Supplement to
DUCKLING OF FEAT PLYWOOD PLATES IN
COMPRESSION, SHEAR, OR COMBINED
COMPRESSION AND SHEAR
Effective Width of Thin Plywood Plates at Maximum
Load in Compression With the Face Grain at
0°
,
150,
30°, 45., 60., 75., and uu to Load
laferniatita-Pevfetued-amod-Reaffirms
htardr1/36
I Nii.,! 1?MAT . I REVIEWED
AND REAFFIRMED
1962
No. 1316-1
11111111111111611
LOAN COPY
Please return to:
Wood Engineering
e
Resarch
e
Forest Products Laboratory •
Madison, Wisconsin 53705
FOREST PRODUCTS LABORATORY
UNITED STATES DEPARTMENT OF AGRICULTURE
FOREST SERVICE
MADISON 5 WJSCONSIN Li
Cooperation with the University of Wisconsin
EFFECTIVE WIDTH OF THIN PLYWOOD PLATES AT MAXIMUM LOAD IN COMPRESSION
WITH 'rt3E FACE GRAIN
D1
By
Engineer
A. W. VOSS, Engineer
and
P. F. McKINNON, Engineer
C. B. NORRIS,
Forest Products Laboratory, 2 Forest Service
U. S. Department of Agriculture
Summary
This report presents data on the effective width of plywood plates at maximum
compressive load and curves for the determination of the effective width ratios
of plywood plates under compressive stress at 0°, 15°, 30°, 45°, 6o°, 75°, and
90° to the face grain direction. Values for other angles may be obtained by
interpolation. An effective width ratio curve at the maximum stress is presented, which for the 0° and 90° directions supersedes that shown in figure 90
in Mimeograph 1316-E. The effective width ratio is here defined as the ratio
of the maximum load sustained by a buckled plate to the maximum load it would
have sustained had it been restrained from buckling.
Purpose
A theoretical analysis and formulas for the critical buckling stresses of flat
plywood plates subjected to compression, shear, and combined compression and
shear were presented in Forest Products Laboratory Mimeographs Nos. 1316 and
1316-C. Applicability of the formula, p = k E h for the critical buckling
cL a
cr
1
–This report is one of a series of progress reports prepared by the Forest
Products Laboratory relating to the use of wood in aircraft. Results here
reported are preliminary and may be revised as additional data become available. Original report issued March 1945.
2
—Maintained at Madison, Wis., in cooperation with the University of Wisconsin.
Rept. No. 1316-I -1-
Agriculture-Madison
stress in compression at 0° or 90° to the face grain direction was verified by
test (Mimeograph No. 1316-D). The same specimens were used also for the determination of maximum loads and effective width ratios (Mimeograph No. 1316-E).
Buckling tests with compression at 15°, 30°, 45°, 60°, and 75° to the face grain
demonstrated that modification of k c was necessary to adapt the formula to such
angles. Data and correction curves are given in Mimeograph No. 1316-G. The
purpose of the present study was to determine an effective width curve, or
family of curves, from a further analysis of the data reported in Mimeographs
Nos. 1316-D, 1316-E, and 1316-G, together with the necessary additional data.
Material
A detailed description of the material used in this study is given in Mimeographs Nos. 1316-D and 1316-G.
Approximately half of the plates subjected to buckling tests were damaged to
such an extent that it was impossible to obtain representative material from
them for supplementary compression tests. It was possible to select coupons
for the supplementary compression tests of the material from the plates that
were damaged over a limited area only. Consequently, only the data from such
plates are available for the present study of effective widths.
Because the plywood was thin, two or more pieces were taken from each acceptable
plate and glued face to face with cold-setting urea-resin glue to make a specimen of such thickness that buckling was avoided during the compression test.
In table 27 there are listed for each plate the number of pieces used to make
compression test coupons.•
Coupons 6 inches wide and 2 inches or less in height for supplementary tests
with compression at 0°, 15°, 30°, 45°, 60°, 75°, and 90° to the direction of
face grain were stressed in the direction parallel to the height with the face
grain at the same angle to the load as in the buckling test. The height of
these coupons was made approximately six times the thickness to prevent buckling or column failure before failure occurred in compression. The width was
made 6 inches in all specimens to facilitate testing. It would have been
preferable to have coupons the same width as the plates tested in buckling,
but this could not be done because the edges of the plates, which varied in
width from 7-1/2 to 12 inches for 0° and 90°, and were all 9-1/2 inches wide
for other angles, were damaged in the buckling test. The maximum compressive
strength as found from coupons 6 inches wide should reasonably represent the
maximum stresses that the plates would have sustained had they been restrained
from buckling.
The figures and tables in this supplement are numbered consecutively with those
of Mimeograph No. 1316 and its supplements, B, C, D, E, F, G, and H.
Rept. No. 1316-I
-2-
Methods of Tests
The data required for the determination of the effective width ratio for each
plate included: (1) the maximum load and (2) the compressive strength of the
material.
The first item was supplied by the tests for maximum load made previously on
the plates used for study of the critical buckling load.
To determine the compressive strength, glued coupons, as described previously,
were tested according to the procedure given in Mimeograph No. 1328-A. In the
0° and 90° angles, tests were also made on coupons of the same thickness as the
plates but 1 inch wide and 4 inches high with support to prevent lateral buckling under load, as described in Mimeograph No. 1316-D. Both methods for determining the compressive strength were used because it was expected that the
laterally supported column method might be made standard for 0° and 90°.
The maximum stresses obtained for 0° and 90° average some 15 percent higher by
the method of Mimeograph No. 1328-A than by the laterally supported column procedure.
The discrepancy may be due to several factors. It has been observed in the
laterally supported column compression test that material less than 1/8 inch
in thickness generally fails in compression and bending between the end surface
of the specimen and the lateral supports. This type of failure may be due to
some unrecognized excentricity of loading, to a slight bending of the specimen,
or to yielding of the spring steel lateral supports. Nevertheless, the maximum
stresses averaged no less than the average maximum stresses obtained in tests
of matched specimens by the same method but with ends widened to force failure
in the central portion. Ends intentionally cut poorly, however, produced low
values. Tests of short, wide plywood specimens in compression at 0° and 90° to
the face grain were not extensively studied. It was noted that at failure such
specimens bulged and occasionally delaminated. The factors causing the discrepancy between the two methods of test were not determined.
Explanations of Tables and Curves
The data from the buckling tests and compression tests pertaining to the effective width of flat plywood plates in compression at 15°, 30°, 45°, 60°, and
75° to the direction of the face grain, are presented in table 27, together
with the computed values used as coordinates in figures 142, 143, and 144.
In this table, column 1 identifies each plate and indicates the direction of
the face grain of the plate in relation to the loaded edges of the plate.
Column 2 gives the effective width ratios, which are used for ordinates, and
Rept. No. 1316-I
-3-
a
column 3 gives the parameters of panel width (g--) which are used for abscissas
O
in plotting the data on figures 142, 143, and 144. In column 4 is. given the
computed maximum load for the plate if restrained from buckling. The observed
maximum load and the critical buckling load determined in the buckling test of
the plates are given in columns 5 and 6.
