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MSU I. An Affirmative ActionlEquol Opponunlty Institution
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NON-SHEAR COMPLIANCES AND ELASTIC CONSTANTS MEASURED FOR
THE WOOD OF EIGHT HARDWOOD TREES

BY

TIMOTHY GRANT WEIGEL

A THESIS
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE

Department of Forestry

1992

J ;: -’7’/\'

'7 ’i,»

4/

ABSTRACT

NON-SHEAR COMPLIANCES AND ELASTIC CONSTANTS DETERMINED FOR
THE WOOD OF EIGHT HARDWOOD TREES

BY
Timothy Grant Weigel

To determine if linear relationships existed between the
non-shear compliances of the wood.of eight.hardwood.trees, the
non-shear compliances were measured from short columns loaded
in compression in the longitudinal, radial, and tangential
directions. Significant. linear :relationships ‘were found
between pairs of compliances with the exception of SLR and San,
and.SLT.and STT, for a given direction of loading. Sij1relates
the strain in the i direction to the applied stress in the j
direction. To determine if the property Sij = Sji found in
orthotropic materials holds true for wood, specimens from each
tree were tested in the longitudinal, radial, and tangential
direction. As predicted by the linear orthotropic elastic
theory the compliances SM and STR were found to be equal.
However, the measured values of the compliances SLR and SRL,
and SLT and STL did not behave as predicted by linear

orthotropic elastic theory.

TO CAROL

ACKNOWLEDGMENTS

I would like to acknowledge my appreciation to my major
advisor Dr. Alan Sliker, for his guidance and assistance
during this project. I would also like to thank the other
members of my committee Drs. Gary Burgess, Henry Huber, and
Otto Suchsland for their suggestions and guidance through out
this project. Thanks also go to Ying Yu and the other
graduate students of the department of forestry for their
assistance on this project.

I am also indebted to my parents Ted and Sarah. Without
their support and understanding none of this would have been

possible.

iv

TABLE OF CONTENTS

Page
LIST OF TABLES ........................................ Vi
LIST OF FIGURES ....................................... ix
NOTATION .............................................. xi
INTRODUCTION .......................................... l
OBJECTIVES ......... ..... .............................. 12
METHODS ............................................... 13
RESULTS ............................................... 23
SUMMARY AND CONCLUSIONS ............................... 28

LIST OF REFERENCES 00.... ...... OOOOOOOOOOOOOOOOOOOOOOOO 90

Table

Table

Table

Table

Table

Table

Table

Table

Table

Table

Table

Table

Table

Table

1.

2.

9.

10.

11.

12.

13.

14.

LIST OF TABLES
Page

Oven dry specific gravities measured for
specimens made from the eight trees tested.... 35

Estimate of variability between individual
measurements of the compliance SLL............. 36

Estimate of variability between individual
measurements of the compliance SRL........ ..... 37

Estimate of variability between individual
measurements of the compliance STL............. 38

Estimate of variability between individual
measurements of the modulus of elasticity EL... 39

Estimate of variability between individual
measurements of the Poisson’s ratio ULR........ 40

Estimate of variability between individual
measurements of the Poisson's ratio 0LT........ 41

Estimate of variability between individual
measurements of the compliance SR3............. 42

Estimate of variability between individual
measurements of the compliance STR............. 44

Estimate of variability between individual
measurements of the modulus of elasticity ER.. 45

Estimate of variability between individual
measurements of the Poisson’s ratio uRT....... 47

Estimate of variability between individual
measurements of the compliance SLR............ 48

Estimate of variability between individual
measurements of the Poisson’s ratio URL....... 49

Estimate of variability between individual
measurements of the compliance STT ............ 50

vi

Table

Table

Table

Table

Table

Table

Table

Table

Table

15.

16.

17.

18.

19.

20.

21.

22.

23.

LIST OF TABLES CONTINUED

Estimate of variability between individual
measurements of the compliance SRT..........

Estimate of variability between individual
measurements of the modulus of elasticity ET.

Estimate of variability between individual
measurements of the Poisson's ratio 0TB.....

Estimate of variability between individual
measurements of the compliance SLT..........

Estimate of variability between individual
measurements of the Poisson’s ratio uTL.....

Fisher's protected least significant
difference test of the mean values of the
compliances and modulus of elasticity for
specimens loaded in the L direction.........

Fisher’s protected least significant
difference test of the mean values of the
compliances, modulus of elasticity, and

Page

52

53

55

56

57

58

Poisson's ratio for specimens loaded in the R

direction and with the lateral strain
measured in the T direction.................

Fisher's protected least significant
difference test of the mean values of the
compliances, modulus of elasticity, and

59

Poisson’s ratio for specimens loaded in the R

direction and with the lateral strain
measured in the L direction.................

Fisher's protected least significant
difference test of the mean values of the
compliances, modulus of elasticity, and

60

Poisson's ratio for specimens loaded in the T

direction and with the lateral strain
measured in the R direction......... ...... ..

vii

61

Table

Table

Table

Table

Table

Table

24.

25.

26.

27.

28.

29.

LIST OF TABLES CONTINUED
PAGE

Fisher’s protected least significant

difference test of the mean values of the
compliances, modulus of elasticity, and
Poisson's ratio for specimens loaded in the R
direction and with the lateral strain

measured in the L direction................. 62

Analysis of variance and statistics of
slope and intercept constants for the
compliance equations........................ 63

Statistical analysis of the differences

between the slopes of compliance equations
developed in this study and those developed

by Sliker (1985, 1988, 1989) and Yu (1990).. 66

Comparison of reciprocal compliances........ 68

Statistical analysis of the difference between
the slope of the equation relating S and STT
developed in this study and the equation
developed by Sliker (1988)................... 69

Analysis of variance of regression equation
relating reciprocal compliances, and t-test
comparing equations determined in this study
with their theoretical values............... 70

viii

Figure 1.
Figure 2.

Figure 3.

Figure 4.

Figure 5.

Figure 6.

Figure 7.

Figure 8.

Figure 9.

Figure 10.

Figure 11.

Figure 12.

Figure 13.

LIST OF FIGURES

Page
Compression samples........................... 73
Gage types and configurations................. 74

Gage arrangement for measuring strains when
loading in the L1direction.................... 75

Gage arrangements for measuring strains when
loading in the Rmdirection.................... 76

Gage arrangements for measuring strains when
loading in theTdirectionOIOIOOOIOOOO00...... 77

Test specimen A in the compression cage. 8 is
end block. C is end bearing block. D is
centering guide. E is hole for metal dowel
connection to universal joint. Ball bearing is
centered between B and C at each end (Sliker

1989)O0.000.000.0000000000000COIOO0.0.0.000... 78

Compression cage connected to Instron
crossheads for loading in the L direction..... 79

Compression cage mounted on steel frame for
loading in the R and T directions............. 80

Compliance SRL plotted as a function of the
compliance SLL for the eight trees tested. . . . . 81

Compliance STL plotted as a function of the
compliance SLL for the eight trees tested. . . . 82

Compliance STijlotted as a function of the
compliance SRR for the eight trees tested.... 83

Compliance SLijlotted as a function of the
compliance SRR for the eight trees tested.... 84

Compliance SRijlotted as a function of the
compliance S'r'r for the eight trees tested. . . . 85

ix

Figure

Figure

Figure

Figure

14.

15.

16.

17.

LIST OF FIGURES CONTINUED

Compliance
compliance

Compliance
compliance

Compliance

compliance 8

Compliance

compliance S

SLT
STT

SLR
SRL

SLT
TL

SRT
TR

plotted
for the

plotted
for the

plotted
for the

plotted
for the

Page

as a function of the
eight trees tested.... 86

as a function of the
eight trees tested.... 87

as a function of the
eight trees tested.... 88

as a function of the
eight trees tested.... 89

NOTATION

L, R, T = longitudinal, radial, and tangential.

i = subscript L, R, or T.
j = subscript L, R, or T.
oi = stress in the i direction. (psi)

to
ll

1 strain in the i direction. (in/in)

Ei = modulus of elasticity in the i direction = 01/31° (psi)

Gij = shear modulus in the ij plane, i s j. (psi)
Sij = compliance with strain in the i direction per unit
tress in the j direction = ei/oj. (1/psi)

v 1 = Poisson's ratio of strain in the i direction to that in
tile j direction for loading in the j direction; i 1' j; =
ei/ej.

xi

INTRODUCTION

The increasing use of computer analysis to solve three-
dimensional stress and strain problems encountered in
structural design allows more efficient use of many
construction materials. To solve three-dimensional stress and
strain problems for wood members 12, elastic constants or
their related compliances are required. Wood is a highly
complex and variable material and an accurate knowledge of all
of its elastic parameters is :needed for precise design
analysis. "Engineers and designers are hesitant to use wood
under complex loading in part because of the uncertainty of
proper values of its elastic constants" (Gunnerson 1973).

There are two general methods for obtaining values for
the elastic constants of wood. The first is direct
measurement of the constants, which involves extensive testing
of each wood species. The second is to predict the elastic
constants from a known physical property. Two of the better
documented physical properties of wood are specific gravity,
and the modulus of elasticity in the longitudinal direction.

This study is part of a larger project, whose aim is to
develop a set of equations relating the various non-shear
compliances to the compliance SLL, the inverse of the modulus
of elasticity in the L direction (EL). Efij relates the strain
in the i direction to the applied stress in the j direction.

