s ratio associated with a contraction parallel to the x axi s
and a tensile stress parallel to the y axis in a given ply of th e
plywood .
X
= l - vxy v .
yx
z
= coordinate measured perpendicular to the middle plane of the panel .
h
= thickness . of the plywood panel .
El
= 12
h3
h_ .
2
I
Ex z 2 dz .
h
2
-The figures, tables, and equations in this report are numbered consecutively wit h
those of Forest Products Laboratory Report No . 1553-A .
Report No . 1553-B
-2-
E2
3.
= 12
h
Ea
Ex dz.
h
2
r
Eb = 1
E y dz .
2
h
2
A
= 12
(6 yx EX + 2Xp. ) z 2 d .
h3
rh
2
Es
= Young' s modulus of the stiffener in the longitudinal direction .
Ny
= buckling load per inch of edge of panel .
p
= average stress in panel .
p
cr = average critical stress in panel .
pc rl
p
= average critical stress in panel when stiffener has zero stiffness .
cr2 = average critical stress in panel when the stiffener is Stif f
enough to remain straight when the plate buckles .
L
= total load on stiffened panel .
Lcr2 = critical load on panel for the case in which the stiffener remains straigh t
when the panel is buckled .
_
P
= compressive load on stiffener .
(ET) s = flexural rigidity of the stiffener and a portion of the plate .
b
= length of the plate parallel to the direction .of loading .
Report No . 1553-B
-3-
a
= width of plate perpendicular to the direction of loading .
t
= width of rectangular stiffener in direction parallel to the width of th e
plate .
d
= depth of rectangular stiffener . .
F
td` = cross-sectional area of stiffener .
w
= a l f(y) sin' = assumed lateral deflection (namely, in the Z direction )
a
of points in the middle plane of the plate .
g
ab
My)?
= f
b
j
;Tr
dy .
Lf' (Y) 12 dY .
0
b
2
L f ►' (Y)J dY •
J
0
m
f
b
b
= n2E 2
Lf '
(Y) ] 2 dy
0
0
12 (EI) s
x
Y
bE 2
h
4E a E-b
2µLT -
Report No . 1553-B
Lf" (Y)] Lf(Y)l dY
Q TL E L
b
-4 -
2hAE b
,1 2
2hE b + ae o kFE s
=b ,
k
=
if the loaded edges are clamped and the panel without a stiffene r
buckles with no nodal lines .
(n + 1) n
b
if the loaded edges are simply supported and the panel withou t
a stiffener buckles with n nodal lines (n having any valu e
from 0 to 1 .
Structure of Plywood--Orientation of Plywood and Stiffener- Choice of Axe s
As in previous reports± issued by the Forest Products Laboratory dealing with th e
elastic behavior of plywood, it is considered that plywood acts as an orthotropi c
material .
For definiteness, the plywood in the plate considered will be assumed to be made o f
rotary-cut veneers of the same species of wood . When this is not the case, suitabl e
modifications may be made of the constants that appear in the analysis . 5
Consider a rectangular plywood plate with its area bisected by a single stiffene r
perpendicular to its loaded edges . Its edges parallel to the stiffener and to th e
direction of the- stress are simply supported . The stiffener is rectangular in cross section . The grain of the plywood face plies makes an angle of either 90° or 0° with
the stiffener . The dimensions of the plate, the positions of the coordinate axes, an d
the direction of loading are shown in figure 20 .
Let the applied load be insufficient to buckle the panel ; the n
L=pah+P ,
and since the deformation of the stiffener is necessarily equal to that of the panel ,
L -
p a h+
Es F
Eb
Now if the load is increased until the panel just buckles and the stiffener is sufficientl y
stiff to remain straight,
•.•
Lcr2 . = Pcr2
Ee F
ah + Eb .
in which equation pcr2 is the critical stress%for half of the panel considered alone . Th e
edge of the half panel at the stiffener is considered simply supported ; that is, it i s
±Forest Products Laboratory Reports Nos . 1312, 1316, 1322A .
!Forest Products Laboratory Report No . 1316, Appendix .
Report No . 1553-B
-5'-
assumed that the tortional rigidity of the stiffener can be neglected . The value of
pcr2 can be computed by the method described in Forest Products Laboratory Repor t
No . 15256 , which applies to plywood as well as to sandwich construction .
It remains to determine the critical stiffness of the stiffener, that is, the leas t
stiffness of the stiffener which is sufficient to cause it to remain straight when th e
panel buckles . This is accomplished by determining by a mathematical analysis th e
critical stress of a panel stiffened with a stiffener of arbitrary stiffness . This stres s
(equation 53) is equated to pcr2, and the equation is solved for the stiffness of th e
stiffener . This stiffness is, by definition, the critical stiffness of the stiffener .
It is found that the critical stiffness of the stiffener is not independent of the cross sectional area of the stiffener so that a cut-and-try solution is necessary . A simplifie d
approximate method is suggested .
Buckling Load by Energy Method
The equation of the deflected surface of the buckled plate will be taken in the for m
w = a l f(y) sin !x
a
(41 )
The choice of the function f(y) in equation (41) is left arbitrary as this makes the
analysis applicable to several different cases . The edges parallel to the load are taken
to be simply supported .
The strain energy of bending of the panel is given by the expression?
b
VP
= 2~
a
f
0
0
E l ( 82~ )2 t E2 ( a yz ) 2 + 2ctTLEL ( 82w ) (82`v )
8 Y~
Y
2
+ 4X LT (8x8Y)2 dx dy .
(42)
It is found by substituting (41) in (42) tha t
h3 a
VP = 24X "
E lbgn4 + E2n41 + 2w 4E2m
2a4
--2
ba-t
al 2 P
where
g
=
[1(y)]2 dy,
6 "Buckling Loads of Flat Sandwich Panels in Compression . "
a
-U .S . Forest Products Laboratory Report No . 1312, equation (3 .21).
Report No . 1553-B
-6 -
(43 )
_ 2b 3
n4
[f' ° (y)] Z dy, and
(44 )
b
ZAµ
b [ft (Y)] Z d Y (rTLEL
LT
f°
a (Y) f(y)
dy
0
Denoting by (EI) s the flexural rigidity of the stiffener when attached to the plate, !
the strain energy of bending of the stiffener when buckled together with the plate i s
Z
b
4(.rI) e
Z
-vs
dy= -a l .
(45 )
4b3
x 2
= Z (El) . 1r
The work done during buckling by compressive forces Ny (load per unit width of the
.plate) acting on the plate i s
a
f
0
Where
08712
2 dx dy =
N b~T Z j a
0
a 1 Z,
(46 )
8
b
j
[ [
f~ (y)] Z dy .
(47 )
The work done during buckling by the compressive load P on the stiffener i s
a.
p
Ls =
Ow,
0
Z
,rZ .P
z
xaa dY= 4b - a ,
(48 )
where the relation between P and N y is given by equation (51) .
The equation for calculating the critical load is 2.
VL + VLS = V P + V S .
(49 )
It is found by substituting equations (43), (45), (46), and (48) in equation (49) tha t
-Since the stiffener is rigidly attached to the plate, it is apparent that (EI) s is greate r
than the flexural rigidity of the stiffener about its own neutral surface . U.S . Fores t
Products Laboratory Report No . 1557 .
-The energy of twist of the stiffener, which occurs during buckling, is neglected .
Report No . 1553:B
-7-
N YTr2ja
8b
E l bgir 4 + E 2 41
2a4
_+
+ n2jP - h 3 a
4b
48X
Tr
2Tr
4E2m
1 u4(EI)s
- + 3
(5o)
h - pcr'
(51 )
Using the notation s
b
a
12(El) x
13,
bE2h3
y
,
FE spc r
Eb
p
where pcr is the average critical stress in the plate, E s is the Young' s modulus of the
stiffener in the longidutinal direction, and F is the cross-sectional area of th e
stiffener, it follows tha t
pcr
r2E2h2 [Eig
2
-12 j
S4
+1 + 4m[32 + 21 .
2E5 F
1+ ahEb
(52)
Critical Stiffness of the Stiffene r
It will be convenient to think of two different average critical stresses in connectio n
with a stiffened panel . One critical stress, pcrl' is the buckling stress in the pane l
without the stiffener . The second critical stress, pcr2, is the buckling stress in th e
panel when the stiffener is stiff enough to remain straight when the panel buckles . It
is apparent that pcr2 is the buckling stress of a panel of height b and width a/2 wit h
proper edge conditions . Equation (52) can then be written a s
2 E2h2f y
pc rl + 6Xabj
2Es F
1+
ahEb
Tr
pcr
(53)
where
crl = a2E2h 2
p
^
1 2 Kb 2 j:
E l gs4 +1 + 4mp
2
E2
(54)
is the buckling stress of the plate without the stiffener . Equation (54) is found fro m
equation (52) by setting y and F equal to zero .
Equation (53) will give the approximate critical stress in the plate for values of y tha t
are small enough to allow the stiffener to bend as the plate buckles .. However, as y
is increased, a value of y is finally reached at which the stiffener remains straigh t
as the plate buckles . This value of y will be called, Ycr' and correspondingly ther e
will be •a value of (EI)s, (EI)scr, where
ak3'
fn
.
Report No . 1553-B
-8-
(El)
scr
-
bE 2h
3
12 x
(55 )
Y cr `
The values ycr and (EI)scr can be said to be associated with the critical stiffener . It
is evident that, for any value of y larger than Y cr , the stiffener will remain straigh t
as the plate buckles . It is also evident that, for any value of y larger than Ycr '
equation (53) does not give the correct critical stress on the plate . When y is large r
than Ycr the critical stress pcr2 is the same as for a plate of height b and widt h
a/2, with the proper edge conditions .
Solving equation (53) for y, it follows tha t
b xb2j
n L E 2h Z I
cr
(1 +
2E B F
ahEb
)
Pc rl
(55 )
or
ZR 2I
2Ee F
(EI)
hab 2 J '
s
= pcr
(1 + ahEb
) - Pcri .
(56)
To obtain an approximate expression for Ycr' it is only necessary to replace Pcr by
pcr2 in equation (55) . Hence,
Yc r
6J .b 2 j
ir2E2h2I
S
Pcr2 (1 + 2 E'EeF ) - Por i
ahE b
(57 )
or
2tirZ ( EI )scr
hab 2 j
2E e F
Pcrt (1 + ahEb) - PCrl
(58 )
Equations (56) and (58) will be found useful in the experimental part of this report .
For a given rectangular plywood plate with two edges loaded, and with the loaded edge s
either simply supported or clamped, equation (57) will give Y cr in terms of F .
Report No . 1553-B
-9 -
Equation for (El) s
From equation (53) the critical stre-ss for a plate stiffened by a stiffening member Ca n
be calculated provided (EI) s is known and is less than (EI)scr• The stiffness of th e
Stiffener, (EI)s, taking into consideration the additional stiffness resulting from it s
10
being attached to the plate, is given by 10
(EI)s =
tdEs
d2 + 3(h + d - 2zn) 2
}
12
+ thEbz n2 ,
where
(60 )
which is the distance between the enter of the panel and the 'neutral axis 6f
combination of panel and stiffener . .
tife
:'.
The constants that appear in equation (59) and (60) are defined in the 'table ldf t;t tatiezt-o
Method of Computingthe Dimensions oftheCriticalStiffene r
An important part of the analysis is to determine for a given plate What erossa. SectiOna l
dimensions the stiffener must have in order to remain straight during buckling bf th e
plate . Before this part can be discussed, .another 'equation must be derWWed . Frbrj
equation (58) it follows that
(El)scr
_ hab 2 j
211.21
Pcr2 (1 +
ZFEs
ahE b
) - Pcr l
(I,1 )
Equation (61) also gives an expression for (EI) s which,• by mean® of equation (59), ca n
be written in the form
FEs
(EI)s
d 2 + 3r (h + d) 2
(62 )
lx
where
.i
=
Y
(63 )
Zh Eb
ZhEb + ae o kFE s
2U .S . Forest Products Laboratory Report No . 1557, Equations (68) and (70) . Eb i s
used here instead of Ea, since for the panel discussed the stiffener is in the y
direction .
Report No . 1553-B
-10 -
The terms thEbzn? and
which appear in equations (59) and (60), .respectively ,
•. .
:.
Es d
Eb
have been neglected . This can be done with small error as numerous c&mputation s
have shown .
If d is taken as the depth of the stiffener of critical stiffness, the right hand naeifber ,B
of equations (61) and (62) can be equated . The following evaluation of (d)resixlts : .
•-3hr +
d
=
6hab2
n24 FEB
FE
2FEs
2
(1 + ahEb ) - Pcrl (I + 3r) - 3h r
[pcr2
(64 )
1 + 3r
This equation gives a numerical value for d if the following things are given : Th e
elastic properties and the dimensions of the plywood plate, the Young' s modulus of th e
stiffener material in the longitudinal direction, the values of per]. and P' r2►-the value s
of f and j, the value of r, and an assigned value of F, •the cross .-sectional area of th e
rectangular stiffener . After obtaining d, t can be found by means of the equatio n
t = F/d. If the two values of t and d are .r of practical, a new value of F can be assigned ,
and d and t can be determined again . ;With a little practice, a few calculations should
furnish satisfactory dimensions for the stiffener . Equation (64) can be convenientl y
applied to the following two cases :
Case I : The loaded edges are 'assumed simply supported . Then f(y) will be of the for m
sin (n + 1) b! , where the panel without a stiffening member buckles with n nodal like s
in the interior of the plate (n having any value from 0 to 00) . In this case it ' follows from
the definitions of f, j, and I (see table of notation) tha t
j
= (n + l)2
1
= (n + 1) 4.