Results of the supplementary compression tests of coupons taken from the plates
after the buckling tests were completed are tabulated in columns 7 through 12.
The maximum stress, proportional limit stress, number of thicknesses used to
fabricate the compression test specimen from the plate, specific gravity based
on volume at test, moisture content based on ovendry weight, and the modulus
of elasticity in compression are given respectively in columns 7, 8, 9, 10, 11,
and 12. These compression test coupons were 6 inches wide and 2 inches, or
less, high (short enough to eliminate buckling).
In table 28 are presented data from Forest Products Laboratory Mimeographs No.
1316-D, "Buckling of Flat Plywood Plates in Compression with Face Grain at 0°
and 90° to Load," and No. 1316-E, "Effective Width of Thin Plywood Plates in
Compression with the Face Grain at 0° and 90° to Load," and the parameter of
panel width ()
–a– computed from these data. The table is divided vertically
ao
to group the data for plates in compression parallel to face grain and perpendicular to face grain.
The material used for the tests is identified by the panel number tabulated in
column 1 (refer to Mimeograph No. 1316-D). Effective width ratios from Mimeograph No. 1316-E were used as ordinates in figures 145 and 146 and are tabulated
in columns 2 and 6. The computed parameters of panel width (E741–.) were used as
abscissas in figures 145 and 146 and are given in columns 3 and 7. Computations
for these parameters were based on the observed critical buckling stresses from
Mimeograph No. 1316-D tabulated in columns 4 and 8 and the average maximum
stresses shown in columns 5 and 9 obtained by compression tests of coupons 1
inch wide by 4 inches long reported in Mimeograph No. 1316-D.
In table 29 is given a comparison of the maximum stresses in compression at 0°
and 90° to the face grain obtained by a short column test method described in
Mimeograph No. 1328-A and the maximum stresses obtained by the laterally supported column test and reported in Mimeograph No. 1316-D. The first column
gives the panel number that identifies the material. The thickness of the
specimens is tabulated in columns 2 and 5. Maximum stresses are given in
column 3, 4, 6, and 7. The ratio of the stresses obtained by the short column
method to the stresses obtained by the laterally supported column method are
listed in column 8 for compression parallel to the face grain and in column 9
for compression perpendicular to the face grain.
A family of curves for the effective width ratio of flat plywood plates in
compression at 0°, 15°, 30°, 45°, 60°, 75°, and 90° to the direction of face
grain are presented in figure 141. These curves are based on buckling tests
Rept. No. 1316-I
-4-
of flat plates and compression tests of material matched to the plates. The
supplementary compression tests with the stress at 0° and 90° to the face grain
were made on 1- by 4-inch coupons laterally supported against buckling. Compression tests with the stress at the intermediate angles were made on 6- by
2-inch (or less) coupons that were short enough to eliminate buckling before
failure in compression. The dashed curves are based on a small amount of data
that do not definitely locate the curves.
Figures 142, 143, and 144 show, respectively, the appropriate curve from figure
141 compared with the test results for the angles 75° and 15°, 60° and 30°, and
45°.
Figure 145 shows the curve from figure 141 and the test data for compression at
0° and 90° to the direction of the face grain.
Figure 146 shows the curve from figure 141 for compression at 0° and 90° to the
direction of the face grain and the effect of changing the basis for computations
from the maximum stresses obtained by the laterally supported column compression
test to the maximum stresses obtained by the short column test (table 29):
Analysis of Results
The effective width ratio is defined as the ratio of the maximum load sustained
by a buckled plate to the maximum load it would have sustained had it been restrained from buckling. It is computed from the maximum load observed in the
buckling test and the ultimate stress obtained in the compression test of the
material.
The maximum loads obtained in the buckling tests of plates apply only for the
precise edge and end conditions existing during the test. These conditions,
which approximated hinged edges, are shown in detail in figures 74 and 75 of
Mimeograph No. 1316-D. Variation in these conditions between one test and another may cause variation in values of the effective width ratios obtained.
The ultimate stresses obtained in the compression tests on coupons of the material of the plates were used to compute the maximum load that the plate would
have sustained had it been restrained from buckling.
The effective width ratios used as ordinates of the curves were based on the
buckling tests of plates and laterally supported column compression tests of
matched coupons stressed at 0° or 90° to the direction of the face grain and
compression tests at acute angles to the face grain of 6- by 2-inch (or less)
coupons of the material from the plates.
The abscissa of the curves is a nondimensional parameter of panel width determined as follows:
Rept. No. 1316-I
-5-
The critical buckling stress in compression may be computed by the formula:
2
(1)
q =kEh cr c L —87
The width of a plate in compression theoretically may be adjusted so that the
buckling stress and the ultimate stress are the same. The symbol a 0 is used
for this width and the formula becomes:
2
(2)
Fcu = k c EL 12--
2
a
0
Dividing equation (2) by equation (1) and taking the square root, the following
is obtained:
F (3)
= cu
a
a or
o
The constant k c is used in both (2) and (3) to allow for the specific edge and
end conditons that occur, as well as the properties and dimensions of the plate,
but cancels out of formula (3). Abscissas of the points plotted were based on
the maximum stresses from compression tests of the material and athe critical
buckling stresses observed in the buckling tests. The ratio (7.(7 ) is therefore
a parameter of panel width that does not depend on the edge or end conditions of
the plate, except as these conditions enter the experimentally determined critical stress q
-cr.
Sufficient data were obtained to locate the curves for compression at 0°, 45°,
and 90° to the direction of face grain. If the material were such that the proportional limit in compression conincided with the ultimate stress and if it
were perfectly uniform in strength properties and perfectly flat at the start
of test, the curves would go through the point 1, 1. Experimental curves, however, will not pass through this point.
Data obtained for compression at 15°, 30 0 , 60°, and 75° to the direction of face
grain indicate the approximate location of these curves but are insufficient to
define them. It was assumed that the relative location of these curves between
the curves for compression at 0° and 90° and at 45° does not change throughout
their length. Because there is insufficient data to substantiate the entire
curves for compression at 15°, 30°, 60°, and 75° to the face grain, they are
shown with a broken line in figure 141.
The curve for effective width at 0° and 90° and the effect of the compression
test data on several of the points used to draw this effective-width curve are
shown in figure 146. Each point based on 1- by 4-inch coupons is shown connected with the, corresponding point based on 6- by 2-inch coupons. Because the
maximum compressive stress (F cu ) determined by test of coupons appears in the
Rept. No. 1316-I
-6-
ordinate,
F
c eff., and in the abscissa,
cal, changing the maximum stress moves
Pcr
-2
the points along the hyperbola (y = ax ) where (a) is a factor depending on the
critical buckling stress and the maximum stress observed in the buckling test
for each point in question.
Cu
The effective width curve is not a hyperbola, but it is sufficiently similar to
one in the range where data were obtained so that small changes in the value of
the maximum stress would not appreciably alter the effective width curve given.