Previously (Sliker 1985, 1988, 1989), specimens tested in the

2
longitudinal (L), radial (R), and tangential (T) directions
were not matched with respect to tree or species. The
objective of this study is to use matched samples to clarify
the relationships found by Sliker (1985, 1988, 1989), and Yu
(1990), and to test if the property Si]. = sji found in
orthotropic materials holds true for wood.

Wood is a cellular, biological material formed by the
secondary thickening of woody plants such as trees, shrubs,
and vines. Most of the commercially important woods used in
the United States come from trees. The term wood as used in
this thesis refers only to the wood produced by trees. Wood
can be divided into two broad classifications hardwoods, and
softwoods. Hardwoods being formed by deciduous trees
(dicotyledons of the Angiosperms), and softwoods formed by
coniferous trees (conifers of the Gymnosperms). This study
deals with the properties of hardwoods.

The wood of hardwoods is composed of four basic types of
cells: vessels (or'pores), fibers, ray cells, and longitudinal
parenchyma. The term pore refers to the appearance of the
vessel element in cross-sectional view. The general size,
number, and distribution of pores within the growth rings
further categorizes hardwoods into two main groups:
ring-porous hardwoods and diffuse-porous hardwoods. In ring-
porous hardwoods the large pores are concentrated in the wood
formed in the early part of the year (earlywood or springwood)

while the pores in the wood formed later in the year (latewood

3

or summerwood) are‘generally’smaller and less numerous. IRing-
porous hardwoods are characterized by distinctive figure on
the tangential and radial surfaces. White oak and white ash
are examples of ring-porous hardwoods. In other hardwoods the
pores are evenly dispersed throughout the growth ring with
little noticeable variation between earlywood and latewood;
these woods are called diffuse-porous hardwoods. Basswood and
cottonwood are two species which fit this category. Some
hardwoods do not fit neatly in either the ring-porous or the
diffuse-porous category. Black walnut for example tends to
form larger pores early in the year with the size gradually
tapering off as growth continues forming no definite zones of
one size pores. Hardwoods such as black.walnut are said to be
semi-ring-porous or semi-diffuse-porous.

Variation in the relative proportions of different cell
types and sizes is reflected.in the wide variation in physical
and mechanical properties of the various hardwood species.
Within a given species and even within a single tree there is
also a wide variation in the cellular makeup of the wood.

When trees are forced out of their normal erect growth
pattern abnormal tissue is often formed. In hardwoods this
tissue is called tension wood. Tension wood is generally
found on the upper side of a leaning trunk or on the upper
side of branches though it may also be irregularly distributed
through out a tree. Tension wood differs significantly from

normal wood in several ways. In tension wood all or part of

4

the secondary cell wall nearest the lumen is replaced by a
gelatinous layer composed mainly of cellulose and is loosely
attached to the other cell wall layers. The secondary cell
wall restricts longitudinal shrinkage; as a result tension
wood usually shows excessive longitudinal shrinkage.
Mechanical properties can also be affected by tension wood.
Tension wood has long ropey fiber bundles which gives the wood
a woolly appearance when rough sawn. Another growth factor
that can affect the physical and mechanical properties of wood
is juvenile.wood, Juvenile wood is formed by immature cambial
initial cells near the pith of the tree. The length of time
that juvenile wood is formed varies from species to species
but is generally between 5 and 20 years (Panshin, De Zeeuw
1980). Hardwood fiber cells formed by an immature cambium.are
generally shorter and thinner walled then mature fiber cells.
In addition the cellulose microfibrils of the $2 layer of the
cell wall are formed at a angle to the main axis of cellular
orientation, the L direction. All of these factors contribute
to juvenile wood's generally lower strength and stability,
when compared to wood formed later by mature cambial initials.
The physical and mechanical properties of mature wood are most
often recorded in tables for structural applications.

Fiber cells provide much of the strength of wood, their
distribution and number within a particular piece of wood will
have an effect. on ‘that jpiece's physical and. mechanical

properties. Growth rate can affect the distribution of fiber

5

cells and as a result the mechanical properties of ring-porous
hardwoods. In ring-porous hardwoods the width of the
earlywood, composed mainly of large vessel cells, does not
vary much with growth rate. Consequently fast growing ring-
porous hardwoods have a higher proportion of fibrous latewood
and will be stronger then a piece of slow growth ring-porous
hardwood composed mainly of earlywood which contains a higher
proportion of weaker vessel cells.

The normal growth pattern of a tree, upwards from the
tips of branches and outward from the pith, forms wood in
annual increments of cylindrical shells about the pith. This
cylindrical symmetry' is reflected in ‘woods physical and
mechanical properties. Conventionally wood is treated as
having three mutually perpendicular axis of symmetry: one
along the main axis of cell orientation called the
longitudinal (L) direction, a second in the direction of the
rays called the radial (R) direction, and a third tangent to
the curvature of the growth rings called the tangential (T)
direction. Wood can then be treated mathematically as an
orthotropic material for stress analysis.

To fully describe the stress strain relationship in an
orthotropic material twelve elastic constants are required.
The elastic constants are the modulus of elasticity in the L,
R, and T directions, EL, ER, and ET; six Poisson's ratios vLR,
VLT, vRT, vRL, vTR, and vTL; and three shear moduli GLR, GLT,

and GET: A matrix equation describing the three dimensional

6
non—shear relationships of stress and strain in an orthotropic
material can be described in terms of these elastic constants

or their related compliances (Bodig and Jayne, 1982).

 

 

 

 

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Additionally the reciprocal relationship 815 = Sji, where i and
j equal L, R, or T but i v j, should exist in orthotropic
materials. If the nine non-shear compliances were known or
could be accurately estimated and either the stress or strain
was known then the other parameter could be solved for. 0f
the elastic constants only one, EL, is well documented for the
majority of commonly used woods (Sliker 1988).

Electric resistance strain gages have had a long history
of use for stress and strain analysis for wood. Radcliffe
(1955) described the use of electric resistance strain gages
on wood for the determination of elastic constants. Also
given were special procedures to be followed in order to
maintain the sensitivity and.accuracy of the strain.gages when

used on wood.

7

Perry (1984) summarized some of the properties of
electrical resistance strain gages and their effect on strain
measurements. Among the properties which can effect the
accuracy of stain measurements on wood are: reinforcement
effects of the wire and backing material, transverse
sensitivity of the gage, and thermal effects on the gage.
When using strain gages on low modulus materials such as wood
the relatively stiff backing material found on most commercial
strain gages can act to reinforce the weaker substrate. The
loops in the strain sensitive wire of many commercial gages
can be effected by strains perpendicular to the main axis of
measurement. This transverse sensitivity can cause large
error in measurements because of the large Poisson effect in
wood. While most gages are supplied with a transverse-
sensitivity constant which can be used to correct for this, as
the test conditions change from those used to calibrate the
gage this constant becomes less accurate. Wood is a poor
conductor of heat, as a result thermal drift can be a major
problem when using electrical resistance strain gages. When
used on wood, the gage must not only be compensated for
changes in resistance due to temperature change but also for
expansion of the wood due to heating and contraction of the
wood due drying induced by the heating.

Sliker (1967, and 1971) described the manufacture and use
of free filament strain gages in order to overcome some of the

problems inherent in commercial gages. He used widely spaced

8

strain sensitive wires bonded directly to the wood substrate
with a low modulus nitrocellulose adhesive. The strain
sensitive wires were widely spaced to reduce the heat
concentration and the related shrinkage and swelling of the
wood substrate. The gages were bonded directly to the wood
substrate with a low modulus nitrocellulose adhesive without
a backing material, which adds stiffness to many commercial
gages. By doing this the reinforcing effect of the stiff
backings is avoided.

In 1970, Goodman and Bodig tested four wood species in
compression and torsion. They obtained values for the
orthotropic elastic parameters and compared them to
theoretical values. They found agreement between the measured
and theoretical values of longitudinal strains when loading at
angles within a principle orthotropic plane. However no
significant agreement was found for general loading. They
concluded that the layered homogeneous structure of wood might
lead to behavior not predicted by orthotropic elastic theory.
Their results also could not substantiate the assumed symmetry
of an orthotropic material. The error involved in measuring
some of the smaller Poisson's ratios ‘might have partly
accounted for this.

In 1973, Bodig and Goodman reported additional
information on estimating the elastic parameters of softwoods
and hardwoods. Data used in their analysis came from a number

of sources and test methods. Significant exponential

9

relationships were found between density and the various
elastic parameters with the exception of Poisson’ 5 ratios
which were considered to be a constants. Significant
relationships were also found between EL and the other elastic
constants with the exception of Poisson’s ratios. Using these
equations, the ‘moduli of elasticity, and ‘the moduli of
rigidity were predicted for most of the commercially important
species grown in the United States.

Bucur (1983) used ultrasound to measure the elastic
constants of increment cores. The results of the ultrasonic
measurements were then compared to measurements made on
standard samples loaded. in static bending. Significant
correlations were found between the elastic constants measured
by the ultrasonic method and those determined by static
bending test. He concluded that the ultrasonic method could
provide a suitable non-destructive quality control test for
wood.

Guitard and Amri (1987) used the results of their own
research along with bibliographical data to look at the
relationship between the elastic and physical characteristics
of hardwoods and softwoods. They found significant
exponential relationships between specific gravity and the
elastic properties hardwoods. As with Bodig and Goodman the

data used came from a variety of sources and a variety of test

methods.