-
Also from the table of notation ,
k = (n 1)R for this case, and the expression for r become s
ZhbEb
2bhEb + aE 0 (n + 1)IrFE s
2
Case II: The loaded edges . of the panel are assumed to be clamped . It is
b 4 a
that
E2 is greater than 0 .81. and less than 1 .35. This los t
also assumed
assumptiona means that the panel without a stiffener will buckle with no interior '
nodal lines ; while if a stiffener stiff enough to divide the panel into two panels tha t
-1 -J,S, .Forest Products Laboratory Report No . 1525, figure 4 .
Report No . 1553-B
-11 -
a,
buckle separately is added, each panel will buckle with a nodal line perpendicular 'to
the stiffening member . In this case f(y) will be assumed to be sin g
and it follows
from the definitions of f, j, and I given in the table of notation, thatb j = 1 and 1 = 4 .
Also from the table of notation, k = 2 .n-/b for this case, and the expression for r
becomes
r
hbEb
1Z
rbhEb
+ae o nFE s
In each case the appropriate values of pcrl and pcrZ are found by referring to figure s
2 and 4 of Forest Products Laboratory Report No . 1525 (figure 2 for case I and
figure 4 for case II) .
The experimental part of this report shows that the value of (EI) scr given by equation
(61) must be corrected by multiplying by a factor of 2 to make sure that the stiffener wil l
remain straight when the panel buckles in all cases . The corrected equation (64) will
then read
-3hr +
2FE s
12hab2•
P
cr2
(1
n Z1 FEs [
+ ahEb
..
p cr l
(1 + 3r) - 3h 2 r
(65 )
d
1 + 3r
This factor of 2 is to be attributed to the approximations involved and to the lack t'f'f _
original flatness of the plywood panels . It is also a safety factor to insure that th e
stiffener remains straight when the plate buckles .
;
The values of , p crl, pcrZ' , io and r are the same as before .
Example .--T o illustrate the method of determining the cross-sectional dimensions o f
the critical stiffener, formula (65) will be applied to an actual plywood panel . A three ply panel will be used with the face grain parallel to the direction of loading (fig . 20) .
It will be assumed that the two loaded edges are clamped and that the remaining edge s
are simply supported . The dimensions and elastic constants 2
1 of the panel and a
stiffening member are as follows :
b
= 29 .93 inches .
a
= 11 .625 inches .
h
= 0 .177 inch .
EL
= 1,466 .7 x 10 3 pounds per square inch .
ET = 73 . 333 x 10 3 pounds per square inch .
µLT
r
= 895 x 10 3 pounds per square inch .
12
-The subscripts L and T refer to the longitudinal and tangential directions ,
respectively, in the wood .
Report No . 1553-B
-12 -
,
°TL =0 .02 .
TL ° LT
= 0 .99 .
X
=1-°
Es
= 1, 700 x 10 3 pounds per square inch .
Ea
= 1/3(ZE T + E L ) = 537 .77 x 10 3 pounds per square inch.. .
Eb
= 1/3(2E L + E T ) = 1,002 .2 x 10 3 pounds per square inch .
El
= 80 x 10 3 pdunds per square inch .
E2
= 1,460 x 10 3 pounds per square inch .
A
= OTLEL + 2X.µLT = 2 .0654 x 10 5 poiinds per square inch .
D1
3
= E lh
. 12X •
,D 2
= E 2h3
12 X
= 37 . 341 .
= 6'81 .46 .
Since the loaded edges are clamped and b \ O 1 = 1 .246, it follows from figure 4 . o f
a D2
U .S . Forest Products Laboratory Report No . 1525 that the panel will buclil .e with no
nodal lines . Hence, the panel falls in case II and j = 1, 1 = 4 . The K used i n
Report No . 1525 is given b y
h3
Na) IT3-2 -
which for this example is equal to 0 .6043 . By again using figure 4 of Report No . 1525 ,
it is now possible to obtain the critical load per inch of edge . for the entire panel withou t
a stiffener (dimensions b by a) ; and for a similar panel whose dimensions are b b y
a/2 where both panels are looa.ded in the direction parallel, to the_side ;of length b and
have the loaded edges clamped . By dividing each of these critical loads by h, th e
critical stresses pcrl and pcr2, respectively, are obtained . Hence, by reading fro m
the curves in Report'No . 1525, it follows that
(4 .08)1Z D 1 D 2
Pc rl
= 326 .55 pounds per square inch ,
(0 . 177)(11 . 625) 2
and
(3 .11)12 D 1 D 2
pcr2
(0 . 177)(5 .8125) 2
Report No . 1553-B
= 995 .55 pounds per square inch .
-13 -
In order to compute the value of r,' it is necessary to make an evaluation of th e
constants (see table of notation) as follows : .
EaEb
O TLEL
.
4-Ea-E2N'LT
K
.
=N
K +
= 4. 0614,
~f
K - 1 = 2 .8Z$O,
and
o
E
= (Eab )
11 4
=. 1 . 1684.
Then for this example ,
5,309,4x 103
5, 309 .4 x 1 0 3 + 17,647 x 1 0 3 F
and the quantity
ZFE s
(1 + ahEb - pcrl
12hab 2j
n2I FE B
that appears under the radical in equation (65) become s
0.2205
F
+ 0 .541 . .
To obtain a value for d, F will be taken as 0 .25 square inch . The substituting in
equation (65), it follows that
d
= -0 . 15838 +42 .70 - 0 .02804
1 .89484
t
= 0.25 = 0 .321 inch .
b'7-7'77
= 0 . 779
and
Hence, for F = 0 .25 square inch, the dimensions of the critical stiffener for the pane l
considered are 0 . 321 inch by 0 . 779 inch where 0 . 779 inch is the depth . For a smaller
value of F the depth :would turn out to be larger and the width smaller . This makes i t
possible to adjust the cross-sectional dimensions of the critical dtifferier over a
considerable range of values .
Report No. 1553-B. .
-14-
Construction of Test Specimen s
The plywood used in the specimens was three- and five-ply•aircraft stock made t o
AN-NN-P-511a specifications at the Laboratory . The various species of veneer wer e
yellow birch, yellow-poplar, and Sitka spruce . Most of the -specimens were made o f
veneers of a single species, but in some specimens,, a dense species was used for face s
and a lighter species for cores . The constructions of the individual specimens ar e
given in table 11 .
The plywood used in the test specimens was cut from larger panels 2 by 6 feet in size .
A representative number of coupons were cut from parrs of the larger panels adjacent
to the test - specimens, and were tested in accordance with tentative A . S . T'. M .
Methods D805-45T for the determination of the mechanical properties' of the materia l
in compression and of the elastic properties in-bending and plate shear . The coupon s
and the larger test specimens were conditioned tb constant weight at 75° F . and
64 percent relative humidity before test .
The stiffening members were made of edge-grained Sitka spruce . They were 1/2 inc h
wide, 1 inch deep, and of varying lengths corresponding to the different specimens .
Their cross-sectional dimensions were cut to test size after they were glued to th e
panels . After being conditioned to constant weight at 75° F . and 64 percent relativ e
humidity, the individual members were tested as centrally loaded beams of 1-inc h
depth and 14-inch span for modulus of elasticity, with loads well below those require d
to . produce proportional limit stresses . A 4-inch length was then cut from an end-o f
each such beam and tested in compression for the determination of modulus o f
- elasticity and proportional limit .
The stiffeners were fastened at one of their 1/2-inch edges to the panels by means of
' a cold-setting urea-formaldehyde glue, at a pressure of about 100 pounds per 'squar e
inch, and the resulting specimens were conditioned for at least 2 weeks at 64 percent
relative humidity and , a temperature of 75° F . before they were tested .
Stiffeners of at least three different widths 'were used in each series of identical panels ,
the most common being 1/2 by f inch, 3/8 by 1 inch, 1/4 by 1 inch, and 1/8 by 5/ 8
inch . The stiffeners were cut to these sizes after they were glued to the panels .
The specimens were proportioned so that the computed ratios of the critical stresse s
to the proportional-limit stresses were 0 .2, 0 .4, or 0 .6, and the ratios of thei r
lengths to their widths wer e
b
a
1. 2
They were cut to dimensions (b + 4 inches) and (a + 3/8 inch) to allow for clampin g
and supporting .
Report No . 1553-B
-15-
Description of Apparatu s
The testing apparatus is shown in figures 21, 22, and 23 .
The specimens were tested in a hydraulic testing machine of 100, 000-pound capacit y
with their loaded edges clamped and their other two edges simply supported . The stiffening member and the panel were held in the same clamps .
The clamps consisted of steel bars 2 by 2 inches in 'cross section and 30 inches long .
One of each pair of bars was stationary and the other movable . The bars were . '
clamped to the specimen by means of six 3/8-inch bolts spaced .along the centerline
of each pair of bars .
The upper stationary clamp was bolted to the head of the testing machine . The lowe r
clamp rested on a 1-inch-thick steel plate 12 inches wide and 30 inches long . • Thi s
plate was centrally supported by a transverse, 1/2-inch-diameter, hard-steel rolle r
resting upon the bed of the testing machine . The two ' clamps were fixed in the same
plane, but the lower one was free to tilt longitudinally with the bearing plate on th e
roller . This arrangement allowed good alinement of specimen and distribution of load .
Both movable bars were slotted across their centers on the side facing the panel .
These slots were 1/2 inch wide and 1 inch deep . The purpose_bf . these slots was to
permit the stiffener to extend through the clamps to the bearing surfaces back of them .
The sides or nonloaded edges of the panel were simply supported . These supports wer e
1- by 1-1/2-inch hardwood rails 1/8 inch shorter than the free length of the panel .
Dovetail grooves about 3/16 inch deep were cut along the centerline of one side of eac h
of these two rails as , shown in figure , 21 . The throat of each groove fitted the edge o f
the panel snugly to give it simple support .
Measurements of the strain in the direction of the stress were made at the midpoin t
of the stiffener and at the midpoint of the face of the panel, opposite the stiffener . To
obtain these strain measurements, a special adaptation of the metalectric SR-4 strai n
gages was developed as shown in figures 21 and 23 . 'These gages were attached to th e
wood by banks of sharp tack points which were embedded in the surface of the wood an d
held in place by an interconnecting spring clamp . This arrangement- permitted ready
attachment and removal .of the gages, so that the depth of the stiffener could b e
altered between tests without undue loss of time . From the , strain readings on th e
gages, the average strain in the stiffener was determined .
Strains were also measured on both sides of the panel at one of its quarter points i n
the direction of the diagonal of the panel as shown in figures 21, 22, and 23 . It was .
found, from many exploratory tests, that the average of these strains gave a goo d
indication of the critical stress, regardless of the shape or type of buckle . Thes e
strain gages in series were connected to a bridge circuit and balanced against a pai r
of similar "dummy" gages .. Thus, the two strains were averaged electrically in th e
bridge and the resulting galvanometer deflections could be observed directly for th e
determination of the critical load .
Samples of the results of some of the exploratory tests are given in table b and i n
figure 24 . The table lists the computed critical buckling load for three test specimens
in comparison with the critical load determined by the laterial-deflection method and
by the diagonal gage method .
Report No, . 1553-B
-16 -
Figure 24 is a comparison ref the resultant curves plotted from the data obtained by th e
two test methods used for the typical specimen ZXB-1-6 .
The rather abrupt reversal of the curve derived from the readings of the strain of th e
diagonal gages gave a distinct indication of the critical load, whereas the curve derive d
from the lateral deflection readings, in the majority of panels, did not exhibit a shar p
break or sudden change of slope . Thus the diagonal-gage method held an adde d
advantage in that the test could be stopped very shortly after 'the critical load had bee n
observed, thereby eliminating danger of damage to the specimen by exceeding th e
proportional-limit stress of the material .
•
Preparation of Specimen for Tes t
The load-bearing edges of the specimen were cut straight and parallel to each other .
The panels were then inserted in the testing machine and pretested for flatness an d
uniformity of beating of panel and stiffener at a low initial load of about 100 pounds .
A feeler gage was used to determine the exactness of fit between the testing apparatu s
and the edges of the panel and of the ends of the stiffener . If the fit was not satisfactory ,
the specimen was retrimmed . When'a satisfactory fit was obtained, the panel was
marked and drilled for the clamping bolts and slotted from each bolt hole to its load b caring edge, so that the specimen could be inserted and removed from the clamp s
without completely dismantling them each time . The specimen was then clamped in
place ready for test .
Test Procedur e
The specimen was loaded at a constant rate of total strain, and readings of strain at th e
quarter points were taken at regular increments of load until the critical load wa s
indicated . The load increments chosen were about one .fifteenth of the computed critica l
load, and the rate of strain was adjusted so that readings were obtained about ever y
5 seconds, The test was repeated for a check, and strain readings were taken at th e
midpoint of the stiffener and panel at 'the critical load . Also, a trace was made of th e
shape of the buckled panel by a simple buckle-tracing device that had a carriag e
traveling over a strip of adding-machine tape parallel to the surface of the panel . A
contour follower in the carriage was free to move in directions normal to the panel, an d
an attached recording pen transferred the shape of the buckle pattern to the tape as th e
carriage was moved the length of the panel . Figure Z5 illustrates a series of thes e
traces showing the buckle forms of a specimen as the stiffener size was progressivel y
reduced . The double half-wave traces were taken at the centerline of the half panel ,
while the half-wave traces were taken at the center of the whole panel .