Conclusions
The curves presented in figure 141 may be used to determine the effective width
at maximum stress in compression at 0°, 15°, 50 0 1 45°, 60°, 75°, and 90° to the
face grain of a plywood plate with its edges and ends approximately freely supported in a plane, providing the critical buckling stress of the plate is com2
puted in accordance with the formula p = k E L — as presented in Mimeograph
C LI h2
Cr
a
Nos. 1316 and 1316-G, and providing the maximum stress is determined for the material considered. This curve is probably sufficiently accurate for edge conditions other than freely supported if these edge conditions are taken into account in computing the critical stress and therefore the values of 22=
80
The common compression formulas are applicable for computing loads, stresses,
or strains before buckling occurs. After buckling occurs a portion of the plate
may be considered to carry the load. It is evident that this portion is a maximum when buckling starts and decreases as buckling progresses. The portion, effective width ratio, at ultimate stress is therefore conservative for lower
stresses.
Further study is necessary to establish accurately the effective width ratios at
the proportional limit stress and at other stresses between the critical buckling stress and maximum stress. Such determinations are not simple because of
the complicated stress distribution in a plate of orthotropic material after
buckling has occurred in compression at an angle other than 0° or 90° to the
principal axes. Further study would involve mathematical analyses and the development of new and more complicated testing techniques.
Rept. No. 1316-I -7-
.2-19
Table 27.--Observed and computed values obtained from the buckling test of flat plywood plates and tile
teat of 6- 7.1.' 2-inch ootiaonm in com pression at 15°. 30°, 45 . . 60 • end 75* to the direction
2g_11Et_Erain
:
.
.
.
.
Compression test results
Plate :Effective:Parameter:Computed: Observed results of : : width :of panel :maximum : buckling teats
No.
:Maximum:Proportional:Number
of :Specific:Moisture: Modulus of
: ratio : width :load for: .gravity :content : elasticity
: plate
limit
: stress:
: plate :Maximum : Critical
a
Fe eff :
.
:thicknesses:
stress
:
:buckling load:
: load
ae
:
.
.
•.
: Feu
(1)
:
(2)
:
(3)
(4)
:
:
(5)
:
, • Pounds : Pounds :
(6)
Pounds
(7)
:
:
: 111 :
(8)
:
(9)
:
(10)
Pei
(12)
: (11) :
s
:Percent : 1,000 psi
Specimens tested with face grain direction at 15° to loaded edge (75° to compressive stress)
900
1 6,321 : 2.108 :
3 q . 15n : 0.333 : 2.65
800
: 4,527 : 1,820 :
64 - 15n :
.402 : 2.38
bal.
:
3,578
:
1,614
:
g q - 15 0 :
2.44
.451 :
0:
1,000
: 5.894 : 2,320 :
12q - 15 • :
.394 : 2.43
2,950
: 9,922 : 4.728 :
.477 : 1.83
14q - 15 . :
5,400
:13.751 : b,230 : .453 : 1.60 159 - 15°:
2,-,00
;
7.173
:
3,470
:
17q - 15°:
.454 : 1.69
2,800
:10,261 : 4,170 :
20q - 155 :
.406 : 1.91
:11,778 : 6.100 :
5.901
21q
15 • :
.518 ; 1.41
3,300
4.040 1
; 7,694
.525 : 1.53
23q - 15 6 :
4,200
9,050
:
4,9610
:
1
24q . 150 :
. 48 : 1.47
: 3.980 :
: 2,630:
: 2,58
: 3.390:
: 4.430 :
: 4.620 1
: 3,120 :
: 4,40%) 1
: 4,030:
: 3,450 :
; 3.120 :
2
1,420
1.580
1,360
1,830
1,929
2.580
1,290
2.140
2.260
2.110
2.04D
2
: 0.654 : 9.1
.440 : 9.6
:
616
435
585
562
1
862
:
:
766
26
:
830
2
.430 : 9.2
.560 : 8.9
.596 : 8.8
.624 : 8.6
. 436 : 8.2
: . 4 99 : 7.6
: .470. ; 7.6
:
691
22
: .g[10'0
: 9.8 !
5
51786
3
2
2
2
2
2
:
:
:
:
:
:
;
:
:
Sp ecimens tested with face grain direction at 30° to loaded edge (60° to compressive stress)
.319 : 2.44
3p - 30':
3m . 30':
.330 : 2.31
.356 : 2.06
bp - 30':
Em - 30':
.341 : 2.15
12o - 30 6 :.360 : 2.00
444 1 1.66
15p - 30 6 :
.569 : 1.44
21p - 30 6 :
.365 : 1.65
24p - 30 6 :
; 8,009 : 2,555 •
: 7,996 : 2.635 :
: 4.884 : 1,740 :
: 5,541 : 1,890 :
: 6.201 : 2,230 :
:14,080 : 6,249 :
:10.107 : 5.750 :
: 9,302 : 3,390 :
1,350
1,500
1,150
1,200
1.550
5,100
4,90o
3,400
: 4,840 :
: 4,620 :
: 2,850 :
: 3,170 :
• 3,540 :
: 4,930 :
: 3,410 :
: 3,200 :
2
2
2
2
2
2
2
2
2,180
2,350
1,100
1.640
1.720
2,200
1.520
1,440
9.4
9.6
9.7
9.3
9.4
8.6
7.4
: 8.8
:
•
:
703
648
504
500
543
638
510
461
: 0.566 : 10.3
: .599 : 9.5
: .628 : 9.2
: .630 : 9.5
: .658 : 9.2
: .445 : 10.3
: .459 : 10.
: .468 ; 9.6
: .560 : 10.1
: .592 • 9.5
: .536 : 9.8
: .578 : 9.5
: .562 1 9.2
: .586 : 8.8
: .564 : 8.8
• .556 : 9.3
: .623 : 9.2
: .434 : 9.7
: .402 : 8.8
: .452 : 9.0
: .448 : 8.3
: .494 : 9.0
: .534 9.5
: .532 : 9.5
: .494 : 9.2
: .568 : 9.1
: .586 : 9.5
: .586 ; 8.8
: .504 ; 8.7
: .442 ; 7.9
: .510 : 8.7
: .506 : 8.3
: .507 : 8.9
:
:
764
612
: 0.640
: .620
: .438
: .481
: .554
: .613
: .485
: .482
:
:
:
•
:
4
Specimens tested with face grain direction at 49° to loaded edge
lr - 45 • :
2e - 45 . :
3e - 45 6 :
3f . 45n 1
3r - 450 :
4r - 45':
Ors- 45':
6r - 45':
lOr - 45 . :
llr - 45':
12r - 45 0 :
13d . 45. :
lje - 45 6 :
14d - 450 :
140 - 45':
14f . 45 . :
15r . 456 :
16r - 45• :
17d . 45°:
18r n 45 5 :
20d - 45 • :
23d - 45 • :
23e . 456 :
23r . 456 :
24r - 45':
25e - 45 . :
25f - 45':
27d - 45 . :
29f - 45':
j2e - 45':
35d . 45 • :
35e . 45. :
35f - 45 • :
3m .. 60 . :
5P - 60 6 :
6p . 60':
6m - 606 :
.