10
Sliker (1985, 1988, and 1989) used a variety of softwood
and hardwood species in compression test to obtain the non-
shear compliances. His research resulted in the following

relationships:

EQUATION CORRELATION COEF

1. 3121. = 0.022810‘6 - 0.405 sLL R2 = 0.900
2. sTL = 0.021810"6 - 0.500 sLL R2 = 0.925
3. sTR = 1.260*10'6 - 0.887 S“ R2 = 0.911
4. SLR = 0.029810“5 - 0.0483 SR3 R2 = 0.539 (2)
5. SM = -0.659*10‘5 - 0.255 Sm. R2 = 0.980
6. sLT = -0.022*10‘6 - 0.274 Sm. R2 = 0.980

for woods tested at between 9% and 12% moisture
content. Units for the compliances Sij are strain (inch per
inch) per unit stress (psi).

Sliker (1990) tested specimens at three moisture content
levels to determine the affect of moisture content on the
relationships between pairs of compliances. Results showed
that moisture content has very little effect on the

relationship between pairs of compliances.

11
In 1990, Yu tested matched specimens in compression in

the L, R, and T directions with the following results:

EQUATION CORRELATION COEF
1. sRL = -O.016*10'6 - 0.353 sLL R2 = 0.613

2. sTL = -0.062*10'6 - 0.360 sLL R? = 0.566

3. sTR = 1.224*10‘5 - 0.967 sRR R2 = 0.858

4. sLR = -0.210a\v10’6 - 0.0143 sRR R2 = 0.332 (3)
5. sRT = -0.309«:10'6 - 0.288 sTT R2 = 0.936

6. sLT = -0.266*10'6 - 0.00605 sTT R2 = 0.100

Units for the compliances Sij are strain (inch per inch) per
unit stress (psi). With the exception of the relationship
between SLT and ST.r the relationship between pairs of
compliances did not differ significantly from those determined
by Sliker (1985, 1988, 1989). While the reciprocal
relationship STR = Sm. was close to its theoretical value, the
relationships between SLR and SRL, and SLT and STL were not,
possibly due to the difficulty in measuring SLR and SM, or to
the different viscoelastic responses of wood when loading

parallel and perpendicular to the grain.

12

OBJECTIVES
The objectives of this research are:

1. To determine if linear relationships exist between the
non-shear compliances of different hardwood species from

loadings in the L, R, and T directions.

2. To test if the property Sij = Sji found in orthotropic
materials holds true for wood through the use of matched

specimens.

13

METHODS

MAIEBIALé

Material was obtained from eight trees representing six
species: cottonwood (Populus deltoides §;), basswood (Till;
americagg _I._.._)-two trees, white ash (anxinus species)-two
trees, black cherry (Prunus serotina Eh;h,), hard maple (Age;
species), and black walnut (Juglans nigga L.). A single log,
having a diameter of over 30 inches, from each of these trees
was sawn into 3.25 inch thick planks and kiln dried to between
8% and 14% moisture content. All moisture contents were
calculated on an oven-dry basis. A slow drying schedule was
chosen to minimize drying defects, no equalization or
conditioning was preformed at the end drying schedule. After
kiln drying, specimen blanks were cut, from the planks,
slightly larger then finished specimen size and conditioned in
a room kept at 68‘F and 65% relative humidity where they
reached an equilibrium moisture content of between 10% and
12%. To avoid juvenile wood only portions of the planks 15
growth rings or more from the center of the tree were used to
cut specimen blanks. Tension wood was very noticeable in the

cottonwood and basswood samples.

14

§2§QIM§N_£BEEABAIIQE

Three types of specimens were prepared from the blanks
corresponding to the three loading directions (L, R, and T)
(Figure 1). Space limitations and strain gage geometry
allowed the strain in only one direction perpendicular to the
load axis to be measured. when loading in the R. and T
directions. 'Two separate samples were required to measure the
two strains orthogonal to the load axis when loading in the R
and T directions. The use of a special strain gage design to
measure the small strains in the L direction when loading in
the R and T directions made a total of five specimen strain
gage types. Two matched specimens of each specimen strain
gage type were prepared from each tree. A total of eighty
specimens were prepared, 16 L type, 16 R type for each gage
arrangement for a total of 32 R type, and 16 T type for each
gage arrangement for a total of 32 T type specimens. In each
case the specimens were carefully machined to closely
approximate truly orthotropic surfaces. 0n planks where the
L direction was difficult to determine a red dye in kerosene
was applied and the major direction of flow was used to
determine the L-direction (Yu 1990). Longitudinal specimens
were 7 inches long by 1.25 inches by 1.25 inches. The 7 inch
dimension was in the L direction and the 1.25 inch dimensions
were in the R and T directions. Radial and tangential
specimens were made by laminating five pieces measuring 1.5

inches by 1.25 inches by 12 inches as described by Sliker

15

(1985). The 12 inch dimension was in the L direction and the
1.25 inch dimension was in either the R or T direction,
depending upon the specimen type to be made. The five pieces
were then laminated with polyvinyl acetate adhesive into
blanks measuring 1.5 inches by 6.25 inches by 12 inches.
Laminates were then machined to a thickness of 1.25 inches,
and specimens were made by cutting in the direction of the
6.25 inch dimension at 1.25 inch intervals in the L direction.
The ends of the specimens were then squared giving the
specimen a final length of about 6 inches. In addition,
moisture content and specific gravity were determined for each
set of test specimens, and matched samples were fabricated for
use in monitoring moisture content during testing. Specific
gravity information is listed in Table 1.

Free-filament strain gages bonded to the specimens with
nitrocellulose adhesive were used to measures strains during
testing (Sliker 1985, 1988, 1989). The two gage types and
three gage configurations used are shown in Figure 2. Type A
gages were constructed by soldering 4 inch lengths of 1 mil
constantan wire, having a resistance of 290 ohms per foot, to
12 mil leads, resulting in a gage resistance of approximately
97 ohms and.a gage factor of 2.05 (Sliker 1985). Type B gages
were made by soldering 1 inch lengths of 1 mil constantan wire

to 12 mil leads (Sliker 1989).

16

Specimens were prepared for gage attachment by lightly
sanding the mounting area to provide a smooth mounting
surface. The gage pattern was then drawn on the specimen.
A thin coat of nitrocellulose adhesive was applied to the
mounting area and allowed to cure for 24 hours, this was done
to insure good adhesion of the gage to the porous wood
surface. After curing, the mounting area was again lightly
sanded. The gages were then placed on the specimens. Finally
a second coat of adhesive was applied to attach the gage to
the specimen.

The gage arrangement for specimens to be loaded in the L
direction is shown in Figure 3. A type A-l gage was used for
measuring longitudinal strains. This U-shaped gage was formed
by pivoting the center of a type A gage 180 degrees around a
straight pin creating a gage length of 2 inches (Sliker 1967,
1985). Similarly, a type A-2 gage was used for measuring
strains in the R and T directions. This gage was formed by
making three 180 degree turns with a type A gage around
straight pins creating a 1 inch gage length (Sliker 1985).
When pivoting a gage around a straight pin, it is advantageous
to give the straight pin a slight slant away from the
direction in which the gage is laid out (Sliker 1967). This
allows the strain gage wire to easily slide down the pin when
tension is applied insuring close contact with the wood
surface during adhesion. To compensate for any bending caused

by eccentric loading of the specimens matching gages on

l7
opposite faces were connected in series, any increase in
strain due to bending on one side would be compensated for by
a decrease in strain on the opposite side (Sliker 1989).

Gages for measuring strains when loading in the R and T
directions were mounted only on the middle layer of the five
layer laminate. One reason for doing this was to eliminate
any differences which might exist between layers when
measuring strains parallel and perpendicular to the load axis.
In addition, gages should be mounted away from the ends of
compression specimens as there is some horizontal shear
between the specimen and the test apparatus. According to
Goodman and Bodig (1970) this horizontal shear dissipates
about one inch from the ends of the specimen. Specimen strain
gage types used for loading in the R and T directions are
shown in Figure 4 and Figure 5 respectively.

Two types of strain gages were used to measure the
strains in specimens loaded in the R and T directions. A type
A-2 gage was used to measure the strains parallel to the load
axis when loading in the R and T directions. A type A-2 gage
was also used to measures strains in the R and T directions
when loading in the T and R directions respectively. Type B-1
gages were used to measure the longitudinal strains when
loading in the R and T directions. Type B-l gages are formed
by mounting four type B gages parallel to each other on the
specimen and then connecting them in series with 12 mil

constantan wire. Type B-l gages were mounted so that all the

18
strain sensitive material was oriented in the L direction
because of the small strains measured in the L direction
(Sliker 1989). Strains perpendicular to the L axis might be
picked up perpendicular to the gage axis by end loops in the
other types of gages used, which could lead to large errors.
Gages mounted on opposite faces were connected in series in
order to compensate for any specimen bending which might occur

during loading (Sliker 1989).