The specimen was removed from the testing machine, and the projecting dimensio n
or depth of the stiffener was reduced a definite amount by means of a portable high speed router . The test was then repeated . This- procedure was continued until th e
stiffener had been entirely removed and the panel alone was tested .
These tests were begun with the stiffener at its maximum depth, usually 1 inch, an d
the increments by which its depth was reduced, varied from 1/4 to 1/32 inch,' dependin g
on the size and behavior of the panel . The-smaller increments were used when th e
shape of the trace of the panel indicated that a change of the 'buckle pattern,was imminent .
Report No . -1553-B • ,
-17-
Explanation of Table s
Tables 7 and 8 contain information pertinent to the plywood panels tested with the fac e
grain parallel and perpendicular, respectively, to the direction of 'stress . . Th e
mechanical properties listed were obtained from tests of coupons cut from the plywoo d
or the Stiffener material .
In column 1 are listed the numbers of "the specimens . These numbers are divided into three parts . The first part is the Laboratory number of the panel from whic h
the specimen was cut . The numerals of this part indicate the construction of th e
panel according to table 11 . The second part is the number of the specimens cut fro m
the panel, and the third part is 10 times the ratio of the computed critical stress to '
the proportional-limit stress of the material .
Columns 2, 3, and 4 give the dimensions of the specimens . The width (a) is th e
distance between-the vertical supports and is 3/8 inch less than the full width of th e
panel, and the length (b) is the unsupported length of the specimen . Columns 5 and 6
list values of the moduli of elasticity of the plywood perpendicular and parallel to th e
direction of stress, respectively, obtained from bending tests and computed according
to the formul a
E l or E2 = p L 33
4bh y
where L = 48h when parallel to face grain and 24h when perpendicular to face grain .
Columns 7 and 8 contain values of the moduli of elasticity in compression perpendicular
and parallel to the direction of stress, ' respectively, computed according to the formula .
E a orEb= P L
bh y
Column 9 contains values of the shear modulus .obtained from plate . shear testa o f
coupons and computed according to the formul a
3 p u2
µLT 2 h
3 Y
where u is taken between 30h and 40h .
In all of these formulas :
P
L
u
b
h
y
= load .
= span .
= span in plate shear .
= width .
= thickness .
= deflection .
Report No . 1553-B
-18 -
s
Column 10 contains values of the proportional-limit stresses of the plywood tested i n
compression . Column 11 contains computed values of the critical stresses of th e
specimens according to the formu1a 1 3
Pcrl
2 2
-= n h
3X a 2
+A
3 E b2
a2
16
Z
+E 2 a
(66 )
which applies to the panel when the stiffener is' completely removed .
Column 12 contains computed values of the critical s-tresses of the specimens accordin g
.
to the formulal4
n2 h2
c=2 = 60X, 2
16E
b2
a2
1
+ 40A + 41E a a 2
b2
(67 )
which applies when the stiffener does not buckle .
In formulas 26 and 27 :
A
= ZX LT + °TL E
X
= 0 .99 .
'T L
= 0 .02 (assumed) .
EL
= 20 (E
21
1
L
.
-
+ E 2) .
Columns 13 and 14 relate to the stiffener attached to the panel in which column 13 list s
the widths and column 14 the compression modulus of elasticityparallel to grain .
Tables 9 and 10 relate to the data obtained from tests of the various specimens .
Column 1 lists the stiffener depth in inches . Column 2 contains the average load
carried by the stiffener just as the specimen buckled . The load was computed fro m
strain readings at the midpoint of the stiffener and panel by means of the formulas :
P
= EE s F,
E.
_ d (p- s )
2(d + h )
(68 )
+ s,
13
--U .S . Forest Products Laboratory Report•No . 1525, p . 8, formula (15) .
14
-U .S . Forest Products Laboratory Report No . 1525, p . 8, formula (16) .
Report No . 1553-B
-19 -
in which
P =
Es
F =
e
d
h
s
p
load on the stiffener ,
= modulus of elasticity of the stiffener in-the direction of-its length ,
cross-sectional area of the stiffener ,
= average strain in the stiffener ,
= depth of the stiffener ,
thickness of the plywood ,
= longitudinal strain in the outer edge of the stiffener at its midlength, = strain, in the direction of the applied *tress, 'at the midpoint of the fac e
of the panel opposite the stiffener . .
Column 3 lists the observed total critical loads of the specimens . .Column 4 contain*; t
the net critical stress of the panel 'obtained by subtracting the stiffener load from th e
observed total critical load and dividing by the cross-sectional area of the plywood '
(a + 3/8)h .
Column 5 lists the distances, in inches, that the neutral surface of the specimen ebi f
from the center of the plywood due to the addition of the stiffener .and is computed by .
the formula
Z
• n =
1
2
d+ h
hbEx
h
+ l+ Eb
Es d
aE otdirEs
in. which Ex = Eb ,
e a
K
=
E a Eb _ °TL E L
211LT
J Ea Eb
Column 6 contains values of the combined stiffnesses of the stiffener and the parts of .
the plywood adjacent to it about the shifted neutral axis . This value-is computed by %
the formula
.
(EI) s = td~ + td
(59 )
(Z + Z - Z n ) Z
E s + Zn 2 t h Eb .
Columns 7 and 8 contain values of the coordinates of figure 20 in which the abscissas X
in column 7 are given by the formul a
-15
U .S . Forest Products Laboratory Report No . 1557, equation (68) .
Report No . 1553-B
-20
( 8r
(El)s
hab Z
)
(69 )
2tdE s
Pcr2 (1+ ahE
-P cr l
b)
and the ordinates Y in column 8 are given by the formula ,
2tdE s
Pcr (1+ ahEb )P cr l
(70 )
2tdE s
P cr2 (1 + ahEb ) - Pcr l
where p r
cr
Pcrl
Pcr2
= observed stress on panel for any size stiffener ,
= observed stress on panel with no stiffener ,
= observed average critical stress on the panels for which the stiffene r
is stiff enough to remain straight when the panel buckles .
Analysis of Results of Test s
Traces of the pattern of the buckled panels were taken in the direction parallel to th e
length of the stiffener . Such traces for one of the panels tested are reproduced i n
figure 25 . The trace to the left in this figure shows the form of the buckle when th e
. stiffener is sufficiently stiff to remain straight . As the stiffness of the stiffener wa s
progressively decreased, the pattern of the buckle changed as is shown by th e
successive traces to the right '
The part of the total load carried by the stiffener can be determined by use of equation s
(68) . This determination was made for each specimen just as . its critical load and th e
result was subtracted from the total critical load of the specimen to obtain the critica l
load of the plywood . The critical stresses employed in this analysis were obtaine d
from these critical loads .
For the purposes of the analysis it is convenient to plot the experimental data t o
coordinates which will, theoretically, cause the plotted points to fall upon a singl e
curve . Such coordinates can be found by dividing equation (56) by equation (58) . Thi s
division results in
ZE s F
Pcr ( 1 + ah Eb ) - Pcr l
(71 )
(El)s
ZE s F
) - P cr l
(El )scr
Pcr2 (1 +
ah Eb
Report No . 1553-B
-21 -
If values of the right-hand member of the equation are plotted as ordinates and the .
left-hand member as abscissas, a straight line passing through the origin and poin t
1, 1 is,- of course, obtained . When the stiffener is completely removed from th e
specimen, (EI)e and (F) equal zero ; also, pcr = Pcrl' This condition is represente d
by a point at the origin . If the stiffener has the critical stiffness, (EI)s = (EI)scr an d
pcr = pcr2' This condition is represented by point 1, 1 . If the . stiffness of th e
stiffener is greater than the critical stiffness, pcr remains equal to pcr2 and the paints ,
plot upon a line parallel to the X axis and passing through point 1, 1 . These two
straight lines are drawn in figure 26 .
Values obtained from the experimental data are also plotted in this figure . Individua l
values of the ordinate were obtained by substituting experimentally determined vat to-8 .
in the right-hand member of equation (71) . Values of pcrl were obtained from th e
specimens from which the stiffener was completely removed . Values of pcr2 wer e
obtained from each specimen by averaging the critical stresses from . the teats in which .
the stiffener remained straight . Individual values of the abscissa were obtained from '
the expression
8nz ( Et4.
ha--Z-.l
2E s F
Pcr2 ( 1 +
) - Pcrl
a h Eb
which is mathematically equivalent to the left-hand member of equation (71) (se e
equation 58) . Values of (EI)s were mathematically determined by use of equation s
(59) and (60) .
The plotted points scatter considerably, but this is to be expected since the plotte d
.values are differences of experimental values and therefore are in error by larger .
percentages than the experimental values themselves . The open points represent test s
i
in which the stiffener was observed to . bend ; and the solid points, tests in which th e
stiffeners were observed to remain straight . It is evident from the plot (fig . 26) tha t
if the ,stiffener is to remain straigh t
(El) s
(El) sc r
>
that is, the experimental critical stiffness-of the stiffener is twice the computed value .
This fact is taken into account in equation (65) . It ' is not surprising that this should b e
the case . The mathematical analysis deals with the behavior of perfect specimen s
at their critical loads . - Actually, the specimens are not perfect, but contai n
imperfections in their form and in the materials of which they are made . Thes e
imperfections have a large influence on the behavior of the specimen when the critica l
load is approached, and throw loads upon the stiffeners that are not taken into .con t I ~'
by the mathematical analysis .
s}t
•
.
The mathematical analysis assumes that the critical stress of the plywood to which U . : ::
attached a stiffener having a stiffness greater than the critical value is equal to that, '
of a plywood plate of half the size ; that is, having dimensions b by a/2, and such critica l
stress is given by formula (67) for the specimens tested . The critical stresses of th e
Report No . 1553-B
-22-
stiffened panels were computed by means of this formula and then plotted in figure 2 7
against their corresponding test values . Also in this figure are plotted the values o f
the critical stresses of the specimens from which the stiffeners were completel y
removed, 3computed by means of equation (66) . The solid points 'represent the panel s
with and the'open points, the . panels without stiffeners . These solid points show som e
scatter, as might be expected since the experimental values involve the differenc e
between the measured critical loads and the load supported by the stiffener . Th e
mathematical analysis, however, seems to be justified .
Appendi x
This appendix gives two formulae that apply to the buckling of a flat plywood panel
with a single solid-wood stiffener in the center of the panel parallel to the direction o f
loading . It includes an explanation of the constants involved in the formulas . One o f
the formulas gives the critical stress on the panel when the stiffener buckles with th e
panel, while the other furnishes a means of computing the cross-sectional dimension s
of a stiffening member that is just stiff enough to divide the panel into two panel s
that buckle separately .' The orientation of axes and dimensions of the plate are show n
in figure 20 . The following two cases are considered :
6
Case I . The loaded edges are taken to be simply supported, 1 and the panel withou t
the stiffener is assumed to buckle with n 1 interior nodal lines perpendicular to the
direction of loading .
7
Case II . The loaded edges of the panel are taken to be clamped . In addition, it i s
b El 1/ 4
assumed thata - ( E 2 )
(these constants are defined ii this appendix) is greate r
than 0 .81 and less than 1 .35 . This last assumption means that the panel without a
stiffener will buckle with no interior nodal lines, while if a stiffener is added that i s
stiff enough to divide the panel into two panels that buckle separately, each . panel wil l
buckle with a nodal line perpendicular to the stiffener .
The following two formulas can be applied in each case :
1'crl+nIE5F [d2+ 3r(h + d) 2 ]
6hab 2j
Pcr 1+
2E 5 F
ahE b
e
which is obtained by substituting in equation (53) the expression for y given in th
notation and the expression for (EI)s given in equation_(62) ; an d
16
--The
two edges that are not loaded are assumed simply supported throughout thi s
report .
17 i can have any value from 0 to co.
The value of n can be determined from th e
dimensions and elastic constants of the panel . U .S . Forest Products Laborator y
Report No . 1525, figure 2 .
Report No . 1553-B
-23 -
-3hr +
1zh FE
b2 B
1d=
Tr
[Pcr2 ( 1 + ahEb) - Pcrl)
( 1 + 3r) - 3h2r
(65) '
1 + 3r
An example illustrating the use of equation (65) is included in the body of this repeat .
Equation (72) gives the average critical stress on the panel when the stiffener buckles •
with the panel . ,Equation (65) furnishes a means of computing the depth of the stiffene r
whose stiffness is just sufficient to cause it to remain 'straight when the panel buckles .
For any given panel and stiffener material, equation (65) furnishes a numerical valu e
of d provided a value of F (the cross-sectional area of the .stiffener) is arbitrarily - assigned . After determining d, t (the width of the stiffener) can be obtained from the .
relation t = F . If the values found for t and d are not practical, a new value of F Fait
d
_ ,
be assigned and d and t be redetermined . A few trials should furnish, satisfactory.
dimensions .
The symbols that enter into equations (72) and (65) and that are different in each
are defined as follows :
eagle .;
-
Case I .
j= (n + 1) Z ,
(n + 1) 4 ,
ZhbEb
r
2
2bhEb + aeo (n + 1) rrFE s
where n is the number of nodal lines that would appear in ,the buckled surface of th e
unstiffened panel .
Case II .
j = 1,
1
= 4,
hbE b
The remaining symbols used are defined in the same way in both cases . Th e
definitions are as follows :
Pcr l
= critical stress on the panel without the stiffener . 1 3
Pcr 2 = critical stress on the panel when the stiffening member is stiff enough ta
remain straight when the panel buckles, that is, the critical stress on a
panel of dimensions b by a/2 . 1 4
Report No . 1553-B
-24 -
Ex
= Young' s modulus in each ply parallel to the x axis . !