.130 : 6.50
.210 : 3.05
.274
2.33
.254 : 2.50
.276 : 2.60
.130 : 5.21
.133 : 4.41
.331 : 2.32
.165 : 4.92
.269 : 2.95
.377 : 2.24
.234 : 3.80
.232 t 3.34
.427 : 1.59
.488 : 1.52
.452 : 1.48
.544 : 1.53
.252 : 3.54
.479 : 1.57
.577 : 1.45
.462 : 1.54
.424 : 1.53
.482 : 1.52
.476 : 1.52
.537 : 1.55
.247 : 3.27
t
.230 : 3.25
.457 : 1.48
.479 : 1.51
.530 : 1.40
.470 : 1.46
.476 : 1.65
.455 : 1.51
410 :
: 3,161 ;
: 6,300 : 1.320 :
: 8,405 : 2,304 :
: 8,991 : 2,288 :
: 8,368 : 2,310 :
300 :
: 2,308 1
325 :
1 2,436 :
: 5,1 2 7 : 1.695 •
500 :
: 3.0V, :
: 6,449 : 1,736 : : 6,506 : 2,450 :
: 6.117 : 1,430 :
: 5,875 ; 1,364 : :11,648 : 4.970 :
;10.0 6 ! 5,180 :
: 9,901 : 4,475 :
:14,116 : 7.675 :
992 :
: 3,940 :
: 7.152 : 3,425 :
: 8,846 : 5,100 :
: 8,824 : 4,075 :
: 8,428 3.575 :
: 8.577 : 4,130 :
: 9,253 : 4,405 : : 9,865 : 5.300 :
• 5,788 : 1,428 :
: 5,801 : 1,333 •
:12.994 : 5.940 :
: 7.166 : 3,430 :
: 7,815 : 4,140 :
: 8,101 ; 3,808 1
: 9.241 : 4,40o :
: 8.397 : 3,820 :
75
675
1.550
1,440
1,240
85
125
950
125
740
1,300
425
525
4.630
4,600
4,500
6.000
315
2,900
4,200
3.700
3,600
3,700
4,000
4,100
540
550
5,900
3,150
4,000
3,800
3,400
3,700
: 5,260:
: 4,610 :
; 4,840 :
: 5,200 :
: 5,140.
: 3,670 :
: 3,990: : 2,940.
: 5,040 :
: 4,630 :
1 3,690 :
: 5.860 :
; 5,680 /
: 4,890 :
: 4,520.
I 4,140 :
: 4,910.
: 3,950 :
: 3.140 :
: 3.080 :
1 3,940.
1 3,670:
1 3,750 :
i 4,000 :
4
t
:
:
:
3,390:
5,440 1
5,546 :
4,480 :
3,210 :
1 3,410 :
; 3,520 :
: 4,070 :
1 3,660:
2.340
2.290
2,030
2,190
2,110
1,680
1,460
1,710
2,420
2,500
1.340
3,110
2,760
3,040
2,520
1.890
2.490
1.680
960
1,020
2,480
1,370
2,140
2,300
2,060
2,390
2,570
2,590
2,020
1.720
1,580
1,820
2,080
;
4
4
3
2
2
2
4
4
2
4
3
2
4
4
2
2
2
2
4
2
2
2
2
2
2
2
4
4
2
2
2
2
2
2
Sp ecimens tested with face grain direction at 60' to loaded edge (30 . to compressive stress)
: .617 : 9.3
2
:
2,170
1,850
: 4.930 :
: 8,796 : 3,090 :
.351 : 2.18
: .470 : 8.5
3
:
1.690
: 3,480 :
590
: 4,784 : 1,263 :
.264 : 2.85
: .484 : 8.9
2
:
1.680
1,500
: 3,730 •
: 6,400 : 2,243 :
.351 : 2.07
: .474 : 8.8
2
:
:
3,480.
1.730
1,300
: 6.116 : 2,215 :
.362 : 2.17
.
.
.
.
.
.
.
.
(Continued)
z 4 59515 F
:
772
:
:
.
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
797
614
610
514
330
721
618
548
690
700
602
657
600
594
566
412
688
:
:
:
554
536
421
512
385
790
685
538
376
538
404
553
489
:
:
:
:
566
430
457
458
:
Table 27.-- Observed and qomputed values obtained from ths hocklipm test of flat pl ywood plates add the
test of 6- by coupons in compressto p at 15 . .. ID . . 45 • . 60 • MO 75• to the direction
face grain (Cmntinned)
tf
Plate :Nffective:Paremet•r:Computod: Observed results of :
Compression test results
Mo.
: width :of panel :maximum:: buckling tests
ratio : width :load for: :Maximum:Proportional:Number of :Specific:Moisture: Modulus of
A
: gravity:content : elasticity
: plate elnsximism 3 Critical : stress: limit : plate
• !sults :
:
: load
:
stress
:thicknesses:
:buckling load:
:
ao
:
:
:
1
:
P on
:
•
•
.
(1 )
:
(2) :
(3)
:
:
'
: (4)
:
:
Itgag
l
:
•
(5)
:
(6)
hags : 2=41
•
:
:
(7) :
(8)
:
:
: hi :
at
:
:
(9)
:
(10)
-:
:
:
(11) :
(12)
:Percent : 1.000 psi
Specimens 'tested with face grain direction at 60 • to loaded edge (30 • to compressive stress) (continued)
7p . 60• :
9p - 60• :
9m . 60• :
12p .
12m •
13p •
14m 15p .
17w 18p 19p ...
2I0 •
22p •
22m •
0.140
.453
.400
60• : .313
60•:
.340
60• :
.197
60• :
.469
60' :
.438
.480
60• :
60• :
.611
60 • :
.231
60• : .520
60.4 : .238
60• 1 .233
1
4.59
: 2.943
:
:
:
:
:
:
:
2.06
2.06
2.55
2.22
4.11
1.80
: 6,398
: 6,05
: 6,46
:
:
1.N
1.
3
3.54
:11,725
:16.605
t 8,010
: 9.446
3 5,002
1.61
3
3.85
: 5,321
: 5,186
:
:
:
1.64
3.60
i 6,877
: 6,746
9.087
: 412
: 2,900
: 2:600
: 2,660
: 2,340
:1.332
: 5,500
: 7,280
: 3,840
: 5,770
: 1.155
: 4,725
1 1,266
: 1.210
:
:
:
:
:
:
:
240
1.500
1,530
1,300
1,400
400
3,600
:
6,200
2,400
:
4,000
:
:
:
400
3,50
360
:
:
: 4,850.
: 3,590 •
; 3,650 :
; 4,860 :
: 3,900 :
: 7,040.
: 5,100.
: 5,800 •
: 3,400 :
1
.260:
: 4,880:
: 3,920:
: 5.340:
: 5,300 :
2,860
2,070
2,050
2,100
1,980
3,680
1,940
2,330
1,500
;
1,920
1,800
2,260
2.330
:
:
2
:
:
:
2
:
2
:
2
4
:
s
2
:
4
4
:
:
1
:
:
9.2
:
802
.496
.506
.514
: 7.9
s 9.4
s 7.1
:
:
:
888
:
:
:
4
t
.470
: 0.489
2
2
2
2
t
t
1.320
680
670
708
768
771
1.037
616
896
504
518
4
: 10.4
: 8.0
.51
: 8.2
.582 : 9.4
: 9. 4
..gZg : 9.8
.608 : 8.9
.608 : 8.7
.440 : 8.9
.453 : 9.0
.49
:
:
:
:
.