T STING PROCEDURES

All testing was performed in a room maintained at 68°F
and 65% relative humidity where specimens reached an
equilibrium at between 10% and 12% moisture content. Before
testing a specimen, the cross sectional area of the specimen
was measured, and the matched sample was weighed in order to
determine the moisture content of the test specimen. Testing
was done by loading specimens mounted in a compression cage
(Figure 6). In order to maintain equal pressure on the end of
the specimens, ball bearings were used to allow the top and
bottom bearing blocks to rotate freely (Bodig and Goodman
1969). In addition, loose fitting guides were used to keep
the specimen centered on the bearings (Sliker 1989).

Loads were applied in the L direction by an Instron model
4206 testing machine with the crosshead speed set at .005
inches/minute (Figure 7). The compression cage was connected

to the crossheads at the top and bottom by universal joints.

19
Strain measurements were made with a Measurements Group’s
model 3800 Wide Range Strain Indicator for each pair of gages
oriented in a given direction. Readings were taken of the
load and the strains in the L, R, and T directions at
intervals of 50 microstrain in the L direction to a maximum of
600 microstrain.

When loading in the R and T directions, the compression
cage was suspended from a steel frame by a universal joint and
weights applied to a hanger suspended from the bottom of the
cage through another universal joint (Figure 8). 'The load*was
applied by placing 10 pound weights on the hanger in
succession until 100 pounds had been loaded. The total time
of loading was kept under 2 minutes in order to limit any
effect creep might have on the strain. Time of loading was
not considered. as critical for specimens loaded in. the
longitudinal direction, as there is very little apparent
relationship between strain rate and EL at the stress levels
tested (Sliker 1973). To measure the small strains in the L
direction when loading in the R and T directions, the
sensitivity of the strain indicator was increased by setting
the gage factor from 2.05 to 0.205, which allowed measurements
of strain down to 0.1 microstrain. Shielded cables connected
the gages in the L direction to the strain indicator in order
to minimize the noise to signal ratio (Sliker 1989). Readings
of the load and the strains parallel and perpendicular to the

load were recorded at zero load and at 10 pound intervals

20

until a maximum load of 100 pounds was reached.

ST ISTICAL ROCEDURES

The compliance Sij can be calculated by multiplying the
slope of the strain versus load line of a specimen by the
cross-sectional area of the specimen. Least squares
regression analysis of the strain and load data collected
during testing was used to determine the slopes needed to
calculate the compliances SLL, SRL, STL, SRR, STR, SLR, Sm, SLR,
and SM. The moduli of elasticity EL, ER, and ET were
calculated by regression analysis as the slope of the stress
versus strain line, where the stress and strain are in the
same direction. Poisson’s ratios were calculated as the slope
of the strain.perpendicular to the load axis versus the strain
parallel to the load axis line. To conform with more
traditional practices the signs of the compliances and moduli
of elasticity are reversed, ie SLL, Saar STT, EL, ER, and ET
are shown as positive even though they were determined from
compressive strains. While the elastic limits of wood differ
significantly in tension and compression the moduli of
elasticity are approximately equal (Kollmann and Cote 1968).

If linear relationship are to be found between pairs of
compliances it must first be determined if the compliances
vary from tree to tree. .An analysis of variance was preformed
on each compliance, modulus of elasticity, and Poisson's ratio

in order to determine if they varied among the trees tested.

21

In addition a Fisher’s protected least significant difference
(FPLSD) analysis was preformed on the compliances and elastic
constants that were found to differ significantly from tree to
tree. This procedure was used to determine if the trees
tested could be divided into groups which did not
significantly differ from each other in a particular
compliance or constant tested.

Once all the compliances were found to differ among the
trees tested, regression analysis was used to determine the
best fit linear equation describing the relationships between
pairs of compliances for a given direction of loading (L, R,
or T). An analysis of variance (ANOVA) was done on each
equation in order to determine its significance. Additionally
a t-test was preformed on the constant and slope coefficients
in each equation to determine if they varied significantly
from zero.

For equations that were found to be significant and where
the intercept coefficient is significant, predictive equations
were obtained for Poisson’s ratio by dividing both sides of
the equation by the compliance Sjj. Poisson’s ratio can be
determined by the quotient of compliances Sij/Sjj. For non-
significant equations and equations where the intercept did
not differ significantly from zero this term would be a
constant and the best estimate of Poisson's ratio would be the

average value determined during testing.

22

T-tests were then performed to determine if the equations
found to be significant in this study differed significantly
from equation (2) developed by Sliker (1985, 1988, and 1989),
and the equation (3) determined by Yu (1991). A t-test was
also used to test if the reciprocal relationship Sij = 531 of
orthotropic materials held true for the eight trees tested.
Regression analysis was then used on the reciprocal
relationships SLR and SRL, Sm. and Sn, and SM and Sm, in
order to determine if linear relationships existed between the
compliances. An ANOVA was preformed to determine the
significance of the equation and a t-test preformed to
determine if the constant and slopes varied significantly from

their theoretical values.

23

RESULTS

The compliances, moduli of elasticity, and Poisson's
ratios calculated from test data are presented in Tables 2
through 19. Also listed in Tables 2 through 19 are the mean
values and coefficients of variability (CV) for the measured
values of the constants for each tree tested. The CV ranged
from a low of 0.074 % for the compliance STL measured for BA2
to a high of 31.5 % for Poisson's ratio measured for WA2, with
the average value being 4.75%. The analysis of variances
between trees for each constant are also presented in Tables
2 through 19.

The analysis of variance showed that the compliances SnL,
SRL, Sn, Saar Sm, SLR, Sm, SM, and Sm. varied significantly
between trees at the 99% level. The modulus of elasticity EL,
ER, and ET along with the um, um, and uTL also showed
significant variance between trees at the 99% level. um.
varied between trees at the 95% level, and uLR and um. were not
found to differ between the trees tested even at the 50%
level. The results of the FPLSD analysis are presented in
Tables 20 through 24. The FPLSD analysis of the compliance
SLL showed the following groups of trees did not differ from
each other at the 95% level: WAL and BCl, BCl and BA2, WAl WA2
BA1 and COT1, WA2 BA1 COT1 and HMl. Similar groupings were

found for the other constants.

24
Since all the compliances significantly differed between
the trees tested, the following linear equations were

developed describing the relationship between pairs of

compliances:
EQUATION CORRELATION COEF
1. SRL = 0.0299440“6 - 0.429 sLL R2 = 0.928
2. sTL = 0.0152*10‘5 - 0.461 sLL R2 = 0.921
3. sTR = 1.79*10’5 - 1.15 sRR R2 = 0.962
4. sLR = -0.247*10’5 - 0.00767 S” R2 = 0.124 (4)
5. SM. = O.089*10'6 - 0.338 Sm. R2 = 0.971
6. sLT = -0.291*10“5 - 0.00648 sTT R2 = 0.359

Units for the compliances Sij are strain (inch per inch) per
unit stress (psi). Plots of the regression lines and
compliances are given in Figures 9 through 14. The analysis
of variance and the results of the t-test of the constants for
the above equations are shown in Table 25. Equations 1, 2, 3,
and 5 in Table 25 were found to be significant at the 99%
level. Equation 6 of Table 25 was significant at the 75%
level and equation 4 of Table 25 was not found to be
significant at the 75% level. The slopes of the equations 1,
2, 3, and 5 Table 25 were found to be significant at the 99%
level. The slope of the equation 6 Table 25 was significant
at the 80% level and the slope of the equation 4 Table 25 was

significant at the 40% level. Intercept coefficients of

25
equations 4, and 6 Table 25 were found to be significant at
the 99% level. The intercept of the equation 3 Table 25 was
significant at the 98% level. The intercepts of equations 1,
2, and 5 Table 25 were not found to be significant at the 90%
level.

As Poissons’s ratio can be written as the ratio of
compliances, the significance of intercepts in the equations
3, 4, and 6 Table 25 allows the use of these equations to
create predictive equations for um, um, and on. By dividing

both sides of equation 3 Table 25 by SRR it becomes:

STR/SRR = 1.79810‘5/5RR - 1.15 = 03.1..

Equations 4 and 6 were found to be non-significant as a result
the validity of this procedure on these equations is
questionable. A better estimate of on and on would be their
average values of 0.597 and 0.0375 respectively. The
intercepts of the equations 1, 2 and 5 in Table 25 were not
found to be significant. The best estimation of the 0L3, our,
and uTR would then be their average values of 0.376, 0.438,
and 0.332 respectively.

The results of the t-test comparing the equations found
in this study with those developed by Sliker (1985, 1988, and
1989) and Yu (1990), are shown in Table 26. Only equation 3
in Table 26 STR = f(san) was found to differ at the 80% level

from the equations developed by Sliker. The other equations

26

did not differ significantly from Sliker’s at. the 90 % level.
Similarly equation 3 in Table 26 was the only equation found
to differ from those found by Yu (1990) at the 80% level.

The t-test (Table 27) of the reciprocal compliances found
that the compliances Sm. and STR did not differ significantly
from each other. Since the compliances SRT and STR do not
differ significantly from each other equations 3 and 5 of
equation (3) can be combined to form a an equation relating
compliance SRR to the compliance STT. The resulting equation

is:

_ -6
sRR — 1.479*10 + 0.294 8.1.1.

The results of the t-test comparing the slope of this equation
to the slope of the equation developed by Sliker (1988) are
found in Table 28. No significant difference was found
between the slopes of the two equations. The compliances SLR
and SR1. differed from each other at the 99% level, the
compliances SLT and STL also differed from each other at the
99% level.