1
Ey
= Young' s modulus in each ply parallel to the y axis .
pixy
07•
x
A
= modulus of rigidity associated with shearing strain corresponding to x
and y .
= the Poisson' s ratio associated with the contraction parallel , to the x axi s
and a tensile stress parallel to the y axis .
i
-
°
Txy °xy .
h
= thickness of the plywood panel .
z
= coordinate measured perpendicular to the middle plane of-the plate .
E1
= 1Z
h3
h
2.
E x z 2 dz .
2
h
2
EZ
Ea
12
h3
f
E y z 2 dz .
h
2
h
2
1
h
E x dz .
h
2
1
h.
A
Es
f
/"
E y dz ;
Z
o'yx E x + ZAµxy l tz 2dz .
4
= Young' s modulus of the stiffener in the longitudinal direction .
= length of panel parallel to the direction of loading .
a
= width of panel perpendicular to the direction of loading .
1 See figure 1 for orientation of axes relative to the panel and stiffener .
8
Report No . 1553-B
-25 -
.
t
= width of rectangular stiffener .
d
= depth of rectangular stiffener .
F
td = cross-sectional area of stiffener .
=
EaEb - OTLE L
Z µLT
EaEb
L
(Note: The K is defined as that used is Report No .
1557, but not as that used in Report No . 1525)
U4
to
Ea
' :i
i: .
ti•
sr.
L
-
-
1
:
Report No . 1553-B
-26-
.2-50f J
.
'.
.
.
'
Table 6 .--Compute& critical buckling load for three tOit ~ . `
'specimens in comparison to the critictel .lOad
determined by the lathral-deflectioh iilethod
and bythe diagonal-page method
.
_Specimen
_______ :
:
Cmopute&
twral: deflection
method
:
Ppr2
:
.
2XD-1~6
~
22g-2-2
. .
.l9X-3-2
:
-
Report No . 1553-B' '.
"
2,1I5
.774
1,070
: .
: Diagonal :
gage
: metho d
:-~~~~---~~~ ~
gI
.
:
2,200
~
:
700
1,100
zu6
2,150
.
~
740
:
/.
1,060 ` . .
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Table 8 .--Dimensions of stiffened plywood panels and their properties obtained from tests of coupons with face grain perpendicular to stres s
Specimen s
number i
t
$
••
s
(1)
17xd-1-4
17xd-2-4
17xd-3-4
17xe-1-4
17xe-2-4
s
•
Stiffene r
Computed
s
Elastic properties
:critical strewn
'---- :
s Shear Stress at :
: Width : Modulus o f
Width : Length :Thicknessi
Modulus of elasticity
:elasticity i n
s
s
:
:modulus :proportional :Single : Double i
limit
s
wave
t
wave
:
: compression
:Perpendicular :Parallel :PerpendiculariParal1e1 i
:
i
t : parallel to
to stress ito stress : to stress ito stress :
i
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grai n
▪
•
•
▪
▪
(t)
s
(h)
2
(El )
s
(Ep)
: U`LT)
(Es )
(a)
:
(b)
:
i
(E2 )
i
(Ea )
(PPM)
(Pcrl)1 (Pcr2 ) t
i
t
i
'-° t
i
t
:
i--'
(11)
s
(12)
:
(13)
t
(14 )
s
(4)
:
(6)
s
(8)
s
(10)
3
(2)
s (3)
(5)
(7)
i (9)
:
. :
- •
t
°---t
t
t
i
t
1,00 0
1 .000 :
1 .000
$ 1y000 s 1 .000 s
P .s.i.
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Inches i Inches 1
Inch
:
1 .000
t
s
v. e. i.
i. s
s p . s .i . s p. s . i. s
s
i u.
p a. i.
Dimensions
e.
23 .025
23 .025
: 23 .025
3 23 .025
i 23 .025
1
. 19 . 98 s ` 0.230 s
20.00
s
.224 i
s 21 .05 s
.227 ,
i 19.98 s
.234 s
t
.224 i
19 .94
s
s
▪
17xe-1-6 i 19.015 i 16.77 a
17xg-1-6 i 18 .995 s 16.79 s
174-3-6 2 18 .995 s 16.72 s
19x-1-2
19x-2-2
19x-4-2
19x-5-2
12.495
a 12.485
4 12.485
s 12.485
22g-2-4
22g-3-4
22h-1-4
221o-2-4
22h-3-4
s
▪
11 .515 1
s
s
t
s
11 .515 s
11 .495 :
11 .505 i
s
:
:
2zc2-1-2 a
2xc2-2-2 s
2zd-1-2
2x42-2
2=43-2
11.495 :
22 .015 i
22 .025 :
22 .015 i
22 .025 3
22 .025 4
4
2xB-2-6
2x843-6
2xB-1 1-6
2xc3-1-6
2=c3-2-6
t
a
s
a
s
s
t
i
•
12 .995 :
13 .015 a
13 .025
3
a
12 .995 i
13 .005 ,
s
i
9403-1-4 s 21 .615 ,
9x04-1-4 i 21 .625 :
9x04-2-4 : 21 .625 :
s
i
9445-1-6 : 17 .625 :
9x05-2-6
17 .635 1
9x05-3-6 : 17 .625 .
9x05-4-6 : 17 .625 i
22h-1-2
22h-2-2
i 16 .245 1
i 16 .255 I
Report No . 3553-B
Z M 7288b F
10.46
10.46
10 .47
10 .48
9 .01
8 .97
9 .00
9 .01
9 .01
14 .2
14 .26
:
a
t
s
iI
s
t
:
a
2
14 .23 t
14.26 s
14 .17 s
1,325
1,325
1,325
1 .37s
1,378
1
s
,
s
420
420
420
463
463
s
s
:
:
:
12.85 :
12.80 s
10 .42 i
10 .51 4
10.51 :
10.50 i
12.70 s
12.73 :
1,097
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.229 s
1,378
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s
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1 .590
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1 .151
i
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s
s
423
423
395
395
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s
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:
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2,811
2,811
4
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.
:1
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i
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s
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.140
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.141
.139
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a
s
s
1,627
2 .811
2,742
2,742
:
.
463
44s
44s
s
i
i
469
469
469
469
1s
s
a
2,814
2,814
2.814
2,836
2,836
s
:
s
:
:
1 .097
1,069
1 .069
2,625
2 .460
a
s
270 :
i
2,46o
1,131
1,131
196 p
196
:
253 i
253
:
253
:
2,280
i
t
s
679
i
a
:
i9
615
s
1
615
;
s
s
615 I
242
2
242 s
242
a
251
s
251
s
1,661
1 .681
922
1
922 a
922' s
a
881
881
s
220
.
220 i
220 i
224 :
224 s
1.
:
263
263
263
266
266
i
a
:
s
1
1,158
1 .131
1,681
1,957
1,957
1 .931
1,931
1,931
1,821
1,821
i
.178
.171
.175
.175
1,515
1,515
i
124
i
s
2
1,515
1
124
124
124
1
1 .111
a
i
395
395
a
:
1,131
1 .627
1 .627
95 s
95 ,
95 s
s
1 .158
159
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s
41s :
443 :
s
4
i
:
1,515
2
858
793
793
4
:
2,475
2,475
2,475
2,475
175
a
t
s
159
:
2
986
1 .050
1,050
1,111
1,111
1,111
1 .131
:
s
s
4
i
s
i
s
:
4
s
s
s
:
:
s
s
:
5 48
i
s
i
:
172
945 4 225 :
225
945
1
945
22 5 :
783 1 210 i
783 + 210 s
592
535
535
1
548
548
54s
615
s 284 i
s 269 s
265 t
t 316 i
290 i
4
a
1
172
i
172 s
172 s
t
:
a
2,450
2,450
2,450
2 .625
2,625
816
816
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816 i
816
s
s
s
s
a
95 i
:
t 95
4
95 ,
856
a
95
656 1 95
:
a
780
780
4
1 .591
1 .654
1,654
a
:
780
1 .139
1,139
1,139
1,139
a
a
.175 i
.171
.171
i
i
i
i
a
s
12.67 s
1,050
1,050
1,097
s
s
8 .40 4
8 .41 s
8 .53 s
8 .42 a
8 .50 a
1,050
4
4
s
100
110
110
.
a
s
s 437 i
s 261 s
s 270 :
270 i
2
▪
t
2 .075
2,075
2 .075
274
265
s 310
s 305
s 310
s
4
:
s
s
s
2,560
2,560
2 .560
2 ,755
2,755
s
s
s
a
$
i
s
s
:
t
2,280
143
136
141
145
146
i
2 .365
2,365
2,365
2,570
2 .570
:
s
s
i
i
1,695
1,525
s
425
430
7
749
761
870
798
: 0 .238 t
s
55 :
s .49s i
s :495 s
, .356 :
:
:
.163
s .177 s
1
1,249 i .372 i
1,229 t .256 8
764 a
737 i
765 t
, 765,6
748
723
900
886
901
s
i
t
s
s
424 s
4062
418 ,
429 :
430 s
:
1,249 s
.197 i
.198 :
.253 :
.155 i
.202
.259
.264
.146
.147
1 .58 2
1,74 4
1,809
1,66 5
1,586
1,722
1 .56 2
1 .508
1,864
1,864
1,728
1,78 0
1,76 3
4
8
s
i
1,612
1 .744
1 .93 2
1,78 4
. 373 :
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.239 s
1 .580
1 .79 7
1 .945
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1,849
1,648
.122 .
1,222 t
.177 :
.247 s
.178 1
1,218 :
1 .249 :
.142 :
.139 i
1,66 0
1,76 0
s 149 t
a 142 s
401 :
393 :
4413 i
.376 :
.136 i
.254 s
1,66 6
1 .68 0
1 .78 9
8
t
413 i
416 t
425 :
1,55 0
1,78 4
1,68 0
2
1 .525
► 97
a
s
97
s
97 :
1
97 t
1 .550
1 .550
1,550
1,550
1
:
s
i
.
540 s
.251 s
.373 i
.195 :
.130 s
1,68 0
1,70 6
1,548
1,66 0
2,037
2,037
153 p
s__153 i
444 :
443 :
.196 1
1 .608
1,592
t
253
615 s 253
:
s
1 150 :
1,265 :
191
175
: 183
: 183
s
496 :
520 8
520 :
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Table 9 .-Data from tests of stiffened plywood panels with face grain parallel to stres s
Stiffener
Depth
(d)
;
Load(P)
(1)
s
(2)
Inh
Pound‘
r
Plate
:
s
Grose critical load s Net critical stress
(L)
(Dcr)
(3)
:
s
Found■
Stiffener effec t
Shift of plate - neutral axis
(Zn)
(4)
s
p•s .l .
`--- ..
(5) .
Inch
11 :0-1. 6
1 .000
.750
.2500
.000
8
s
:
s
-496
-57
-19
+45
0
900
4 . 700
3,500
2,200
1,500
s
:
?1,251
1 .07 5
so 6
520
347
t
:
s
1 .000
938
.818
.694
2
439
.316
.190
.127
.000
1 .000
.872
46
.625
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•376
.252
.130
.000
1.000
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0. :12
.500
.375
.250
126
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s
s
r
s
s
s
r
1
s
3
:
r
s
r
s
:
s
s
:
s
:
:
1
t
:
s
s
s
s
r
s
s
s
-469
-444
-329
-235
-145
+17
+22
+34
+37
+20
+2
0
-322
84555
-144
-53
-33
-7
+5
-5
-7
0
-251
-76
+13
1j
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+9
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-47
0
-324
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t
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-41
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0
Report No. 1553-8
10
7
72886 F
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s
s
s
;
s
s
s
s
+
:
s
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:
s
a
:
s
s
s
:
s
4,950
4,850
4,450
4,450
4,400
4,105
3 .535
2,910
2,200
1,600
1,275
1,260
+
s
:
s
s
s
s
s
s
5,500
2 zoo
4 .650
3 .600
2.930
2,400
1 .775
1.600
1 .550
6,400
6 .200
150
4.300
3.350
2,550
2,150
1,900
1,600
s
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30 0
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4 9. 50
4,165
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r
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s 2.400
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92,235
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s .54
r 111 .300
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a
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62 6
46 5
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+
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Stiffness s Coordinate s
(x)
(z1 5 )
: (Y )
s
17xcr1- 4
1 .000
934
88
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50
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371
248
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:
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r
0 .26503
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100041
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20932
16657
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s
r
s
r
r
t
170,119
124,627
87,922
59 6333
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4
8
+
a
1
s
3
r
:
s
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1 .016 0
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5
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s
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r 1 .345 3 1 .0010
s
95 s .7590
r .655
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s .257 1 .1940
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r .0386 s .0323
3
:
:
1.610
1 .175
s
s
(Sheet 1 of 5 )
9 .-Data from tests of stiffened plywood naaels with face grain parallel to stress (continued )
Table
Stiffener
Depth s Load
(d)
t
(P)
:
3
(2)
(1)
Inr
0 .627
X00
.439
.371
.254
.124
.000
s
a
s
1
:
t
1
t
t
997
.623
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•375
.313
.064
.Goo
.751
.624
.505
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.376
.251
.122
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,
1
1
t
1
:
t
3
t
t
t
t
1
1
t
t
s
t
Zaa da s
t
-27
-3 6
-21
-1 5
-9
0
0
1
t
t
s
-204
-142
1
a
- -9
-a l
-28
-26
-1 3
-3
o
•
-108
-70
-47
-143
-3 9
-1 3
-4
0
S
I
s
4
A
a
4
t
t
Stiffener effec t
Plate
t
Gross crit1 al load
(L)
(3)
Ponnda
1,215
1,250
1,190
975
575
400
375
t
t
t
i
~.
t=::
t
t
t
Net critical stress
(Per)
(4)
Z.I.04
..«__ .._-_ ..-
2Il,040
1,018
1,002
823
485
343
321
2211 .098
132
,097
Z1,112
1,o56
966
1 .500
1,4 0
1,30
1
1.290
1.16o
633
460
32o
540
370
350
1,290
1,200
1,200
1 .100
970
675
38o
330
306
'j.