:
2
:
664
723
8pecimene tooted with face /cram direction et 7_5' to loaded edge (15. to compressive strove)
3n . 75• s
5n . 75' :
64 • 75• :
6a:1 -. 754 :
.259
:
2.82
:12,647
.259
:
i
3.41
:
lln - 75• :
12q • 75' :
14n a 75! :
15q • 75 • :
.239
:
.288
t
: 7, 2
8
: 8,764
:10.507
16q • 75 8 :
1 79 n 75
75e' :
.207
• 96
2.84
2.77
3.21
3.02
2.00
1.81
3.97
1:g
i 9:465
19q -.75•
20n • 75 •
22q . 75•
23n . 75 •
:
:
I.
:
.223
:
4.40
.435
I
1.69
.219
s
3.98
.469
:
1.71
: 5,811
:11,459
: 5,552
:11,639
Z h 52518
r
17n 4,
•313
. 266
.406 :
.436 8
.a 52
:
:
3
6,3114
:15,173
318,346
: 4,894
:10,103
I 1,077
: 1,600
2
: .610 : 9.5
: 7,130: 3,020
: 4,460 : 2,800
1 576
550
: .3p s 8.2
3
:
900
: 4,160. 1,460
:2,266 :
2
0 9.
,
5
:
: .419
: 2,2
90
:
: 2.370
4,7
2
1 0. : 9.1
! 1,205
: .594 : 8.4 :
870
3
: 2,092 :
850
: 6,220 : 2,560
2
1 .554 : 8.2 1 802
1,150
s 6.090: 2,530
: 3,030 :
6.155 : 3,800
: 6,600: 2,960
: .622 : 9.2 r 1,154
2
: 6.560 : 2,950
2
:.635 : 8.9
1 1,281
5,600
: 8,010 :
• 1,014 :
310
: 4,770 : 2.170
921
4
1 .434 : 9.9 :
: 952
t 4,350: 2,690
.434 : 8.4
2,800
2
3
1 4.000 1
i 4,285 4 2,800
: 4,050: 1,870
2
1 .442 : 8.6
;
780
4
: .482 : 9.1
: 1,470
: 1,294 :
300
t 5,670 : 3,290
: 4,985 :
: 4,130 : 2,94o
842
3,200
2
1 .487 : 7.6 :
4
1 .500 : 9.4
: 1,384
: 5,680 : 2,700
: 1,327 :
350
1 4.940 : 2.200
2
: .518 1 9.5
: 5,460 : 4,00
:
934
: 3,285
: 1. 653
Table 28.-- Computed values and data from Forest Products laborator y Mimeos.
No. 1316-.0 and No. 1316-1 partlaent to the effective width of
plywood plates in compression at O e and 90 • to direction of face
'rain
: Compression perpendicular to face grain
Compression parallel to face grain
: :
Panel : No. : Effective : Parameter : Observed : Average : Effective : Parameter : Observed : Average
: width : of panel : critical : maximum : width : of panel : critical : maximum
: stress : stress
ratio
:
width
:
: stress a stress
width
:
ratio
: (1" x 4"
:
a
: (1" x 4" : re eff
•.
a
: fa_211._ : : coupons
coupons)
: coupons) : Or )
:
ao
ao
.
curb
:
•
(P ada
lc
2c
3a
3b
4a
14a
15c
16a
17c
l8a
l8b
18c
(1)
(2)
:
:
(5)
:
Psi.
:
bi :
4.44
:
230
:
.
185: 5,140
181
: 4,760
497
• 5.710
596
• 5,780
473
•: 5.580
791
: 5,030
0.289
.286
.309
:
5.27
5.13
2a :
.340
:
3.39
:
2b :
:
:
:
30 :
:
.384
.400
.
3.11
:
4b
4c
5a
5b
5c
6a
6b
:
:
:
3.43
:
:
:
2.52
2.27
2.50
6.52
:
: 1,012
:
SOO:
:
104
:
:
:
143
:
:
123
:
451
:
:
:
682
:
:
.246
5.69
6.28
3.43
a
:
(g )
:
(9)
:
Psi.
:
Psi.
3.29
:
273
:
4.02
:
204
2,960
3,300
3.99
2.99
:
:
230
360
3.670
3,220
(7)
b
: 4,540
:
.406
(6)
(4)
la :
lb :
:
.472
.422
.271
.279
.
:
(3)
5.230
• :
:
:
:
0.351
.348
.305
.339
:
:
:
:
:
:
.291
:
3.02
:
394
3,580
.361
:
2.56
:
357
2,910
5.000
4,420
4,620
4,840
•
•
5,320
.320
342
:
:
.400
.382
.440
.394
.343
:
:
:
:
:
4.92
7b :
.230
:
5.42
:
3.06
:
.326
:
500
:
: 4,820
,910
:•
: 3
154
:
3,500
:
145
: 4,740
161
:
7c :
.259
:
5.58
:
8a :
.370
:
2.98
:
.386
.373
.382
:
:
:
3.13
3.40
2.35
:
:
:
.362
.418
.258
:
:
:
2.45
:
.240
.337
:
:
2.40
5.30
5.95
3.29
:
:
:
:
3.32
3.34
2.42
2.35
2.4 9
2.90
:
;
:
:
:
:
:
:
6c :
7a :
g b :
8c :
9a :
9b :
9c :
10a ;
10c :
lla :
llb :
.327
.345
.385
11c :
12a :
12b :
12c :
13a :
13b :
.410
.419
:
:
:
:
:
.400
:
13c :
.376
.412
:
:
:
14b :
.616
:
.583
:
.596
.625
:
:
.627
:
.641
:
.335
:
. 337
:
.372
.597
.573
.645
:
:
:
.
.529
.574
.650
:
:
:
14c :
15a :
15b :
a
:
16b :
16c :
17a :
17b :
:
:
:
:
Z 14 59517
r
2.88
2.77
3.11
2.69
3.12
:
.
665
:
:
.338
.319
:
:
3.38
:
4.06
:
442
641
634
635
: 4,330
: 5,350
: 5,150
: 5,120
: 3,560
: 3;810
: 3,660
182
166
: 5,120
: 5,880
554
588
: 6, 7 20
: 6,480
: 6,050
: 5,090
:
:
:
:
.331
.303
:
:
3.54
3.64
.340
.326
:
3.49
3.15
5,200
:
.350
.310
.269
:
a
139
604
527
543
872
944 '
: 5.200
839
579
: 4,880
54g: 5,290
• 5,340
578
: 5,310
2,520
3.11
:
3.04
1.45
1.52
:
:
: 2,518
1.43
1.33
1.42
1.44
3.45
3.38
3.39
:
:
:
:
:
:
.
2,690
2,920
2,638
2,322
1.55
1.44
404
456
424
: 1.636
: 1,609
: 1,678
1.53
1.44
1.38
: 1,765
: 1,979
: 2,059
1.50
5,680
: 5,100
:
:
:
:
:
:
.274
.284
:
:
3.73
3.84
!
.279
.329
.320
:
:
:
3.54
:
.359
:
3.35
3.34
2.94
243
159
299
:
:
:
2,780
2,620
2,800
•
:
226
214
242
187
177
257
.