The results of the regression analysis of the reciprocal

compliances Sij = f(Sji) are as follows:

Equation Coefficient of corr.
_ -6 2 _
1. sLR — -0.0866*10 + 0.912 SRL R — 0.565
_ -6 2 _
2. sLT — -0.285*10 + 0.329 sTL R — 0.051 (5)

- -6 2
3. sRT — -0.279*10 + 0.895 sTR R

0.952

27
Plots of the regression line and the compliances along with
the theoretical line are shown in Figures 15 through 17. The
results of the ANOVA (Table 29) show that equations 1 and 3 of
equation (5) are significant at the 95% level. Equation 2 was
not significant at the 75% level. The results of the t-test
(Table 29) of the regression coefficients show that the
constants in equations 1 and 3 of equation (4) do not differ
significantly from the theoretical value of 0. The constant
of equation 2 does differ from the theoretical value at the
90% level. In addition the slope of equation 1 does not
differ significantly for the predicted value of 1. The slopes
of equations 2 and 3 do differ from the predicted values at

the 50% level.

28

SUMMARY AND CONCLUSION

Matched specimens taken from eight trees representing six
hardwood species were tested in compression in the L, R, and
T directions. All testing was done in a room maintained at
68°F and 60% relative humidity, where the specimens had
equalized at between 10% and 12% moisture content. Strains
parallel and perpendicular to the load axis were recorded.
The non-shear compliances were calculated from the strain
readings parallel and perpendicular to the load axis per unit
stress in the loading direction (L, R, or T). From this

information the following conclusions were made.

1. The CV of the measured values of the constants and
compliances varied from 0.074% to 31.5% with the average being
4.75%. WA2 samples tended to have a higher CV then the other
samples tested. White ash being a ring-porous hardwood has a
less homogenous cross-sectional structure then the other,
diffuse-porous or semi-diffuse-porous, species tested. The
differing properties of the earlywood and latewood of white

ash may partly explain the large CV observed.

29
2. The wood from the eight trees examined differed
significantly in their measured compliances and moduli of
elasticity, but not in their Poissons ratio's, when specimens
were loaded in the L direction. The woods examined also
differed significantly in their compliances, moduli of
elasticity, and.Poissons ratio’s when specimens were loaded in
the R and T directions. The relationship between creep and
the rate of loading in the R, and T directions may partly
explain the significant differences between the Poisson's

ratios when loading in the R and T directions.

3. Linear equations relating pairs of compliances were

developed. The equations are as follows:

EQUATION CORRELATION COEF
1. sRL = 0.0299410'6 - 0.429 sLL R2 = 0.928
2. sTL = 0.0152410‘6 - 0.461 sLL R2 = 0.921
3. sTR = 1.79810‘6 - 1.15 sRR R2 = 0.962
4. sLR = -0.247vk10‘6 - 0.00767 SRR R2 = 0.124
5. sRT = 0.089*10'6 - 0.338 sTT R2 = 0.971
6. SLT = -0.291=v:10‘6 - 0.00648 sTT R2 = 0.359

The equations relating SRL and SLL, STL and SLL, STR and $33,
and SRT and STT, were significant at the 90% level, however,
the equations relating SLR and SRR, and SLT and STT were not.

The difficulty in measuring the smaller compliances, SLR and

30
SLT may have partly contributed to the lack of significance in
these equations. The effect of loading rate on the
viscoelastic behavior in the R and T directions may also have
contributed to the lack of linear relationships. Because of
the small number of samples used more testing may be required

to clarify these relationships.

4. The intercept of the linear equations relating SLR and
San, SLT and STT, and STR and SRR were significant. Poisson’s
ratio can be written as the ratio of compliances following

predictive equations were developed:

_ -6
2. vRL = -0.00767*1O'6 / sRR - 0.247
3. mm = -0.00648*10'6 / Sm. - 0.291

The intercepts of the equations relating SRL and SLL, STL and
SLL, and SRT and ST.r were not significant. Thus the ratio
between the compliances becomes a constant. The best estimate
of VLR, vLT, and vTR would be their average values of 0.376,

0.438, and 0.332 respectively.

5. The equations relating the compliances SRL and SLL, STL
and SLL, SLR and SRR, Sm. and SM, and SLT and Sm. did not
differ significantly from those developed by Sliker (1985,

1988, 1989), and Yu (1990). This suggests that the

31
relationships between pairs of compliances found in this study

may exist for a broader range of species then tested.

6. As predicted by orthotropic theory the compliances Sm.
and STR were found not to differ from each other. The
equations relating SRT and SR3, and STR and 8.”, can be
combined and a predictive equation relating SRR and Sm. can be

produced:

_ -6
sRR — 1.479*10 + 0.294 s.rT

This equation is not significantly different from the equation
found by Sliker ( 1988) . The compliances STL and SM, and SRL
and SLR were found to differ from each other. The difficulty
in measuring the smaller compliances may partially explain
this difference. The different viscoelastic behavior of wood
in the L, R, and T direction, and the effect of rate of
loading on the viscoelastic behavior in the R and T directions
may lead to behavior not predicted by linear orthotropic

elastic theory.

32
7. Linear equations were developed relating the compliances

SLR and SRL, 8LT and STL, and SRT and STE.

1. sLR = -O.886*10'6 + 0.917 sRL
2. SLT = -0.285*10‘6 + 0.329 sTL

_ -6
3. sRT — -0.277*10 + 0.895 sTR

Equations 1 and 3 were found to be significant. Equation 2
was not found to be significant at the 90% level. The
intercept and slope of the equation relating SLR and SRL did
not differ significantly from those predicted by linear
orthotropic elastic theory. The intercept of the equation
relating SM. and STR also did not differ significantly from its
theoretical value. However, the slope of the equation did
differ significantly from its predicted value. The highly
linear relationship between these two compliances may partly
explain the significance of this difference. Both the
intercept and the slope of the equation relating SLT and STL
differed significantly from the values predicted by

orthotropic elastic theory.

8. The existence of linear relationships between compliances
can provide engineers and designers with an easier method of

applying orthotropic theory in the design of wood structures.

33
9. Several sources of potential error were present in the
manufacturing and testing of specimens and need to be taken
into account when interpreting the results. During the
manufacturing of specimens tension wood was observed in the
cottonwood and.both of the basswood logs“ The extent to which
this tension wood affected the strain measurements is unknown,
and it should be considered as a possible error source. Human
error in mounting the gages on the specimens may have allowed
some of the gages to be mounted slightly off axis. This would
result in transverse sensitivity errors in the strain
readings. The different viscoelastic properties of wood in
the L, R, and T directions would introduce varying degrees of
error based on variations in the loading rate. The
alternating current used in the lighting and other electrical
equipment in the testing laboratory can cause an interference
in the electrical signals passing through the cables
connecting the specimen and the strain indicators. Human
error must also be considered as various people were involved
in the loading of test specimens and the recording of strain
levels. ‘While in most cases these error were negligible, some
of the smaller measurements, such as those used to determine

SLR and SM, the error involved would be proportionally larger.

34

The results of this testing can not substantiate the
symmetry condition of an.orthotropiC‘materialJ ‘While this may
partially be explained by the difficulty in measuring the
compliances SLR and SLT, and the different viscoelastic
behaviors of wood in the L, R, and T directions may lead to
behavior not predicted by linear orthotropic elastic theory.
The small number of sample tested in this study make firm
conclusions about the orthotropic behavior of wood difficult.
In order to clarify the relationships between compliances
additional testing on a broader range of species needs to be
undertaken. Additionally, testing needs to be done on the
viscoelastic behavior of wood and its effect on the

relationship between compliances.

35

Table 1. Oven dry specific gravities measured for specimens
made from the eight trees tested.

 

 

 

 

 

 

 

 

 

 

 

SPECIES* Specific gravity
at 0 %HMC

COTTONWOOD (Populus deltoides Sp) 0.48
(COT2)

BASSWOOD (Tilia americana L;) 0.49
(BA1)

BASSWOOD (Tilia americana L;) 0.42
(BA2)

WHITE ASH (Fraxinus species) 0.63
(WAl)

WHITE ASH (Fraxinus species) ‘ 0.61
(WA2)

BLACK CHERRY (Prunus serotina Ehrh.) 0.65
(BCl)

HARD MAPLE (Acer species) 0.75
(ml)

BLACK WALNUT (Juglans nigra LL) 0.54
(WAL)

 

* The number after the abbreviation of the species
designates the log from which specimens were taken.

36

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 2. Estimate of variability between individual
measurements of the compliance SLL.
SPECIMEN sLL MEAN STANDARD CV % MC%
# DEVIATION
COT2-Ll 0.5431"10'6 0.520 0.0314 5.783 10.89
COT2-L2 0.498 10.93
BA1-L1 0.526 0.522 0.0060 1.139 10.20
BA1-L2 0.518 10.20
BA2-Ll 0.676 0.674 0.0028 0.409 10.11
BA2-L2 0.672 10.05
WAl-Ll 0.519 0.545 0.0376 7.250 11.67
WAl-LZ 0.572 11.67
WA2-Ll 0.487 0.540 0.0752 15.454 11.08
WA2-L2 0.593 11.09
BCl-Ll 0.722 0.702 0.0276 3.829 11.33
BCl-L3 0.683 11.33
HMl-Ll 0.461 0.462 0.0016 0.339 11.91
HMl-LZ 0.463 11.91
WAL-L1 0.756 0.756 0.0001 0.020 10.68
WAL-L2 0.755 10.68
ANALYSIS OF VARIANCE
SOURCE DF SS MS F P
m
TREES 7 0.1548 0.0221 20.02 <.001
ERROR 8 0.0088 0.0011
TOTAL 15 0.1636

 

37

Table 3. Estimate of variability between individual

measurements of the compliance SRL.