2102 2
97 7
97
914
80 5
57 2
32 5
28 5
a
t
t
41
s
s
--i
s
22x-}-2
=
s
s
s
Shift of plate - neutral axis s Stiffness
(RI)
(2n)
(5)
...
In .h
0.11539
.08124
.06631
.05096
.02822
.00956
s
22x-2-2
t
s
1
t
1
1
.28247
.22989
.16555
14430
.10469
.06794
.05178
.02416
•00530
22x3- 2
s
s
s
4
1
.15589
.11753
.08479
.06796
.05357
.02657
.009614
22x-4- 2
1 .000
.7141
.501
.362
.311
.188
.063
.000
i
1
s
1
e
t
t
1
t
.625
•565
X0 0
438
t
. 250
.124
.000
a
t
t
-245
-161
-8 7
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-1 1
-3
0
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-7 9
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444
14
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1
Report No . 1553- H
M e88? P
o
i
1
t
t
s
•1
4
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1,570
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1
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1,180
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oo
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t
4
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375
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1,01 1
91 1
81 7
147 8
376
336
2
1195656
756
506
32
s
s
s
:
22x-5- 2
1
t
s
1
t
1
t
1
t
.27226
.17682
. .09910
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.00487
.10279
.08765
.07221
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04568
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t
(6)
•
s
t
s
a
s
I
I
1
1
t
.
t
t
17,384
10,092
7 .399
4,967
2,061
436
65,772
46,002
32,029
21,169
12,655
6 .452
4,267
1 .381
170
1
t
t
1
1
1
1
1
4
1
t
t
3
:
t
1
1
1
t
(7)
%
t
•
3.250 i 0.997 0
s 1 .990 s 1 .0260
8 1.500
.9760
1 1 .035 1 . 7320
.455 t 2640
1
: .103 1 .0500
s
------- t
t
1
1 .
1
s
s 5.380 1 1 .0330
t 6.230
1 .0000
t 4,590 s
.9970
3 .230 s 1 .0150
9500
t 2.060
s 1 .130 s .8690
3
.776
.6820
i .273 t .2230
: .036 t .0320
t
t
27,350
17 .466
10,527
7,500
5,227
2.048
431
4.740 s 1 .0280
3 .190 a .9680
t 2 .020 1 .9960
t 1 .486 s .6870
.741 0
1 1 .062
8
.442 t .4220
1
.101
t
t .07260
t
1
t
6 5.771
31,780
12 .559
900
4,169
1,369
166
8 .810 a 1 .050 0
4 .790
1 .017 0
2 .100 s .9260
1
.090
t
.600 0
t
t .792 t .6770
: .281 t .2250
.036 1 .065o
1
1
t
1
1
t
1
1
t
1
1
t
1
1
1
1
1
1
t
(s)
1
I
1
i. .: . ..W.raii_.;.
t
t
z
Coordinate s
(Y )
s (X)
15,127
11 .836
8,801
6 .395
4,408
1,701
367
a 3.200 t .9800
1 2.550 t 1 .0350
t 1 .950 1 1 .0060
1 1.450 1
.9600
1 1 .025 t
.6880
1
.415 1 .3070
1
.095 1 .1030
(Sheet 2 of
l
5)
Table
9 .--Data
from tests of stiffened plywood panels with taco `rain parallel to stress (continued )
Stiffener
Depth a
(d)
s
Loadb
(s)
I
i
(1)
s
(2)
s
I h
,
basis
1
a
0.990 , -365
. 871
1
-31 5
1
.627 I
.505 t
.22557 s
.12E ,
.000 1
plats
1
1-88
-1 18
-9 7
-1
1
-21
0
(3)
1 .000
.875
14
. 624
▪
.501
.378
25
.1526
.000
1 .000
.870
50
• 623
. 500
.377
.250
130
.000
. 991
▪ 749
.
.622
s
s
s
1
I
1
a
1
s
i
1
1
I
s
1
a
s
(4)
Y.e .1 .
t
1
1
t
2 .500
2,360
2.200
s
a
s
s
2,350
1
2
1 .750
t
825
11,241
,200
,22 1
-1 .29 7
1,13
t
6915
a
479
a
s
s
t
t
1
a
I
1
,
I
i
1
I
1
t
a
1
1
1
I
,
691
. 683
1 .623
a
s
,
,610
$
1 .403 ,
s
958
673
1
511
446
t
1
-31
-11
-6
0
-368
-221►
s -227
s -127
1
76
t
2,
t
2,660
2,600
a
i
s
1
1
1
s
1
s
a
s
a
2 .350
2,180
1 .515
1,080
840
800
3 .000
2 .800
2,750
2 .325
2 .350
1,650
a
t
t
t
s
1
1
pp1,456
457
11,415
1,300
1,237
867
625
487
I
1
s
t
s
a
465
a
,
1
31,486
81 .456
a
s
a
a
1 .265
1,400
-44
927
I
•373 1
+17
1 .175
6u
.250 a
a
a
1
. 129 i +23 I 1 .053 s 619 a
. 000 I
0 a 550
1 490
a
1
a
a
a
.499
Report No . 1553-B
2 M. 72888 F
t
(z)
t (t)
s
(6)
1
(7)
I
1
8
,
.15606
.12230
09
.06631
.04272
.02308
.00823
s
s
1
1
r
a
1
.18820
.14886
.12011
Coordinate s
1
s
1
1
t
I
t
s
93 .830
68 .733
47 .078
31 . 0 73
18 .530
9 .013
3,906
916
5 .670 t 1 .0000
r 4 .310 s .9520
1 3 . 080
1 .9 630
s 2.120 11 .0460
1 1 .325 a .8700
s .721 s .6830
i .30 6 s .3060
1
.076 8 .1180
t
98,993
1 3 . 930
t
s
68,501
s 2 .830 s
49 .103
a
, 2 .100 ,
.09032
31,707
a
s 1 .410 ,
.36529 a 19 . 90
I .895 ,
.04102
s
,
466 t
9 .683
.02179 , 3 .536 , 3 ,
.00822
a
, .051
. i9 ,
97 2
t
1
I
.17886
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t
1
s
,
,
s
.11196
.05450
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.00725
.19915
.16082
,
s
s
11
s
68 .570
46,002
30 .107
17 .746
9 .109
3 .705
552
103 .412
73 .747
I
s
1
.10409
.07403
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I
a 3.530 11 .150 0
.8980
t 2. 1 150 a
, 1 .660 , .5290
: 1.010 , .5710
1 .541 ,
466 70
a .227 1 .2370
t .055 , .0810
a
s
t
5 .110 s 1 .0130
3 . 790 , 1 .0140
t 2. 750
97
a 1 .830 1 8640
s
1
s 1 .130 s
.608 t
1
i .251 a
1
a
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1
i
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.4350
1567
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s 4 .980 s 1 .0260
a 3 .930 t 1 .0000
s 2 .730 , .9720
s
55,218
a 1 .835 s .7970
s
35, 434
t
21,049
1 1 .142 t .9160
10,707
a
t .612 t . 11670
4.367
a .263 s .2270
a
a 1,120 s .070 I .1460
a
1
s
i
1
I
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1 .0270
1 .0230
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1
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09556600
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a
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s
3 .972
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I
1 .021
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t
t
a
95,091
(5 )
1
,
1
t
t
,
0 .19028
1
s
t
a
2aci-1-4
21 .519
Stiffness
(Hi e)
1
a
2:c4-1-4
1
1
I
t
1
t
1
lash
2zc-2-4
2 .550
-142
s
t
. 385
s
s
2.575
-89
I
, 606
1
1
2,400
1,3 4
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s
s
-65
s
2 .250
I
1 .260
a
s
1,750
s
1
-33
990
-18 , 1 .550 , 553 $
-16
1,150
s
654
1
575
1
503
-3
1
a
0
s
750
s
32
s
s
s
2=4-2-4
-64
(5)
22x4-3,-!t
I
a
-166
1
s -179
t
126
,
s
& ABU
1.000 1 -359
3,300
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3, 200
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,
3,100
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1
3 .125
. 510
a -191 a 2,630
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-34
a
1 .700
. 253 , -4
1,175
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-2
,
890
0
1
.000 a
775
I
Stiffener effect
dross critical load s Not critical stress s Shift of plate - neutral awls
(L)
I
,
(per)
(al)
,
1
1
1
s
109 .994
78 .704
(Sheet 3 of 5)
Table 9 .-Data from tests of stiffened plywoodpanels with face grain parallel to. stress (continued )
Stiffener
Depth s
(d)
s
(1)
Inch
1 .000
.873
t
Ioad1
(P)
s
(2)
t
lbunde
:
s
:
Plate
t
-97
11
s Gross critical load s Net critical stress
,
(L)
s
(pcr)
s
s
t--
t
s
s
. 624
:
-71 ss
-62
.500 s
a
2
• 0265
s
..128
t1
+8
+1
s
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s
0
s
t
t
Pounds
2,000
$
b
1 .350
1,000
575
550
1 .150
850
700
:
.998 , -709
s
2,725
2,450
.865 s -572
s
45
-229
:
2,275
•.618 4t -188
t
2,150
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t
2,250
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+13
3
:
1,225
▪. 120 ,
-28 , 800
0
600
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t
t
s
2.150
1 .950
1 .750
3 .100
2,950
2 .350
2,290
1,800
1,500
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.887 t -527
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.615 t -31 9
.497 : -302
.364 1 -21 5
.2
t
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-35
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0
t
-
(3)
t
f_
+
a
s
t
t
a
t
a
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.870
t
-136
46 t -1214
▪.622
t
-96
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-37
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s -13
.249
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s
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0
t
t
Report No . 1553-B
72889 F
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2,475
2 .750
2 .570
1,75 0
1,850
a
t
1 . 9'+0
820
880
t
t
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s
t
t
t
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s
t
s
Iti
t
t
t
(6)
2849
2907
2841
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313
260
245
21,160
21088
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2672
77
494
366
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t
s
s
s
t
s
s
a
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t
2=c3-1- 2
t
s
t
t
s
s
s
s
t
2=4-1- 2
s
s
s
J
s
s
s
t
t
0 .19890
.16141
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911
998
787
50 4
464
t
,
,
:
s
t
S
s
9zc3-2-6
:
s
t
a
a
s
a
a
s
3
131 .106
p
t
t
:
63 .820
41 .933
24 .720
12,900
5.714
1 .249
s
4
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:
:
t
s
s
s
.18827
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t
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s
t
.'
s
s (s )
113 .050
74 .379
47,112
28 .512
13 .861
5 .723
1,332
:
$
4.270 s .9740
s 3 .190 s 1 .0610
t 2 .255 s
.9640
s 1 .537 t .8220
i .919 t .5540
s . 515 s 3 30
, .238 $ .34 0
t
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t
94 .267
149 .541
"
a
:
t
.22383
:
(7)
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2so-1- 2
k 626
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21.643
1 .5 1
1.
949
723
605
435
t
t-~
(5)
t
t
t
,
s 4 .060 t
3 .170 t
s 2.220 s
s 1.465 i
s .931 s
s .478 a
, .209 s
t .052 s
t
t
3
1.1850
1.0920
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.
.4050
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t
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11586
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2
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s
3,250
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3 .12o
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-2 3
t
2,950
2,34 0
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-26
,
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i
1, 350
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-13
:
1 .125
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s
s
(4)
t
t
t
Stiffener effec t
Shift of plate - neutral axis s Stiffness s ooordinste s
(Zn)
(NI B)
s (2) s (Y )
.27100
.22363
.17888
.14114
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s
s
t
s
t
s
s
s
t
t
t
t
t
,
t
:
:
s
t
t
4
s
s
s
a
s
s
t
164 .349
116 .467
81,486
52 .299
31 .5014
16 .070
6 .92
1,479
s 5.030
s 3.740 8
t 2.740 s
t 1 .854 t
s 1 .171 s
s .635 t
.267 s
t
s .066 s
:
4
79 .905
58 .003
40,21
27 .564
16,603
8,860
3,887
1,053
10360
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1 .0660
1 .0020
.9600
.5620
.4680
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t
2 .830 t .9880
2 .160 s 1 .0130
: 1 .580 a 1 .0000
a 1 .145 a .9460
:
.732 t .7020
s .418 ,7t .4550
.2670
i .196
i .056 i .1570
t
t
t
64,156
46,654
32 .575
21 .397
13,009
6 .736
2,867
783
11
t 3 .470 ,
.9330
s 2 .640 t 1 .080 0
t 1 .930 s
.990 0
t 1 .330 s
. 5330
s .850 , .619 0
.465 s .3830
t
.209 : .069 0
t
t
t
t
(Sheet 4 of 5)
Table
9 .--Data from tests of stiffened
Stiffener
with taco grain parallel to stress (continued )
plywood panels
C=
Plats
t
Depth t Load}
(P)
(d)
:
----(1)----$
(2)
t
#
4
Inch
Pound.t
(3)
t
..-
4
pounds
t
~
Stiffener effec t
..... .... .....-° neutral.....