3,140
3,160
3,040
2,100
1,970
2,220
•
:
.244
.226
1
.4')9
1
2.87
3.15
4.54
4.35
4.16
2.09
243
247
242
318
363
316
174
227
262
923
: 1,042
923
:
:
•.
..
.•
•.
-.
3,050
3,270
2,940
;tg
3,130
4,2140
4.300
4,520
4,010
4.220
.441
.247
2.01
2.00
1.98
1.82
1.82
: 1,127
: 1.257 a 1,2:31
4.68
136
.246
4.70
.261
.478
.397
.409
.464
.440
5.13
136
109
4,180
4,170
2,980
3,000
2,870
570
2,760
: 5,830
.450
: 5,500
: 5,140
: 5.310
: 4,790
: 4,800
: 5,200
: 4,870
: 3,a70
: 3,560
: 3. 460
: 4,120
: 4,050
.487
: 3,940
.472
.1439
. 7
2.21
2.39
2.33
1.92
1.81
1.85
527
556
742
: 1,038
932
(Continued)
3.680
4,440
3,020
3,0?ig
2,7
3,410
3,200
Table 28.--Computed
values
:.nd data from Forest Products Laporatorz_Milleos.
No. 110 -1.1 and No. 1316-E_pertinent to the efiectivs width of
comcression LA 0° and 90° to direction of face
plywood plates
&Etta (Continued)
ratio
: Fc eff
:
.
width
: (11;:5:.
:
:
ao
:
(3)
(1)
(2)
:
a
:
:
stress : stress
: (1" x 4“ :
(4)
ratio
Fe eff :: coupons): (F )
cu b :
.
a
ao
:
(7)
(5) ,:
(6)
Psi.
:
.
266
Psi.
panel : critical : maximum
: stress : stress
width
:
:C10:2:nr)
:
: (9)
Psi.
:
:
(3)
Psi.
4.43
•
.
.
•
795
856
:
:
:
3,520
2,490
2 , 570
2,580
:
770
882
823
-,320
346
:
.3108
3.51
:
:
1404
,•
zM 59618
59618 11
.235
.230
:
:
4.7o
4.55
210
:
4,34o
.
.
.
.
.
.
.
.
.
r4 0
id
w4
1:1
0
0
O 0 9
0 14
a)
O 0
0
4) 42
0
E
ll
O
re
rl
O 0
,03O o C.)o
••n• •••• ,•••• •
-P
42
4• •3
crS
O .10 0
r4
S-4 0
0 .1-)
0
eaft
r-4
0 .0 f.•
r•I
0
.r4
4-a
••-i
4a (D p,
al$4
O 1,1 al
aS
C
li
d
fA
E
O
.
g
c•-•
•-•
4, 0
.0 r.
Cr+ 4-)
K
W I-1
O g
-1.3
.4a 0 tO
aS 0 <E)
4-)
o • g
014 0.1 H
CO re .-4
•• 1 0q
0 14 •i
q
as
0
-P
O 0
to ota
ED
CO 42
O Ad •-•1
I.
-IA al
al
R.
•
K
▪
11
.2
▪
1-•
O
0
.0
▪ '0
0
•••1ea 0 ori
cd
-P
• •.o
.0 0
•
ON
CU
O
rl
••
O 0
.4 0
'd
V
a
E"4
O
o
+2 4) 0
O ;4
(1)
•l P,
alW
......
••
I pi
..
••
gel
0. 0
V 5:1
.2
42 "4
•
O
8
in
0
14
I 1
,--I
O
O
••••••
f•-•-
A,
•• •• •• •• •• •• .•
a
a)
T/
o
011
0a)
$4
O 0 0
$• .4
0
A
0
•• 00 •• •• •
•
.
g
•
.
• &
.
.
.
trt re \ re N M• . %.0
• •
•
•
•
•• •
•
: g .0 000
Le-1 OJ r-I
• r:=1
r.1 N-NA• CU . 43
. . .
.
. • .
• -1- • -4 .4 -4
.
.
• ...
••. ••• .• 5 ..
•••
.. •• -•
•• •• •
•• ••
ed
•pg
.0 ..-1 I
''
,0- --,
1.--,.
ri
al1• ,_...
ill0
$II.I
• •• •• •• ••
a •
0 0
CI)
41
•
• • .
• •
.. .• •• •• •• •• .. •• •• .• -•• •• •• •• .. .• •• •• ••• ••
••
0
a)
0 •
.1 ,11
•• •
•• •
$40
.4
P•
•• .. ... .. ...
at
.4-
a
00
"
E'
0
O .4
6 .4
o
•cl M w
e a 0CO 49)4
4a
34
$• o 40 R,
1:11
0
8
P..r1 0
00
tn wil
..4
lh g 11
r-1 co
.-4 4.1
441 0
.
3 : . R
0 0 0
0
0 PrN
fel 141 M1..C1 . • 1/4.0
CV 0 1/40 C11.4 ON (TN i.c .‘ a\ 0 c• r- cv re\.4- r- 111 tO ON
0 cu CV C‘I •-1 •-•1
CU reN -1 r4 0 re\ cu re\ a.1 PeN PrN 0 •-4 re\
44"1 01 re\ re ‘ ef \ fel l•r1 re 1 tel Pe\ reN reN prn 14-1 reN re\ reN reN
• • • • • • • • • • • • • • • • • • •
Q A
TN
43 1
...•
W
0
0
4D
..-1
O
aPI •4
CO 42
•• •• •• se • •• •• •• •• •• •
U)
. •
cLi; 0 0 0 0 0 0 0 0
g
c
to n.t) cu re\ •-4
reN e0 trn in
= ,.
- --, 1 3 8 @ 3 P.,
N0 MA'
CU
CU 14 1 IIN 00 r-I I-- N.0 r--.. N- 0 0
.-4 N.0
0 •n •n • 4k4.0 •
lama •
.
0
P.
L.
ks;) 1/4.0 LC1 U1 U1.# .4- .4 .4. LC1.4 .4 -4 tr‘ rrN
a) 0
.4
4a 011
0 40
8 0
I 4)r..
.
•
•
• • • •• -
•• ••
. •• •• •• - • . •• -• ...
••
•
••
.
ft
a)
4.0
▪
. .
....1
01
tif
...4
▪
•
00 01 I11 al In CU
al .-4 ...4 r.4 0 CV
• • • • • •
r4 r4 r4 r4 r4 r4
.....
00
v
Il• .. .. - - •• .... •• ••0... •• •• ••
40--•
$4
..Or:11
0
0 W
-P
g "
••
k.00 .-I
e---- • ...1"
01 •
0 0 re
0 • re
0 ..
• • •
r4 r4 r4
r4 • r4
r4 •.
.
.
i•e •• •• •• • •• ••
•
•
C1.I r-- r•-- tr1 to Qz) in 7.% Cr.
•
CU ri 0 •-•1 CV 0 0 CV N-+
.
• • • • • • • OO
•
r4 r4 r4 r4 r4 r4 r4 r4 r4
0 10 • rl •
rl r4 • .--1 •.
r4 r4 • r4 •
.