     
   

SPECIMEN

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

SRL MEAN STANDARD CV % MC%
# DEVIATION
(1/p81)
COTZ-Ll -0.186*10'6 -0.181 0.0064 3.518
10.89 COT2-L2 -0.177
10.93
BA1-Ll -0.174 -0.189 0.0211 11.158 10.20
BA1-L2 -0.204 10.20
BA2-Ll -0.261 -0.244 0.0246 10.079 10.11
BA2-L2 -0.226 10.05
WAl-Ll -0.168 -0.186 0.0252 13.542 11.67
WAl-LZ -0.204 11.67
WA2-L2 -0.185 -0.218 0.0460 21.103 11.08
WA2-L2 -0.250 11.09
BCl-Ll -0.293 —0.276 0.0239 8.664 11.33
BCl-L3 -0.259 11.33
HMl-Ll -0.176 -0.185 0.0119 6.445 11.91
HMl-LZ -0.193 11.91
WAL-L1 -0.293 -0.298 0.0073 2.448 10.68
WAL-L2 —0.303 10.68
ANALYSIS OF VARIANCE
w
SOURCE DF SS MS F
m
TREES 7 0.02921 0.004173 7.20 <.005
ERROR 8 0.00464 0.000580
TOTAL 15 0.03385

38

Table 4. Estimate of variability between individual

measurements of the compliance STL.

   

SPECIMEN

MEAN

 

 

 

 

 

 

 

 

 

 

 

 

 

STL
# DEVIATION .
(1/P31)
COT2“L1 “0.209""10”6 “0.213 0.0067 3.143
10.89
COT2“L2 “0.218 10.93
BA1“L1 “0.245 “0.207 0.0547 2.457 10.20
BA1“L2 “0.168 10.20
BA2“L1 “0.279 “0.280 0.0008 0.296 10.11
BA2“L2 “0.280 10.05
WA1“L1 “0.221 “0.233 0.0168 7.188 11.67
WA1“L2 “0.245 11.67
WA2“L2 “0.229 “0.244 0.0217 8.869 11.08
WA2“L2 “0.259 11.09
BCl“L1 “0.320 “0.301 0.0273 9.067 11.33
BCI“L3 “0.282 11.33
HM1“L1 “0.218 “0.220 0.0029 1.334 11.91
HM1“L2 “0.222 11.91
WAL“L1 “0.339 “0.346 0.0110 3.168 10.68
WAL“L2 “0.354 10.68
m
ANALYSIS OF VARIANCE
SOURCE OF SS MS F P
m
TREES 7 0.03398 0.004855 8.47 < 0.005
ERROR 8 0.00459 0.000573
TOTAL 15 0.03857

39

Table 5. Estimate of variability between individual
measurements of the modulus of elasticity EL.

   

SPECIMEN EL MEAN STANDARD CV % MC%

 

 

 

 

 

 

 

# (psi) DEVIATION
m
COT2“L1 1843000 1924500 115258 5.989 10.89
COT2“L2 2006000 10.93
BA1-L1 1899000 1933500 48790 2.523 10.20
BA1-L2 1968000 10.20
BA2-L1 1479000 1483500 6364 0.429 10.11
BA2-L2 1488000 10.05
WAl-Ll 1923000 1836000 123037 6.701 11.67
WA1“L2 1749000 11.67
WA2-L2 2055000 1870500 260922 13.949 11.08
WA2-L2 1686000 11.09
BC1-L1 1385000 1424500 55861 3.921 11.33
BCl-L3 1464000 11.33
HMl-Ll 2170000 2164500 7778 0.359 11.91
HMl-LZ 2159000 11.91
WAL-L1 1323000 1323500 707 0.053 10.68

 

 

TREES 7 1.233*1012 1.762*1011 13.8 < 0.001

 

ERROR 8 1.021*1011 1.276*101°
TOTAL," 15 1.335*1012

 

   

40

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 6. Estimate of variability between individual
measurements of the Poisson's ratio uLR.
SPECIMEN ”LR MEAN STANDARD CV % MC %

# DEVIATION
m
COT2-L1 0.303 0.329 0.0368 11.200 10.89
COT2-L2 0.355 10.93
BA1-L1 0.331 0.367 0.0501 13.663 10.20
BA1-L2 0.402 10.20
BA2-L1 0.386 0.362 0.0350 9.665 10.11
BA2-L2 0.337 10.05
WAl-Ll 0.324 0.340 0.0226 6.658 11.67
WA1-L2 0.356 11.67
WA2-L2 0.381 0.402 0.0292 7.276 11.08
WA2-L2 0.422 11.09
BCl-Ll 0.405 0.392 0.0186 4.739 11.33
BCl-L3 0.379 11.33
HMl-Ll 0.383 0.400 0.0244 6.103 11.91
HM1-L2 0.417 11.91
WAL-L1 0.387 0.394 0.0097 2.472 10.68
WAL-L2 0.401 10.68
ANALYSIS OF VARIANCE
= w

SOURCE DF SS MS F P
m
TREES 7 0.008260 0.001180 1.53 > 0.25
ERROR 8 0.006159 0.000770

 

"TOTAL 15 0.014420

     

41

Table 7. Estimate of variability between individual
measurements of the Poisson's ratio 0LT

 

COT2-L1 0.385 0.442 0.0799 18.100 10.89

   

 

 

 

 

 

 

 

COT2-L2 0.498 10.93
BA1-L1 0.466 0.398 0.0956 24.008 10.20
BA1-L2 0.331 10.20
BA2-L1 0.413 0.415 0.0029 0.702 10.11
BA2-L2 0.417 10.05
WAl-Ll 0.426 0.427 0.0013 0.301 11.67
WA1-L2 0.428 11.67
WA2-L2 0.470 0.454 0.0231 5.099 11.08
WA2-L2 0.438 11.09
BCl-L1 0.444 0.428 0.0220 5.140 11.33
BC1-L3 0.413 11.33
HMl-Ll 0.473 0.476 0.0044 0.922 11.91
HM1-L2 0.479 11.91
WAL-L1 0.448 0.459 0.0146 3.192 10.68
WAL-L2 0.469 10.68

   

ANALYSIS OF VARIANCE

 

 

SOURCE DF_ 88 MS F P
TREES 7 0.00886 0.00127 0.60 > 0.25
ERROR 8 0.01674 0.00209

 

TOTAL_ 15 0.02560

 

42

Table 8. Estimate of variability between individual

measurements of the compliance SRR.

 

SPECIMEN SRR

 

 

 

 

 

 

 

MEAN
# DEVIATION
(1/psi)
COT2-R1 5.831810"6 5.739 0.166 2.892
10.99
COTz-Rz 5.907 10.99
COTZ-R3 5.689 10.99
COT2-R4 5.530 10.99
BA1-R1 8.132 8.068 0.125 1.549 10.32
BA1-R2 7.882 10.21
BA1-R3 8.143 10.26
BA1-R4 8.115 10.28
BA2-R1 9.639 10.006 0.628 6.276 10.14
BA2-R2 9.340 10.15
BA2-R3 10.334 10.17
BA2-R4 10.711 10.17
WAl-Rl 3.842 4.118 0.239 5.804 11.72
WAl-RZ 3.995 11.72
WA1-R3 4.293 11.72
WA1-R4 4.341 11.74
WA2-R1 3.413 4.675 0.873 18.674 11.19
WA2-R2 5.024 11.12
WA2-R3 4.853 11.15
WA2-R4 5.409 11.15
BCl-Rl 3.464 3.558 0.065 1.827 11.38
BCl-R2 3.565 11.38
BCl-R3 3.609 11.39
BCl-R4 3.593 11.39
HMl-Rl 3.233 3.266 0.039 1.194 11.97
HMl-RZ 3.232 11.97
HM1-R3 3.303 11.98
HMl-R4 3.295 11.98
WAL-R3 3.902 3.776 0.091 2.410 10.66
WAL-R4 3.773 10.60
WAL-R1 3.687 10.67
WAL-R2 3.743 10.67

W

43

Table 8 (cont’d)

 

SOURCE DF SS MS F P
TREES 7 164.817 23.545 148.28 < .001
ERROR 24 3.811 0.159

TOTAL 31 168.628

 

 

44

 

 

 

 

 

 

 

 

 

 

 

 

Table 9. Estimate of variability between individual
measurements of the compliance STR.
SPECIMEN STR MEAN STANDARD CV % MC%
# DEVIATION
(1/951)

COT2-R1 -5.365*10‘6 -5.344 0.0303 0.567

10.99

COT2-R2 -5.322 10.99
BA1-R1 -6.333 -6.387 0.0764 1.195 10.32
BA1-R2 -6.441 10.32
BA2-R1 -9.592 -9.745 0.2171 2.228 10.14
BA2-R2 -9.899 10.15
WA1-R1 -2.336 -2.428 0.1297 5.345 11.72
WA1-R2 -2.519 11.72
WA2-R1 -3.118 -3.018 0.1416 4.690 11.19
WA2-R2 -2.918 11.12
BCl-Rl -2.369 -2.443 0.1045 4.277 11.38
BCl-RZ -2.516 11.38
HMl-Rl -2.275 -2.293 0.0264 1.152 11.97
HMl-RZ -2.312 11.97
WAL-R3 -2.272 -2.285 0.0183 0.800 10.66
WAL-R4 -2.298 10.60

ANALYSIS OF VARIANCE

SOURCE DF SS MS F P
m
TREES 7 103.4366 14.7767 1198.08 < 0.001
ERROR 8 0.0987 0.0123

TOTAL 15 103.5353

45

Table 10. Estimate of variability between individual
measurements of the modulus of elasticity ER.