--'-°8---"---`-Coordinate
aris
s
Stiffness 3
s
i
'
s Gross critical load s Net critical stress
s
(L)
t
(p )
Shift of
t
(4)
------------------ _--- .
P0901 0
_
s
plate -
(Zn)
(5)
Inc
9224-146
e
0.996 t -272
.810 t -134
.687 1 -202
65 t
-51
-68
131 t
. 311 -16
.183
:
-9
.063 t
-6
0
.000 s
t
s
s
-239
.996
.866
-150
-402
46
s
•.62o s -296
-39
• 495 1t
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-11
.250 t
-4
.124 t
-26
0
.000
t
1
3 .450
3 .30 0
3 .03 0
2,830
:
s
,
21 .738
11, 7 1
1,547
1 .520
1,13 9
85 5
69
48 9
46 1
:
2 .150
1 .560
t
t
1 .250
900
880
i
t
t
s
s
t
t
t
s
;
s
1,170
1,100
+
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27
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-103
-48
-3 5
- 27
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-7
0
+
.04509
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00525
t
s
22,063
-2,111
1 .585
1 .555
1, 5
1,131
837
619
595
1
+
t
,
s
t
9ac2-1-4
s -476
3,03 0
2.850
s -226
2,450
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t
-2
900
.000
0
66o
t
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.67o 1
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.000 s
s
s
t
79 .529
48,840
33 .416
t
t
t
5 .211
I
21 .430
11 .731
1,991
328
2.975
2,700
2 .550
2,680
2 .375
2,080
1,48 0
950
800
700
1220
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s
785
9
315
:
:
:
t
1 .168
t
1 .0020
.9980
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t
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.103 t .1800
.018 t .015 8
t
1 .910 t
1 .370 s
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2 .890
4
a
t
t
t
s
,
s
. . . . . . . . . . t
t
:
t
2 188
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1,100
+
:
:
96 7
687
442
375
331
t
t
s
s
s
:
4
102 .881
.30026
:
.24955
t
74,574
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s
34 .690
t
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21 .133
11,364
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1
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5 .128
t
.01742
1 .417
s
:
i
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:
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4
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+
9292-2- 4
t+
'
t
s
t
s
s
=
s (Y )
------ •-__....y....
s
4sc4~~b
4,050
=
4,050
3 .330 s
3,170
t
2 .930
=
2,100
1
1,550
1 .000
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1 .000
0 .24754
18 30
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10626
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.. .. ..._- :----
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t
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t
s
4s
110 .906
56 .811
28 .380
14
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s
s
t
4 .1+39
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t
112,503
51, 25z
37 .268
30 .095
12,780
5 .515
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t
s 2 .660
s
1 .550
a
:
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;
.873
6
.9850
1 .0130
-700 0
.660 0
.660 0
•4040
.205 0
.043 5
1
.9840
s
.1620
t 1 .016 0
t
.931 0
t
t 2 .890 s 1 .016 0
t 1 .607 s
.9760
s 1 .371 +
.9560
s 1 .205 s 1 .0500
37,778
29 .631
s
22 .155
s
.14279
.11883
:
t 2.006 s
s 1.510 s
1 1.065 s
t .700 t
t
.407 s
t .199 t
s .060 t
s
s
s
:
.31224
t
111 .090
. 20499 ,568
.18247
:
. 16597 =
+ 2.600
.966 +
11,209
s
1,080
s
:
.770
.427
.187
.050
t
t
1
s
.9250
-7800
.4660
.1770
.0762
4
9x22-4-4
1 .000 t
47 s
▪.617
=
.560 s
t
.▪ 247
.117
.000
t
t
1 comprassl2a ;
-44 8
-320
-17 1
-22
+48
+40
+8
0
3,000
2,780
2 .580
2 .460
1 .850
1 .180
900
700
+ tension .
?These values were. used for average pcr2 '
'Report No. 1553-B
1k
72890
F
a
s
t
t
t
t
t
:
-l .185
142
=1 119
?1 .142
881
567
8x22
325
s
+
:
t
t
=
t
.161%g
.14174
.08148
.04587
.01703
s
+
s
+
:
:
1 .431
: 2.930 t
s 1 .705 s
t 1 .198 t
s 1 .000 s
t .480 1
t .227 1
t .o65 +
:
1 .0380
. 9950
96
.99
.7000
.33220
1 5
(Sheet 5 of 5)
Table 10.--Data from teats of stiffened plywood panels with face grain perpendicular to stres s
Stiffener
------------------ Loadl
Depth
a
(d)
(P)
:
(1)
a
(2)
Inch
1 .000
.875
4466
.683
.620
6 57
.498
.374
.246
.124
,
a
a
a
:
s
a
a
a
a
1 .000
a
.000
Grose critical load
(L)
a
a
a
(3)
a
s
a
:
a
Stiffener effec t
,
Plat e
Net critical stress
(Pcr)
(4)
Pounds
Z25-t .
4,390
; 65
4,
4 .225
4 .360
4,120
3 .7`50
2,750
2,025
1,550
1,450
3 766
276
3
=742
2 791
4,380
4,250
4,250
4,144
3 .950
3,800
3,380
2,575
1 .875
1,440
1 .400
3784
2760
5 .000
4,800
4,70 00
4,580
4,490
3 .500
2,700
2,130
1,600
22841
Shift of plate - neutral axle i
(Zn)
:
s
a
a
s
,
0
a
(5)
a
I nInh
a
4
s
s
a
a
a
a
a
:
-27 1
-26 7
-30 4
a
a
s
;a
-19 9
-15
-502
-3 7
+5
+8
a
a
a
a
0
1 .00 0
-461
.87 7
. 25
6 1
.50
.37 7
.25 2
.12 7
.000
-382
-3 25
-11 5
+162
+124
-124
0
492
368
284
269
3755,22
3 44
X725
19
646
484
359
276
267
217
-813
' 801
5
3824
689
532
378
301
0 .28234
.235 5
.18919
.16752
.14653
s
a
a
a
a
a
a
a
a
17xd-2- 4
,
a
s
a
a
a
a
a
a
a
a
_
17xd-3- 4
:
a
a
s
s
:
a
a
a
s
.1og4
1
.07277
.04111
.01685
a
1 .000
.874
.689 a,
.629
.558
. 503 t
.372 a
.255
.132 a
000 s
t
a
a
-209
-308
-234
-3
+30
+6 6
0
-267
-213
1,220
a
a
1
-20
:
-12
+7
+7
0
0
a
a
:
1553-8
72891 F
s
a
a
a
s
a
a
s
3824
-800
?225
-851
18
612
449
315
223
4,360
2781
450
2808
4 , 360
2817
4,280
795
4 .29514
4,280
-t13
742
3 .900
2,900
555
2,220
425
1,600
305
233
1,220
a
a
Z
1,660
-112
-29
.998 a -221
.872 : -209
.802
-166
45 a -136
▪.687
a
-139
.625 a
-61
-45
.500 a
-26
.379 a
.252
-13
.125
-7
83port No .
4 .720
4,690
4,750
4,660
3,850
3,250
+106
s
.000
(6)
0
a
a
a
a
a
a
a
a
a
a
a
a
5,100
5000
1 4 .950
000
4,950
4,175
3,500
2,680
2,030
1,570
1 .450
21 .123
,
,
a
,
a
a
a
.35345
.30058
.24696
19360
.16842
.14585
12288
.080133
.04164
.01221
a
s
a
s
a
a
+
a
a
a
a
a
17x.-1-€1
a
~-1 .103
s
11 :1026
1a
X1,108
a
a
94
,
696
11
s
464
s
360
a
a
334
a
4
s
s
a
a
76,446
56 .502
39 .633
32 .670
26 .496
169 .6L9
.267
4,130
1,269
(7)
a
:
,
a
a
a
s
a
,
t
a
(8 )
a
a
a
s
4 .500
a 3 .430
a 2 .470
a 2 .070
a 1 .700
.375
, 1 .1
: .633
.292
s
s
092
, 1 .00 2
-99 5
, 1 .01 3
s .95 8
a 1 .05 0
.98 0
:
a .46 6
.21 8
a
t
041
------- -
A
a
a
100 .728
74 .613
5 2 .538
34 .646
27,528
21 .831
16,681
8,783
3 .54 7
762
a 5 .360
s 4.140
s 3 .050
a 2 .110
s 1 .710
a 1 .390
1 .090
s .601
a .257
, .058
a
: 1 .054
s 1 .01 2
s 1 .000
4
.98 5
a .945
s
334
: .792
a .471
: .21 2
a .029
a
39311
-3367 4
.2 7954
.22457
.17178
.12143
.07427
.03269
152,456
97 .247
68 .064
45 .621
28,719
16 .39
7 .886
2 .651
: 5.120
.034
a 3 .970 a: 1 .997
a 2.940 s .988
a 2 .090
s .96 8
t 1 .400 : 1 .005
s .854 a .77 0
a .475
. 4 75
a .159 a .17 3
a
t
130,4637
96,476
66,074
45,533
28 .636
16,181
7 .986
2 .542
a
a
a 5.350 a .997
s 4.o 4o a .96 2
s 2.960 s 1 .00 0
a 2.130 t 1 .040
a 1 .400
a .250
a .83+ a .66 0
a .433
.393
,
146 s .165
a
I
a
a
t
a
,
a
s
a
a
a
t
s
a
•37643
31823
.26218
.21236
.16109
.11223
.06939
.02936
a
▪
17s s-2-4
,
a
,
a
a
a
s
a
;720-1- 4
1 .000 a
.870 a
.742 a
.625 a
.500 :
. 254 a
.125 a
.000 a
Coordinate s
(X)
(Y)
Stiffness a
(EI s )
a
a
17sd-1-4
-268
-268
-231
-104
-58
-69
-104
-45
-20
s
.000
.872
.751
.620
.4517
. 31 2
.187
.067
Poutde
:
a
a
t
s
a
a
a
a
a
a
a
53184
a
98 .902
a 4.900 : .962
.27925
72,656
a 3 .720 a 1 .006
a
.23149
52,522
a 2.780 , 1 .01 9
a
.20514
a
42,848
a 2.310
.96 5
.18209
a
35,192
, 1 .935 a 1 .01 5
27,291
,
1
.530
s
1
.01 2
15559
a
•13571 s 21,984 a 1 .253 a .895
.09114
a
11,978
a .841 a .57 8
05556
+
t .361 : .351
5 .86}
.02407
1,914
a
.012 a .138
a
a
a
a
s
s
a
a
a
a
.27269
.22646
.20167
16201
.16255
.14240
10413
.07066
.04025
.01600
+
a
a
a
a
a
a
a
a
a
a
6 2 . 591
46 .o65
38,180
32 .406
27,105
22,051
13 .677
7 .708
3,465
1 .015
4. 290 a 1.01 4
a 3 .230 a .930
a 2 .720 a .98 8
s 2.335 s 1 .01 0
a 1 .975 a :9 6s
a 1 .629
a .793
3
1 .035
606
a
.600 a .372
a .276 a .182
a .0836 4 .041
a
a
a
a
a
a
a
(Sheet 1 of
6)
Table 10 .--Data from tests of stiffenedplywood panels with face grain perpendicular to stress (continued )
Stiffener effect
Plate
Stiffener
-
a Load° t Gross critical l;;ad
d-"t-;Net
"
critical stress
(P)_
a
- (L) (Pcr)
-- ---(d)--(4)
t
(2)
t
(3)
a
(1)
&
t --1 +
Po
r
Pounds
e
De th
a
1 .000 t -300
.677 t -361
.7149 t -312
.623 : -326
.496 a -157
.374 a
-72
65
.251 a
-26
.125 a
0
.000 a
r
t
1.000 t -229
.875 a -189
. 750
-190
.625 a -100
. 5oo a -56
-141
-17
.240 i
.123 a
-5
0
.000 t
a
r
t
. 746
.627
.5502
t
4
4
.313
.246
.190
.096
.000
a
a
r
a
i
.621
.502
.37 5
.31 3
.249
.12 2
.000
a
4
a
a
a
t
e
5 .350
5.280
5.150
5 .080
5,080
3 .670
2 .580
1 .780
1 .370
t
4
t
4
t
r
r
14,760
4 ,550
4,60 0
4 .470
4,050
2 .95 0
2,150
1 .650
1,300
t
-70 a 930
-82
,
680
870
-143
a
a
840
-16
-21
t
810
-17
t
710
-9
t
525
+2
t
325
250
0
a
-26
-19
_-4
-_ 32
0
t
600
790
7~o
660
1470
270
180
k .12 9
aa
a
t
a
t
a
a
t
4
.
a
a
=
t
t
a
t
a
r
t
1
=1,08
063
51,10 0
804
562
3 6
30
2 022
83
-- 998945
900
656
461
371
293
a Shift of plate - neutral axis a
a (Zn)
'---a
a
(5)
t
+
t
17x221- 6
a
a
t
a
a
{
t
17xw-5-6
a
t
=
t
a
a
a
t
14742
z7
397
296
187
143
Z 22 72892 F
0.36111
307x2
252551
.20040
.1.5019
.10490
06331
. 02682
1
t
.[~5S34
. 1 Sg T
, 64
.16495
.12207
.08160
.04565
.019 ]
a
a
r
;=; ---te s
t
(T )
(7)
a
a
a
a
a
a
t
192-2-2
a
a
a
t
a
t
a
a
t
a
t
a
a
t
t
a
a
t.
t
s
t
t
13557
.09869
.06352
.04829
.03414
.01190
a
a
a
a
a
}Sz-1- 2
a
t
a
a
t
.23487
.18547
.13697
.09168
.07085
.05100
03 50 2
.01404
I
3
a
4
a
a
a,
r 5 .250
t 4 .070
a 2 .960
a 2 .090
a 1 .353
t
.812
.408
a
a
.136
a
t
72 .777
53, 7 44
1
25 .666
16 .052
8,784
3,846
1 .242
t 5 .110
t 3 .880
650
t
t
1 .980
t
1 .280
.726
a
a
.330
t
.1096
a 1 .034
s .98 2
t
998
a .98 5
.870
a
t
.574
a .28 2
.110
t
t
a 10 .860
a 7 .62o
a 4.880
t 2 .675
a 1 .900
a 1 .200
+ . 7 20
a .213
a 1 .06 3
a .966
a 1 .01 2
a .98 3
.947
a . 7 87
a .49 0
t . 155
20 .347
13, 3149
7,9141
14 .127
2,752
1,665
953
263
s
+ 6 .210
9 .503
a 3.960
5 .756
2,921
a 2.120
t 1 . 1435
1,931
1,154
a .878
t
255
a
.205
:.