.
.
.
%
•
t4" \
CU
.
r4
cr%
.....
.
.
.•
le
04
O a) 0
-P -0 0
•
•
r4 42
l
CU
A
0
0
•• •• •• •• •• •• 00
0
•.
.0 .• •• •• •• •• • • ••• •• •• •• .• •• •• •• •• •• ••
.
• .
•
•.
•
•
.
.
•• ••
'.
'.
.
•
• c-.• •
• • 0 0 • .C21 23 P• CO •
• 0 • 0 t"--
Ni - ON r•r\ an
•• re-,. ••0.of7
ON
• ••• .
• a a .
.
. .
. .•R.
• ,4- . p,-", or • r-^%. 1.1) • • reN ..• • reN.4- rcn
•
.
•.
•
•
.. ... ..
..
.
•
on •v. .. •
.
..
• -
••
.•
.
.
.
0 C) C) C) 0 C) C) 063C)CU
0 0r4C)
C) CD 0
60 (:).. tOW
00 010 0 r---150
0
60 OJ 60 CU tO 60
CO 0 .4 .4 r4 0 CO 1-C \ .-1...1- 111...0- l(1.....1- I.-% Prt..1• .4- .4- r1.? M CU CU
•• e• ... •• .. .4 • .4. .4. .6 .a. ... 4.. -es .. .• •
.. •
••
0 0 tfl re‘..4-..4- cu.A• 150 150 0 c‘1..4• pc\ ci.) cu to ,...o k.o
•-•1 r4 C) 0 0 ri r4 •-.400.-1000,1•-•1000
r4 r4 r4 r4 r4 r4 r4 r4 r4r4 r4 '71 r4 r4 • r4 r• •4 r4
• • • • • • • • • • • • • • • • • • •
•• •• •• •••• •• •• •• -•• -•• 09 •• ••• •• 00 •• •• 4,0 •• •• ••
03 ,0 ,0 0 al p odA00,0
0 0 0 gip°
c)Nm cr% w‘Lnao 150 •-4
\ rev.° .C:1
.0*
r4 r4 r4 r4 r4 -4 r4 r4 NCU CU CU CV CU Pr\Prl MK\ rrN
1
1
1
!
1
11
I
I
i I
1I
II
/ I
/ I
/
/
/ I
II
/ I
1 1
I I
II
/ /
0
.p I
Ctl 0\
<1k / rk''q
,' 1 7/ .V.
Z (I °))n),
/ Q3/ Q";
/I
/
/
1 //1
0
„/„..,.../<•*%/
o
141
0
0 cn
a)
4-) > ca
03 A. 0 cq
0 o
0U 0.. ›,
o 0 4
9-1
0
`^
U)
0 CI)
(f)
•
Xf. •—••..,
ft!
e.
Ci
C.
.
(1)
1-9
COI
3rmi
-.
R., 03
ci
E F..., co Ch
.._..
0 tt -1-) 0
0
0
cn 4
Ni
a) a) 0 ...-...
g C.) -1-.) g •
03
9-1 0
is4-1 0
10
u)
0c
0 4-1 .1-1
.-.1
+ 0 ca b&.
r6 *
od
cn = o
NT
1-4 = a) 03
fl.
.,
R. 0 r.
Lk
9-i c., o o
0
V +) 5 0 0
0 0 0 0) CD
k
u.
0 CD C.)
ni -4
K.
3
4,1
›') • /-1 'C
I 0 o
,I MI 0
10
Nt
•c:1
o t4
Ck
0
0
NC
..,
+3 4, (i)
ti
ra1 0 ::), t "c,
't
4-4 0 oS 4-1 CfD
Cn r-i
co4
Pm. bl) •N
...-1
0 ;4
0 CI-I
4
0 r0-I I+2 ..
'
.
H
T
o
.p
c
o cct) 0
C-1
;:0`
0
3 N (i) 4 4-1
0 C.)
Ln
0 o " +), g b4
-...:
•ri Z
-t-I
WO
0
-1-> COD g Tim' r-1
O
•1•1
4.W4 0 ' .e-4 ,.>" 4/)
rn
0
4-4 10 c.)
a)
-...:
re T14 Z a) r-i
1
4 10
I ...
•r-I G.
r•-n
-.
...
• o 0 3 0
4-,
cs
cs)
::)
•St
(4. /11234
21V78 0171/.2/70/11 COWS 71P1V4I7/) . 01 5-57,Y1C
2/1/193-1.11 J0 0/1b2/
r-f 0 0
ti ct
4 co
r'l
'0 0 a)
^ a) z 4
0 o tn "-I 0
;-. In cd 0
0 r-I .0 1-4 •r-I
bO
n-I
44
-I
0
-4-D
In
Zi T(
ik k
k5
LL.1 LL.I
L)
Q 'et
kl Lk
.1
h
Nt:
-o
0
\ --
4., 4,
0 cz,
k
0 c:3
Z.-. 1.:
L) ;..)
4.1 14.J
14:
-.1
d' cz)
K
,S.).
00
k......1..
+
1....
Q
(1,
Lk,
tr.
0
o
1-.. 1....
k
..Z(
'R
-IZn C:
'--) ‘,...
L'nv-,
kJ k j
en 44
<
Q
.
oc k
cl.. 4,
. Z
cY 0 0n
1
I.,
Lk,
Je
kr% k
cn ---.1
.A./o, ecii
..)
o+x
o
o
---:.
41
o
a)
Z o up
c..) in ad
I—I 4
4
-4- -P W
N-I cd >
3
rd
',
_4
r.
O
_,--i
-,
0
(4-,
U)
a)
0
W
S. l0 4-3
0 t0
4-t
qt/ 0
a) 0
> 03 rd
'`t
o <
N .....1
a
al
r-i a)
•-4 c.) i
cd 4C.
4-4 44
O
rd
4.-1 Z
4 0 al
-P
li Z cn
•r-I 0 a)
W
-I-) al
W c.) y—i
> a) P•H R.
+) •ri Co-i
U rd c
4-4 0 p)ir,.
0 0
o o
cn
.1-1
t.,
al VI
ia a)
E $-. ..--,
o pq
c.) E in
0 I—I
al c.)
rd ---.
al Z Z cii
7:1 -,-i al Z
O
4.) u) o
P.
cn a) LC Z
-i-D
r•-•
0
a)
c.)
E-4 it
I ,-1 1 I
4
i R.
cr3 c.)
0
cl ,t)
9-1
ti 0
I—I 0
I
. ,:73 N
a)
i. - t.
0 P., b0 4
ao
O
aZI
.24
kr%
( i .,0
NS.
O
O
fo
0 od)
1-ar 7c1 0_77)0/79N/7 30 SIWILS _711714//17/7 Ol CS17815- g1feN/17/7 JA /1.9.7idg 30
O
outs/
\.§
o
•
Q)
C1.-1
cd CC
H tk
O
44 kJ
U
Q •;1
14, 14,
4.. t1/4
Cl..1
+
MI
4
c:cs
3
Ntz
•
+
I::
k...) c„)
k1 4..j
(:t k
0 CD
. 1-1 4.)
•
al
a> 0 r•-1
4Z6 Q,
'Z:n Q,
0 cd
-'
..