 

COT2-R1 171000 174250 5377 3.086 10.99

   

 

 

 

 

 

 

 

COT2-R2 169000 10.99
COT2-R3 176000 10.99
COT2-R4 181000 10.99
BA1-R1 123000 124000 2000 1.613 10.32
BA1-R2 127000 10.21
BA1-R3 123000 10.26
BA1-R4 123000 10.28
BA2-R1 104000 100250 6397 6.381 10.14
BA2-R2 107000 10.15
BA2-R3 97000 10.17
BA2-R4 93000 10.17
WAl-Rl 260000 243250 14221 5.846 11.72
WA1-R2 250000 11.72
WAl-R3 233000 11.72
WAl-R4 230000 11.74
WA2-R1 293000 220500 49197 22.311 11.19
WA2-R2 199000 11.12
WA2-R3 206000 11.15
WA2-R4 184000 11.15
BCl-Rl 287000 280500 4509 1.607 11.38
8C1-R2 280000 11.38
BCl-R3 277000 11.39
BCl-R4 278000 11.39
HMl-Rl 309000 306000 3464 1.132 11.97
HMl-RZ 309000 11.97
HMl-R3 303000 11.98
HMl-R4 303000 11.98
WAL-R3 256000 264750 6344 2.396 10.66
WAL—R4 265000 10.60
WAL-R1 271000 10.67
WAL-R2 267000 10.67

46

Table 10 (cont’d)

ANALYSIS OF VARIANCE

 

SOURCE OF SS Ms F p
m
TREES 7 1.559*1011 2.227*101° 64.35 < .001
ERROR 24 8.307*109 3.461*108

 

TOTAL 31 1.642*1011

     

47

Table 11. Estimate of variability between individual
measurements of the Poisson's ratio uRT.

   

SPECIMEN “RT MEAN STANDARD CV % MC%

     

 

 

 

 

 

 

 

COT2-R1 0.920 0.911 0.0135 1.487 10.99
COT2-R2 0.901 10.99
BA1-R1 0.779 0.798 0.0274 3.435 10.32
BA1-R2 0.818 10.21
BA2-R1 0.995 1.027 0.0457 4.451 10.14
BA2-R2 1.060 10.15
WA1-R1 0.614 0.622 0.0119 1.917 11.72
WA1-R2 0.631 11.72
WA2-R1 0.914 0.747 0.2355 31.510 11.19
WA2-R2 0.581 11.12
BC1-R1 0.684 0.695 0.0156 2.245 11.38
BC1-R2 0.706 11.38
HMl-Rl 0.704 0.709 0.0080 1.135 11.97
HMl-R2 0.715 11.97
WAL-R3 0.582 0.596 0.0189 3.166 10.66

0.29700

 

 

0.05931

0.00741

 

 

48

 

         

 

 

 

 

 

 

 

Table 12. Estimate of variability between individual
measurements of the compliance SLR.
SPECIMEN SLR MEAN STANDARD CV % MC%
# DEVIATION
COT2-R3 —0.2331|*10"6 -0.245 0.0168 6.831
10.99
COT2-R4 -0.257 10.99
BA1-R3 -0.260 -0.264 0.0056 2.113 10.26
BA1-R4 -0.268 10.28
BA2-R3 -0.353 -0.361 0.0106 2.936 10.17
BA2-R4 -0.368 10.17
WA1-R3 -0.218 -0.219 0.0010 0.472 11.72
WA1-R4 -0.219 11.74
WA2-R3 -0.339 -0.344 0.0075 2.187 11.15
WA2-R4 —0.349 11.15
BC1-R3 -0.340 -0.310 0.0419 13.505 11.39
BC1-R4 -0.281 11.39
HM1-R3 -0.230 -0.234 0.0051 2.199 11.98
HM1-R4 -0.237 11.98
WAL-R1 -0.341 -0.337 0.0062 1.836 10.67
WAL-R2 -0.333 10.67

 

 

 

==================================E============flfl=é;l-fl-I
TREES 7 0.04303 0.006147 21.57 < 0.001
ERROR 8 0.00228 0.000285

TOTAL 15 0.04531

49

Table 13. Estimate of variability between individual
measurements of the Poisson's ratio URL.

 

SPECIMEN “RL MEAN STANDARD CV % MC %

   

 

 

 

 

 

 

 

.“__t______________1___1__ __DEVIATION _W _ _ 3
COT2-R3 0.0410 0.044 0.0039 8.810 10.99
COT2-R4 0.0465 10.99
BA1-R3 0.0320 0.033 0.0008 2.370 10.26
BA1-R4 0.0331 10.28
BA2-R3 0.0341 0.035 0.0019 5.224 10.17
BA2-R4 0.0368 10.17
WA1-R3 0.0508 0.051 0.0002 0.321 11.72
WA1-R4 0.0506 11.74
WA2-R3 0.0698 0.067 0.0039 5.835 11.15
WA2-R4 0.0643 11.15
BC1-R3 0.0942 0.086 0.0114 13.195 11.39
BC1-R4 0.0781 11.39
HM1-R3 0.0697 0.071 0.0017 2.365 11.98
HM1-R4 0.0721 11.98
WAL-R1 0.0926 0.091 0.0026 2.914 10.67
WAL-R2 0.0889 10.65

 

 

 

TREES 7 0.007181 0.001026 48.56 < 0.001
ERROR 8 0.000169 0.000021
TOTAL 15 0.007350

   

 

 

 
 
 

50

 

 

Table 14. Estimate of variability between individual
measurements of the compliance STT.
— 5 ~~~ :- um
SPECIMEN STT MEAN STANDARD CV % MC%
# DEVIATION

   

COT2-T1

 

 

 

 

 

 

 

17.217410"6 17.836 0.507 2.842 10.99
COT2-T2 17.636 11.00
COT2-T3 18.321 10.89
C0T2-T4 18.171 10.98
BA1-T1 21.213 20.853 0.861 4.129 10.16
BA1-T2 21.787 10.16
BA1-T3 20.648 10.24
BA1-T4 19.765 10.21
BA2-T3 23.062 22.323 1.355 6.070 10.14
BA2-T4 23.840 10.14
BA2-T1 21.434 10.11
BA2-T2 20.956 10.08
WAl-Tl 6.278 6.438 0.113 1.755 11.72
WA1-T2 6.439 11.72
WA1-T3 6.522 11.65
WA1-T4 6.515 11.70
WA2-T1 7.186 7.137 0.169 2.638 11.14
WA2-T2 7.163 11.20
WA2-T3 6.900 11.10
WA2-T4 7.297 11.10
BCl-Tl 8.282 8.156 0.202 2.477 11.42
BC1-T2 8.245 11.42
BC1-T4 7.854 11.30
BC1-T8 8.243 11.30
HMl-Tl 5.934 6.109 0.143 2.341 12.00
HMl-TZ 6.215 11.96
HM1-T3 6.235 11.88
HMl-T4 6.051 11.88
WAL-T3 8.107 8.353 0.216 2.586 10.65
WAL-T4 8.292 10.65
WAL-Tl 8.627 10.59
WAL-T2 8.388 10.59

 

51

Table 14 (cont'd)

 

 

TREES 7 1344.760 192.109 515.23 < .001
ERROR 24 8.949 0.373

   

 

 

 

52

 

   

 

 

 

 

 

 

 

     

86.9541

4713.00

Table 15. Estimate of variability between individual
measurements of the compliance SET.
SPECIMEN SRT MEAN STANDARD CV % MC %
f DEVIATION
__ WW _

COTZ-Tl --5.0441"10'6 -5.031 0.0183 0.365 10.99
COT2-T2 -5.018 11.00
BA1-T1 -7.l47 -7.182 0.0502 0.699 10.16
BA1-T2 -7.218 10.16
BA2-T3 -8.386 -8.390 0.0063 0.074 10.14
BA2-T4 -8.395 10.14
WAl-Tl -2.152 -2.168 0.0231 1.066 11.72
WAl-TZ -2.184 11.72
WA2-T1 -2.722 -2.729 0.0102 0.375 11.14
WA2-T2 -2.736 11.20
BCl-Tl -2.341 -2.330 0.0166 0.711 11.42
BC1-T2 -2.318 11.42
HMl-Tl -2.069 -2.153 0.1193 5.541 12.00
HMl-TZ -2.237 11.96
WAL-T3 -2.668 -2.628 0.0564 2.147 10.65

 

 

 

TREES 7 12.4220
ERROR 8 0.0211 0.0026
TOTAL 15 ° 86.9752

   

 

53

 

 

 

 

 

 

 

 

 

Table 16. Estimate of variability between individual
measurements of the modulus of elasticity ET.
SPECIMEN ET MEAN STANDARD CV % MC %
# (psi) DEVIATION