. . . . . . . . . . . . . . .t
.27181
.15206
.11 1453
.0667
x.02565
.01205
a
t
t
a
a
r
#
;,
i'
;
1
t
t
94 .911
70,128
49,239
33, 0 3 4
20,560
11,768
5,644
1 .804
t
.27154
.16390
.11322
.09006
46774
.014639
.01150
(8 )
t
+
t
a 1 .040
a
1 .00 5
t .965
a
. 96 9
t
1 .006
t
.64 7
.3444
a
.12 2
t
t
a
22h-2-2
t
Report No . 1553- B
(6)
(x)
l-
t
-49 3
749
a
. 74 5 a -75 1,125
1,140
a
2
-790
499 t
-32
1,100
t
763
.375 a
-30
2746
-29
1,075
31
a
-26 1,0 t -716
. x54 1
840
a
594
.191 i
-7
460
t
328
o
.065 a
27 1
360
a
.000 t
0
r
r
a
-819
1 .200
a
.742
1 .120
.1468 a
-62
=769
2 63
1,080
t
. 76 a
665
6
960
t
.249 t
-1
1412
570
a
3
450
t
325
.067 t
273
0
4
.000 a
375
a
1224
22h-1-2
34443
X5244442
-435
376
268
154
103
Stiffnea■
(EI ® )
20 .557
7 .869
4,122
2,819
1 .789
1 .004
147
20 .226
6,721
4 .099
1,693
41
151
a
1
a
t
a
a
a
t
i
t
a 12.750
a 5.720
a 3.x70
t 2.335
a 1 .556
a .920
t
.151
r
a
1 .006
1 .003
.96 7
.84 1
.498
160
.992
t
ta 1 .01
, 5
a
.926
t
.930
1
.690
a
.13 8
a
t
a 12 .070
a 4 .780
t
3 .1 40
a 1 . 420
t
389
t
.1 149
:
a
a
a 1 .05 6
a
.97 '
r
.96b
a
.620
4
.30 2
.12 3
t
a
a
(Sheet 2 of 6 )
from tests of stiffened
Table 10 .--Data
Stiffener
Depth
(d)
▪
(1)
,
Load(P)
t
t
:
(2)
Inch
s
0 .999
.748
501
;
s -189
a -111
a
63j
-16
s
s
-1 0
.248
.191
.094
.000
.626
.500
.372
.314
.251
.125
.000
Pounds
t
t
a
a
t
a
a
a
t
t
t
t
Y
i
t
:
a
-6
0
-57
-29
-29
-11
6
-3
a
a
0
.56o
s
.408
349 ,a
000 a
a
.616 a
•378 a
▪.22 66
a
.164 a
.126 a
.063 a
.000
a
-45
-35
30
-17
0
-52
-21
-28
-1
-5
0
0
a
.742
.501
-378
.313
254
.191
.12T
.000
a
s
a
t
a
a
a
a
-93
-61
-46
-4 1
-22
-14
t
Report No. 1553- B
Z t' 72b93
-6
0
Plate
Gross
critical
(L)
load
t
a
t
.$
s
s
r
s
s
t
aa
a
t .,
a
critical stress
(p cr )
s
s
t
Pouade
P . s. i .
1,41 5
1,360
287 5
2891
880
540
2802
621
381
27 5
-840
1 .040
1 .03 0
1 .01 0
2714
495
362
351
258
-666
559
950
790
(continued)
Stiffener effec t
s
Net
(3)
385
a
s -171
.511
-67
s'
a
.319 s
-86
a
25
a
-33
s
-11
t
.196 a
.0714 s
-8
a
.000 a 0 a
.61o
panels with face grain perpendicular to stress
1 .240
1 .140
1 .004
▪
plywood
a
t
s
- 4- "c
s
a
a
s
a
t
a
Coordinate s
Shift of plate - neutral axis a Stiffness
(EI .)
t
(%)
(Y )
(7s)
a
i
a
( 6)
(7)
:
(
:6 ) ---- a- - (7 )
a
)-- - Inch
t
s
1
0 .40428
.28670
.17544
s
,
s
i
:
a
a
.07164
0510
.02056
:
19x5- 2
a
:
a
,
a
a
a
i
.19560
:
.14430
.09650
07641
.05605
.02150
s
s
s
i
s
a
is 1-4
1 .420
1,425
1 .330
1 .325
850
390
:
s
a
s .
t
300 a
1,200
1 .26o
1 .22200
1 .220
400
z3 z
2330
3'~+
22 3
102
80
307
2325
-322
2316
2320
106
t
s
t
i
s
s
20564
s
.11926
:
.09101
a
a
.06756
02209
t
a
9x24-1-4
a
:
s
s
a
1,44 0
1,390
a
a
s
a
a
0
1,16
950
730
500
380
I.
X361
2356
338
300
247
188
130
99
. 16770
a
14936
a
s
a
.11936
.09694
07627
aa
:
s
:
t
s
s
s
a
s
a
r
690
740
6 10
a
a
a
a
t
s
a
1,00 0
960
330
593
493
270
1,130
309
14,1154
5,401
3,484
2,219
508
11,590
9 .598
6,718
4,866
3 .519
t
17 .713
.08387
.05295
.03352
.01491
t
a
a
4 .402
s
.103014
a
:
6 .231
3 .203
1 .642
886
325
:
.26642
.17726
.12444
.09782
.07475
.05166
.03046
•
a
a
s
:
a
a
a
s
a
t
21 .130
11 .600
, 5.190
s 1 .360
.847
:
, .255
a
,
s
s
s
s
t
1 .034
1 .058
.982
.920
.623
.210
:
t
i
11, 401
a 9 .300 s
.99 3
6 , 701
a 5 .690
r 1 .0 1 6
3 .440990
a 3.15p a
2,373
: 2.250
s
.917
1, 4t?1
t 1 .455 s .694
366
s .393 s .233
a
,
23076
.12781
2222-4
1,080
1 .020
1,909
t
E4-2-4
a
a
49,790
23,672
8,950
18 .176
6,952
3 .635
2 .396
1 .539
663
397
. 110
:5 .050
s 2.110
t 1 .415
s
.9 388
a
2 5
. Q50
s
: 1 .048
t
:
a
a
5.830
a 4.930
a 3.510
a 2.600
s 1 .920
:
t
a
s
a
1
a
s
a
:
s
.945
.968
.550
.096
-950
1 .030
1 .015
.988
1.008
a 6.450
, 2.540
s 1 .650
, 1 .380
742
s
a .413
a .015
:
t 1 .036
1 .01 5
t
t
950
t
.606
.596
,
s
.366
a
.01 3
:
a
a 14.550
a 6 .62o
a 1 .236
a
.999
r
.99 3
:
.97 2
a
.667
a
.655
a
.463
a
a
t
3 .650
2.690
s
,
541
a
a 1 .630
a 1 .095
t
(Sheet 3 of 6 )
F
d
Table
10.-Data from testsof stiffened plywood panels with face grain perpendicular to stress (continued )
Stiffener
Depth
(d)
s
(P)
a
(1)
s
(2)
a
Inch
t -
ai .
a
.751
.500
I
a
a
a
.249 a
.189 a
.125 a
.062 a
.000
a
,1
1.003
.752
.505
.251
.189
.125
.000
.621
.502
.372
.251
.165
.123
.000
1
a
s
a
a
a
a
s
a
t
a
a
a
a
a
a
-123
-80
-59
-33
-18
-6
-2
0
critical Iced
(1)
(3)
1a
1 .000
Ad
bet critical ■trees
s
a
(Fcr)
a
a.
E2121.2
Y
9 994 4•
3
,
A
4
935
940
890
830
775
650
425
300
t
!
1
1
1
a
a
8
a:
i;
a
:
a
a
4
&677
'
271 7
3
2693
5
6
631
953
2 50
1
1,600
-6
1
1
1
.a
a
1,380
1,130
890
66o
315
-34
-10
0
1,540
1
-88
-41
-32
-20
-6
-4 '
0
a
t
a
1
t
s
a
a
1 .190
1,125
1 .075
1,000
775
54 5
320
•
a
a
a
~
=
t
.1
1
a
a
4
4
a
a
e
a
a
a -
t
t
1'
s
a
1
a
a
1 .740
1 .550
1,370
1 .340
890
670
335
s
1, 1470
1
s
1
4
t
1
s
a
1
1
1
a
21 .070
1 .112
1 .005
870
701
516
250
s
0.42246
.30351
.18709
.07893
.05569
.03300
.01384
a
a
s
s
77 6
2727
271 1
702
6600 1
50
31
2 58
a
s
106
,f
1,180 2w5
1,400
i'
-4+5
409
1 .280
a
994
31 7
t
2436
170_
t
440
1
142
a
(6)
Coordinates
(x)
a
(Y )
a
(7)
(E)
a
.02305
t
s
a
e
a
I
2zh-2- 2
4
'/
I
a
t
S
s
s
a
a
a
=.
1
s
I
44 .807
21,077
7 .656
1,607
919
424
130
149,943
23,1477
8 .770
1,859
1,054
488
2
04002
a
a
.275
31
'5
10348
.06067
_
t
is
07694
.05514
03269
4
1
18778
.30190
.19326
13263
09867
.07769
.05725
. 03695
.01127
2zM1-2
1462
2452
41
413
282
210
a
.42147
221x3-4
a
4
a
a.
*
22h.2-4
84
-870
2
283 7
786
617
434
25 7
(81 8 )
a
22x•3- 4
-251
-138
-114
-79
. 739 t
.495 a -142
-23
.373 a
-17
.309 a
.250 a
-10
. 179 : +1
.126 s
-2
0
.000 a
x
Report No . 1553- 3
z
(5)
Stiffness
t
a
221-4
a -263
.500 i
.22
54 s 124
-11
.190 a
-38
130
t
0
.
.068 a
-6
0
.000
e
1 .000
Shift of ate - neutral axis
(Zn]
a
s
,
(4)
1
1,050
73g
a
1
-14
s
970
. 372
5 i 940 a
. 312
.4
e -36 a 920
.250 1
a
- -4
64o
t
1
.075 a
.182
-2
1
400
a
.000 a
0
s
325
7
.1
.613
. 1462
Stiffener effec t
Plate
lased- , Groan
.36111
.24783
.14840
.06016
.01084
.02481
.01097
a
10, 1463
a
6,350
3 .224
a
,
739
336
s
t
t
t
s
a
,
s
t
,
t
a •
a
a
a
a
a
t
s
a
a
1 .381
9 .8314
5>l~
3,134
2,132
1 .329
692
134,
81,556
39 .581
15.991
3 .818
2,166
1,080
372
.11131
.07414
.05654
.04172
.02599
. 01602
a
s
a
s
a
a 0 .98 1
a 1 .054
a
,
s
18 .810
, 10 .460
a 4 .760
a 1 .302
s .794
a .399
a
a
,
a
t
.950
68 3
• 7
1
--------- -
a 1 .007
a 1 .0 5
a
a
a
s
a
a
a
a 8 .300
a
a 5.460
s 3 .050
t 1 .443
824
,
a .393
1 .010
93
.77 7
. 579
. 357
a 1 .030
a 1 .007
a •959
s
881
, .61 9
a
.31 5
a
a
s
s 9,860
+ 5.560
s 3 .7120
s 2.6650
a 1 .740
s .960
a .204
s
a
,
a
a
a
a
a
a 18.700
1 9.950
a 4.430
a 1 .180
, .692
a .355
a .127
a
a
, 1 .012
a 1 .012
a .968
a .910
a .860
:
a
a
1 .066
979
946
932
906
.5142
.144
.500
.297
a
a
.19621
, 32 . 1400
, 18.100
a 8 .070
s 2 .190
, 1 3 350
, .67
.
a .228
27,368
10 .923
5,829
3 .878
2,479
1 .259
645
s 8.900
a 3 .810
1 2.120
s 1 . 1430
t . 93 4
a .486
a .253
a
a
.990
s
t
a
1 .036
a
:
.572
a
.977
.861
.3d
.2
(Sheet 14 of 6)
'
Table 10 .--Data from tests of stiffened plywood panels with face grain perpendicular to •trees (continued )
Plate
,
Stiffener effec t
Stiffener
t
----------------------- --------------------------------------------------- ------------------------------------------------------------------------- Coordinates
:
Loed
t
Gross
critical
load
:
Net
critical
stress
Shift
of
plate
neutral
axis t Stiffness t
Depth
(EIs)
, (%)
(T )
(d)
t
(P)l
(L)
t
(Zn)
(Per)
°
•---°
---
-•- --- :
(8 )
(2)
t
t
(6)
:
(7)
t
(1)
:
(3)
t
(4)
(5)
:
Inch
1
pound'
,
p s .i .