•
O P.
9..1
CH
C.) 'CI 0
+
-I:S
1+.1
‘i
o
I.
0 co
(/)
0 0
0 P
%.9 01
I... K
Q
•:K
Lk]
0 c:...1
v-n 4-..,
4144
ec k
ei.. 4,
Lk.1
ec
+
o
q qU t,5
4'1
N
0
44
,-,D 0 +
O
-...1+
4.
0
>
C.•
CD
C.9 °C
•
▪
crid
4:1
cd
•
'CI 0 C.)
cc3
P.
++
•
'CC
CD
•
N
q
0
+
0
CD •
0
C1 E
+
0
4-)
cdd
1:1
.;° ;
0
ci)
•
)
o
)
41
1 f•i
-c411
c)
P. 4
! 0
et•
o
3
$1
0
-..:
a.
o;
t-.
cs
sb
cs
4-,
o
Nt•
o
VS
N
tl
(flod/ga oi)
72Y7d 077)49/19N/7.10SK7Y1S- 71171/41/17a 01 CS991C 716?a//1717 94/1973J2!0 OLLPSI
O
•1-1
▪:11)
$-1
1
.
.
10
41
En
4-)
cd
t—i
4-1
P
0
PZ
P 0
C-1 -ml 0
h
d
+
0
,---,
CI
cd
;-n
4 (4 c.)
+)
P
rd a) -1-1
• r-I 0
1
3 03 N
o,•...._3
o
f
a)
> c4-4 4
-1-i o
-c-5
k.
El
+
C.)
W 0
CH -1-i
n.I
erj 44
+
In
';I
rci
4-1 4-) Z
a) 0 cd
a)
&I $•
C -H
tk
0
_
ni k
tki
in
co
4-
133
CD 0 ,--I
-I-)
Lli
L
i
4-
•-1 cd u)
a)
3
-4
+
-4-
Q
''t
N
Z)
Z 4-)
Q
(..?;
144
-d o
a) • 1-1
++
-it
lel
'-
4.
.1-
P.
Z o c*.4
0 In 0
rt4
cn
4
Q
rN QC
,:x
c.; ck
4-
U)
cl)
0
cn 0
cd u)
P- a) -d
E a)
0 P- u)
0 E 03
0 ,IZ
-.:
cd 0
+)
a)
03 P P.
rci
•,•f ;-.
P
0
+)
•-..:
V)
W C...)
CD
E-I cd
i
1
•
Ie.
cs
,•I
•
P. ---,
0
4 S3
"-I o
3 II
O P,
;.. --1 cb
b.0
c:s
••••n
74
CO
CA
cs
A
es
4-1
c;
V
cs
Cs
cv
CS
Zis
(n, /112 °.Y /
3101 7c/ 077)42/)61N/7 JO Srgeir 21184/117/1 01 SSJ2/1C girl //17/1 4/19.7112 30 01.10'Y
c
O
kg
0
+ ++
+
0
'..•
0
,...._
q
+
0
+
q q
,...al
__ L.,
o
+
+
+
cz.
4-)
al a)
h
+
0
`3
ri 0
4-1 cd
ca 7..
LI 'r.:?,.
..)
Zk
nC
0 "
k. .Si
---1 (.1.,1
••••J
rk
.
-P Z Z
Z7/ 0 0
•-1 •-1
c)
IZ.
j'
L.,‘i
(1..
CS
4-
4.
O
•
44
1,
1-
o
.--
l,.
d
u') c'")
kl t")
EC 4-1
tr)
kZ
-
q o (z,
‘.-) k.3
3 4-)
c.) 4
CD W c.)
> $-. P
-r-i •1-1 9-1
4-) t-.1 i
r
C.)
--1
,..
r,
-,.,
0 s
ci-4
4. w
Lk)
--1
0
CM -4.) rd
oi (k
K
k)
W
cc9
> S..
r.. O cn
Q
CC
le1 •Ct
4
c
.P
o
q
o
NI
0
6
00
cta
ov 0
0
0
0
e
4.
00 €59
•
t
A
+
Q-
c
Z
CD
C.) 0 -0
0 al
.—i
-P 4-) p..
9-I cd
3
4-4
P o
cl 0
a) 9-1
In
F.
ti) 4..)
al co cn
,
*
+ .4.
+
++
I-
+
GI
t
+ ++
4)
0
0 n
cn ,-1
k.
I
rn
+
'Ct4
0
CL)
'1/41
0 ,0
00 0
c
4-4
td,3
rk
cza
--.
•
•-I ..-..
vl
0 44 Z
h0 0
-Z
R.
e-N
L
c:4
N LL,J
1+1.
t,-)
+ ++
P. a)
44.
+I.+
CL
0
l&l.
0
0
0 p.
c.) E P
0 0
cd c.)
4-)
'Li
al a)
d 1-1 cn
al
4-) cn ,3
r
-.4.
CD
.
(I) CD
CO
CD -+)
E I
I
•-1
C.
I in9 :
C.)
-
cd >
•CI4
r1 0
w
bo
'ZS
(ma,/ .24
4Zi
C
O
.71V7d 077)19n9W/710 C517,111.0 9161/117/1 01 5-51ZJ1.0 .71VW/171) JA/.19_7112 JO Oil*/
O
4.1
••I
b.0
A
,z)
4_
cz)
Q.
a)
A..
cl)
0 0 4
U
o
0 0 R.
Lei
f:.
c,
Lza
vt
..`
:c
,
ccl
h
Is.
14.1
Lll
et)
CO
3
3
L2::' L ka 3 3 4-c'
4, Q 4.1..)
c,,--,
ck ,..., 4, c, c.
Q..
CIS
V)
. .„.
)
LL1
•Zz
off.
R
CZ1
L...j
&kJ
r; 't
o
0
v)
CD
c4-1
0 cid 0
1..1
cn
Ai
Zt 1
?-1 (r,
II
4D
.0
0 0 0
0
uJ
R.,
,0
0
U)
(..) 'Z'
'" '--)
%
Et)
P $.4
o
.
;1. c)
1_, .••., :.i.
= .
, -... 0 .Nc
14'''J Nr"
1c
,S Tt cm n;:, 'cK
(/)
0 -P
-P
44
L..,
k
Li
4.,
,.
ce 0
'44
.>,
...
4.)
cl)
kI
1 :b
kr,
•
cdi
b.0
.
.--..—.
......---.
0
..•III X.-4111
•
0
4) 0 0
(4.
114
•,1
0
cci c.)
al
•
R< CH CH
u)
V)
(1)
kr,
4)
0 cH 4•4
C.) 0 0 R.
ciA O 0
0 4,•) 0 C.)
-P
.7
-P
0 0
CD
4-1
4-4 > •r-i I
fr.1
Tti
0 0 >›
•
cD
CC 4.4
I
rl
CI•I 0
I
cL)
O
7:1
O R.
0 +)
eH
lap
o
CS
sre
c:i
(n2y/fia2d)
.71177c1 0.77)/9/I gN/7.10 STRI1C -71141/117/7 01 STRILS .711;11//17/7 7/1/1.17.1.1 210 0/1 PW
44