t
Eh,
s
t
2:A-3-2
0 .32194
1
62 .327
1 .016
0.967 t -137
,
1,325
,
X379
t
s 23 .400
1,400
9
s
23170
,
34,103
s 14 .089 , 1 .14 2
752 , -117
t
t
2
.500 t
-87
:
1,200
1
t
13303
t
13 .450
t 6.170
, .913
55
3 .460
4
1 .016
374 t
-64
s
1 .250
t
08987
t
7,132
t
378
4,856
2.430
1 .020
.312 ,
t
1,240
t
t
-52
379
.06999
05270
, 1.6 5 ,
9012
.2514 1
-26
:
1,130
,
3 .179
g3
-18
t
850
t
~
t
03566
1,806
t
.960
,
.515
.191 ,
511
t
.285 s .280
.095 i
-2
t
680
u6
,
.01412
0
500
16o
000 e
t
t
•
2xc2-1- 2
.613
.1496
.439
.372
313
.252
.190
ass
.000
s
t
,
,
t
t
2
,
-44
-3 2
-16
-11
+2
-4
-1
0
0
1
1
t
:
,
t
,
t
,
:
1,400
1,390
1,350
1,220
1 .050
830
650
500
450
t
t
t
t
,
,
4,29
2430
-422
383
333
262
206
158
143
.11730
4
t
:
a
t
,
03525
.07088
0 518
04254
03077
02032
t
t
,
1
s
1
.00697
,
13,865
8,1491
6,421
4,415
3,006
1,876
1,038
243
,
,
5.300
3 .330
2.540
t 1.700
i 1 .010
: 1 .010
, .984
s .850
s .676
s .42 7
234
t
.062 5
:
t
t
:
t
t
000
1
.118
:
s
:
,
,
-62
-36
-7
-10
-6
0
0
t
1
t
t
t
s
t
t
1 .470
1,450
1,440
1,160
970
530
350
,
s
2446
2448
21454
,
t
305
t
t
a
t
.188
.127
.000
•737
.599
377
.311
.248
.187
.091
.000
t
,
,
s
s
1
t
3
3
t
t
t
t
a
t
-245
-100
y1
-142
-48
-15
-23
0
-89
-59
-1
-25
-19
-2
-2
1
t
0
t
i
1
1
t
t
t
i
t
t
t
t
1
1
s
t
,
2,260
t
2 .050
1,900
1,550
1,090
720
a
s
t
t
t
s
2,180
2,130
2,280
2,200
2,130
2,170
1,800
1,300
780
675
160
111
t
t
s
t
.181480
.10083
.06812
.05176
.03762
.01326
t
t
t
t
t
t
25 .908
9,871
5 .423
3 .599
2 .256
526
, 7.980
t 3.240
t 1 .830
t
t
t
1.230
750
.190
t
21,125
21,096
-1 2030
993
-1,025
21,017
800
56 9
401
2z5 .2- 6
:
t
,
t
,
s
t
.23062
.17705
12245
. 08753
06779
05011
.03464
01941
3
t
565
3s1
s
313
:
,
t
t
35639
.27382
16257
11300
.06676
.04642
.02812
t
21 .176
1150
,121
1 ,152
956
697
41s
362
t
t
t
1
t
+
t
1
t
21, 4
13 .6127
7 . 412
s
t
1 .876
1 .099
1
i
4,357
2 .94
1
492
t
t
t
t
t
t
a
,
t
.993
.998
1 .01j
75'+
553
.175
14.670
9 .750
t 5.650
3 .470
: 2 . 1410
t
1
1 .560
950
.439
t
t
8
3
t
t
t
:-
.22697
.17380
09265
.07113
.05212
.035 45
.01370
t
t
t
t
t
t
t
t
Report No . 1553-B
7881 72895 F
1
1 .11 1
t 1 .06 8
t
975
t
t
t
t
r
.921
.96 7
. 955
631
277
s
56 .777
28,231
10 .737
5 .782
2 .518
1,470
729
t
2:$•14-6
t
,
t
- .8- .12k
g
21,067
-1,102
21,101
21,064
981
, . :
,
t
,
.762 ,
-64
i
2,175
3
.626 :
-39
s
2,090
-412
478 t
t
t
-.21
t
t
. 375
.11''
312 ,
-21
t
144
, 9g93070 5
-26
1 .930
251
,
t
192 t
-17
t
1 . 51t
1,075
.125 t
-10
i
t
.000 1
0
t
750
t
,
t
,
1 .001
.754
.497
374
.249
364
.776
430
.105
1
2x02-2-2
.743
.480
. 373
.309
.245
1.225
t 27 .550
t 15.360
s
:
:
t 6 .580
t 3 .870
1 1 .824
1 .10 7
t3
574
t
20,831
12,888
4,616
3 . 0 70
1,926
1,102
302
t
t 11 .520
t 7 .520
s 2 .950
t 2 .020
t 1 .300
t
.765
, .220
3
57 1
1 .02 2
s 1 .02 0
t
-97 3
t .86 1
,
63 1
t
.28 5
1
•
: 1 .030
t 1 .000
t
.966
s 1 .00 2
.76 2
1
r .440
t
.083
s
(sheet 5 or 6 )
1
Table 10.--Data fromtests of stiffenedplywood panels with facepain perpendicular to stress (oontinued)
Stiffener
Depth
(d)
t
,
(1)
a
a
5
Load(P)
a
s
Plate
Gross critical load s Net critical stress a Shift of plate - neutral as
(L)
(pcr)
s
(Zn)
(2)
a
n , s
a
.1,u nde
1'
,
a
pounds
a
a
0 .624
.496
a
.772
a
.247
s
.168 s
.125 ,
.ooo
a
s
-92
-53
-37
-12
-7
-3
0
a
2,220
2,150
1 .980
1 .530
1 .170
870
550
t
s
s
a
,
a
s
a
a
a
a
,
,
a
a
2+476
X454
463
5497
1477
383
300
215
156
1
1387
2385
2372
-389
356
272
205
140
744
370
.315
.247
.190
.034
000
r
a
a
a
a
,
t
-6
0
-267
-194
-155
-41
-19
-14
+1
0
-71
-38
-32
-5
-10
-5
0
a
s
,
2,150
2,060
2,060
1 .980
1 .630
1 .060
740
21 .145
-1,128
1,046
81
626
467
296
a
a
a
s
a
a
a
a
a
1,460
1 .380
1,300
1,240
1,120
650
630
450
a
s
a
a
s
a
a
1,360
1,280
1,240
1 .150
850
620
525
- 148
-18
-9
-10
-7
0
-1
0
a
a
a
a
a
s
s
(5)
a
,
jgp_
s
a
0 .17786
.13010
.08748
.04956
.03406
.01966
a
a
2
a
a
a
a
s
a
a
a
a
a
s
,
,
a
a
2xc3-2-k
a
a
a
s
s
a
s
a
551p.kl5l
.42461
a
.30 1406
.18994
a
s
•13359
a 08236
s
•05663
a
.03616
a
.01578
s
a
9xc5-2-6
t
a
a
a
a
a
a
s
.46313
.34053
.21903
.10279
.08036
.0517 14
.02719
1,430
1 .250
1 .380
1,250
1 .090
750
520
500
23
-384
5364
267
195
167
s
s
s
a
a
a
s
a
a
a
a
a
a
a
?439
z
as
91
$435
a
394
a
344 a
238
16 5
aa
159
a
s
9xc5-4- 6
a
s
a
a
a
s
a
a
s
a
s
a
a
t
s
$
s
Coordinate s
(8)
,
(Y)
s
(7)
a
a
a
a
a
a
a
a
a
s
a
a
a
s
.18789
a
.12073
a
03046
a
.06319
a
.04539 a
.0256 5
a
.01008
a
a
(8 )
t
s
11 .492
6 .643
3 .647
1 .550
901
421
s 6 .570
a 4.090
a 2.290
, 1 .020
a
.609
.292
a
a 1 .010
a
.993
.696
a
t
.630
11 .913
7 .119
3 .772
2,637
1,678
425
a 7 .770
a 4.890
a 2.740
s 1 .9 4 0
s 1 .260
347
a
t
s
40
.214
t
a
50,575
24,461
9 .694
5 .204
2,405
1 .465
762
276
70,047
33 .289
12 .535
3 .078
2,083
1,105
1136
t 21 .100
t 11 . 1120
, 5.130
a 2.960
s 1 . 1465
s
.969
s
.505
a
.191
s
a
a 1 .036
a 1 .004
s ' .996
a
.954
t
.693
s
.260
...........
s
a 1 .000
s
.9314
a 1 .01 3
a 1 .054
a
.996
a
.71 6
.462
s
s
. 195
a
t
: 31 .100
a 17 .150
a 7 .700
a 2 .340
a 1 .650
s
.942
.427
a
a 1 .009
a 1 .00 3
a
.953
a 1 .020
.692
a
s
. 552
a
.262
a
a
19 .6418
4,319
3 .141
1 .980
1 .236
335
s 14.050
a 3 .660
a 2 .750
s 1 .800
a 1 .16o
s
.333
a
a
a
1 .063
1 .025
.98 2
.89 8
.478
.148
10,1492
5 .084
2,722
1,904
1 .187
546
169
a
a
a
a
a
a
a
a
1 .052
.91 2
1 .07 5
.921
a
27166
11412
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.04929
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a
s
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t
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(6)
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9x25-3-6
a
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a
440
,
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,
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. 210 s
15
s
063
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4,104
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357
559
392
$ Stiffness
s
(NI .)
a
2x03-1-6
1 .745
a
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a
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1,620
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a
, -112
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1,660
,
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a
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1
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a
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Stiffener effect
a
t
1
7 .310
3 .900
2.170
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.73
0
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} compression ; + tension.
2
-These values were used for average p cr2'
Report No . 1553-B
2 M 72896 F
(Sheet 6 of 6)
Table 11 .--Description of plywood constructions used in tes t
specimens
.
Construction : Arrangement
number
Ply
thickness
Species
of
face plies
Species o f
cross band
and core .
Inc h
2
y. 1 :1 :1
9
1 :1 :1
17
: 1 :1 :1 :1 :1
:
:
1/20
: Birc h
1/16
: Sitka
spruce
Sitka
spruc e
1/20'
: Yellowpoplar
: Yellow
popla r
:
Sitk a
spruce
: Sitk a
spruc e
19 .
1 :1 :1 :1 :1
1/48
22
1 :1 :1 :1 :1
1/48
Report No . 1553- B
Birch
: Birch
Yellow poplar
Y
t
E2
b
A
I•
1
1
1 1
i
~I
Figure 20 .--Stiffened three-ply plywood panel in compressio n
with face grain parallel to direction of loading .
g
n
7? ' 9
d0
800
2,400
CRITICAL BUCKLING
LOA D
•
o
2,020
1,60
4200
400
0
O./
0. 2
LATERAL DEFLECT/ON (/NCH)
0
20
40
DIAGONAL STRAINS 000000/ //CH PER &'H)
Figure 24 .--Comparison of typical load-deflection and loaddiagonal-strain curves plotted for the determination of th e
critical buckling load .
,+Z ri 72880 F
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COMPUTED CRITICAL STRESS r PROPORTIONAL-LIMIT STRESS OF MATERIA L
(26
0. 7
Figure 27 .--Comparison of observed critical stress to compute d
critical stress, both expressed as ratios of proportional limit stress of the material .
Z M vG883 r
{
l
SUBJECT LISTS OF PUBLICATIONS ISSUED BY TH E
FOREST PRODUCTS LABORATOR Y
The following are obtainable free on request from the Director, Forest Product s
Laboratory, Madison 5, Wisconsin :
List of publications on
Box and Crate Construction
and Packaging Data
List of publications on
Chemistry of Wood and
Derived Products
List of publications on
Fungus Defects in Forest
Products and Decay in Trees
List of publications on
Glue, Glued Products ,
and Veneer
List of publications on
Growth, Structure, and
Identification of Wood
List of publications on
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Structural Uses of Woo d
and Wood Products
Partial list of publications fo r
Architects, Builders,
Engineers, and Retail
Lumbermen
List of publications on
Fire Protection
List of publications o n
Logging, Milling, and
Utilization of Timbe r
Product s
List of publications on
Pulp and Pape r
List of publications o n
Seasoning of Woo d
List of publications on
Structural Sandwich ,
Plastic Laminates, and
Wood-Base Aircraft
Component s
List of publications on
Wood Finishin g
List of publications o n
Wood Preservation
Partial list of publication s
for Furniture Manufac turers, Woodworker s
and Teachers of Wood shop Practic e
Note : Since Forest Products Laboratory publications are so varied in subject, no single list is issued . Instead a list is made up for eac h
Laboratory division . Twice a year, December 31 and June 30, a
list is made up showing new reports for the previous six months .
This is the only item sent regularly to the Laboratory' s mailing list .
Anyone who has asked for and received the proper subject lists and
who has had his name placed on the mailing list can keep up to dat e
on Forest Products Laboratory publications . Each subject lis t
carries descriptions of all other subject lists .