COT2-T1 57900 56050 1533 2.735 10.99
COT2-T2 56700 11.00
COT2-T3 54600 10.89
COT2-T4 55000 10.98
BA1-T1 47100 48000 2012 4.192 10.16
BA1-T2 45900 10.16
BA1-T3 48400 10.24
BA1-T4 50600 10.21
BA2-T3 43400 44900 2707 6.029 10.14
BA2-T4 41900 10.14
BA2-T1 46600 10.11
BA2-T2 47700 10.08
WA1-T1 159300 155350 2783 1.791 11.72
WA1-T2 155300 11.72
WA1-T3 153300 11.65
WA1-T4 153500 11.70
WA2-T1 139200 140175 3351 2.391 11.14
WA2-T2 139600 11.20
WA2-T3 144900 11.10
WA2-T4 137000 11.10
BC1-T1 120700 122650 3113 2.538 11.42
BC1-T2 121300 11.42
BC1-T4 127300 11.30
BC1-T8 121300 11.30
HM1-T1 168500 163725 3860 2.358 12.00
HM1-T2 160900 11.96
HM1-T3 160300 11.88
HM1-T4 165200 11.88
WAL-T3 123300 119750 3080 2.572 10.65
WAL-T4 120600 10.65
WAL-T1 115900 10.59
WAL-T2 119200 10.59

 

 

54

Table 16 (cont'd)

 

 

ERROR 24 2.003*108 8.345*106

 

TOTAL 31 6.817*101°

 

 

   

55

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 17. Estimate of variability between individual
measurements of the Poisson’s ratio UTR.
SPECIMEN uTR MEAN STANDARD CV % MC %
_# DEVIATION
COT2-T1 0.292 0.288 0.0053 1 837 10.99
COT2-T2 0.285 11.00
BA1-T1 0.337 0.334 0.0040 1 185 10.16
BA1-T2 0.331 10.16
BA2-T3 0.364 0.358 0.0081 2 270 10.14
BA2-T4 0.352 10.14
WA1-T1 0.343 0.341 0.0025 0 730 11.72
WA1-T2 0.339 11.72
WA2-T1 0.379 0.380 0.0023 0 606 11.14
WA2-T2 0.382 11.20
BC1-T1 0.283 0.282 0.0011 0.389 11.42
BC1-T2 0.281 11.42
HMl-Tl 0.349 0.354 0.0080 2.267 12.00
HM1-T2 0.360 11.96
WAL-T3 0.329 0.321 0.0120 3.734 10.65
WAL-T4 0.312 10.65
E
ANALYSIS OF VARIANCE
SOURCE DF SS MS F P
========
TREES 7 0.01629 0.002327 55.73 < 0.001
ERROR 8 0.00033 0.000042
TOTAL 15 0.01662

56

Table 18. Estimate of variability between individual

measurements of the compliance SLT.

   

SPECIMEN 8LT

 

 

 

 

 

 

 

 

# DEVIATION
(1/P81)
C0T2-T3 -0.3221Ir1o'6 -0.343 0.0286 8.343 10.89
COT2-T4 -0.363 10.98
BA1-T3 -0.420 -0.411 0.0135 3.289 10.24
BA1-T4 -0.401 10.21
BA2-T1 -0.487 -0.486 0.0008 0.170 10.11
BA2-T2 -0.486 10.08
WAl-T3 -0.422 -0.413 0.0137 3.323 11.65
WAl-T4 -0.403 11.70
WA2-T3 -0.266 -0.281 0.0204 7.254 11.10
WA2-T4 -0.295 11.10
BCl-T4 -0.377 -0.384 0.0091 2.380 11.30
BC1-T8 -0.390 11.30
HM1-T3 -0.284 -0.270 0.0195 7.202 11.88
HM1-T4 -0.257 11.88
WAL-T1 -0.360 -0.363 0.0045 1.235 10.59
WAL-T2 -0.367 10.59
m
ANALYSIS OF VARIANCE
M
SOURCE DF SS MS F P
m
TREES 7 0.071795 0.010256 39.15 < 0.001
ERROR 8 0.002096 0.000262

 

TOTAL 15 0.073891

w

57

Table 19.

Estimate of variability between individual
measurements of the Poisson's ratio UTL.

 

SPECIMEN

   

 

 

 

 

 

 

 

 

 

 

 

 

UTL MEAN
# __ DEVIATION
COT2-T3 0.0176 0.019 0.0017 8.961 10.89
COT2-T4 0.0200 10.98
BA1-T3 0.0203 0.020 0.0000 0.174 10.24
BA1-T4 0.0203 10.21
BA2-T1 0.0227 0.023 0.0003 1.449 10.11
BA2-T2 0.0232 10.08
WA1-T3 0.0647 0.063 0.0021 3.240 11.65
WA1-T4 0.0618 11.70
WA2-T3 0.0386 0.040 0.0013 3.273 11.10
WA2-T4 0.0405 11.10
BC1-T4 0.0480 0.048 0.0005 1.008 11.30
BC1-T8 0.0474 11.30
HM1-T3 0.0456 0.044 0.0022 5.063 11.88
HM1-T4 0.0424 11.88
WAL-T1 0.0417 0.043 0.0014 3.244 10.59
WAL-T2 0.0437 10.59
ANALYSIS OF VARIANCE
SOURCE DF SS MS F P
w
TREES 7 0.0034224 0.0004889 223.51 < 0.001
ERROR 8 0.0000175 0.0000022
TOTAL 15 0.0034399 .

58

 

 

 

 

 

Table 20. Fisher's protected least significant difference
test of the mean values of the compliances and
modulus of elasticity for specimens loaded in the
L direction.
TREE SLL TREE EL
(llpsi) (psi)
WAL 0.7555*10’6 .A * HM 1 2164500 A
BC 1 0.7025 AB BA 1 1933500 AB
BA 2 0.6740 B COT 1 1924500 AB
WA 1 0.5455 C WA 2 1870500 B
WA 2 0.5400 CD WA 1 1836000 B
BA 1 0.5220 CD BA 2 1483500 C
COT 1 0.5205 CD BC 1 1424500 C
HM 1 0.4620 D WAL 1323500 C
FPLSD = 0.0707 FPLSD = 240718

= 1 m
TREE SRL TREE STL

(1/psi) (1/P_1________A _ _
COT 1 -0.18151"10'6 A. BA 1 "0.2065410"6 A
HM 1 -0.1845 A COT 1 -0.2135 A
WA 1 -0.1860 A HM 1 -0.2200 A
BA 1 -0.1890 A WA 1 -0.2330 AB
WA 2 -0.2175 AB WA 2 -0.2440 AB
BA 2 -0.2435 BC BA 2 -0.2795 BC
BC 1 -0.2760 CD BA 1 -0.3010 BCD
WAL -0.2980 D WAL -0.3465 D

FPLSD = 0.0513 FPLSD = 0.0510

mm

 

* means with the same letter within the same column are not
significantly different from each other at the 95%

probability level.

59

Table 21. Fisher’s protected least significant difference
test of the mean values of the compliances,
modulus of elasticity, and Poisson’s ratio for
specimens loaded in the R direction and with the
lateral strain measured in the T direction.

 

 

 

 

 

 

1 __1PS____*___ -__3_ __1_A. _ _
BA 2 9.4900810”6 .A * HM 1 309000 A
BA 1 8.0070 B BC 1 284500 AB
COT 1 5.8690 c WAL 260500 AB
WA 2 4.2190 D WA 1 255000 B
WA 1 3.9180 DE WA 2 246000 8
WAL 3.8380 DE COT 1 170000 C
BC 1 3.5150 DE BA 1 125000 CD
HM 1 3.2330 E BA 2 105500 D
FPLSD = 0.8915 FPLSD = 50896
TREE STR TREE om.
WAL -2.2850*10‘5 .A BA 2 1.0275 A
HM 1 -2.2935 A COT 1 0.9105 AB
WA 1 -2.4385 A BA 1 0.7985 BC
BC 1 -2.4425 A WA 2 0.7475 BCD
WA 2 -3.0180 B HM 1 0.7095 CD
COT 1 -5.3435 C BC 1 0.6950 CD
BA 1 -6.3870 D WA 1 0.6225 CD
BA 2 -9.7455 E WAL 0.5955 D
FPLSD = 0.2363 FPLSD = 0.1834
m

 

* means with the same letter within the same column are not
significantly different from each other at the 95%
probability level.

60

Table 22. Fisher's protected least significant difference

test of the mean values of the compliances,

modulus of elasticity, and Poisson’s ratio for
specimens loaded in the R direction and with the

lateral strain measured in the L direction.

 

TREE

            

 

 

 

BA 2 10.5230"‘10'6 .A * HM 1 303000 A
BA 1 8.1290 B BC 1 277500 B
COT 1 5.6090 C WAL 269000 B
WA 2 5.1310 D WA 1 231500 C
WA 1 4.3170 E WA 2 195000 D
WAL 3.7150 FG COT 1 178500 E
BC 1 3.6010 GH BA 1 123000 F
HM 1 3.2990 H BA 2 95000 G
FPLSD = 0.3703 FPLSD = 12505

 

I

TREE SLR TREE uRL
(1/psi)

WA 1 -0.2185*10'6 .A WAL 0.0910 A
HM 1 -0.2335 AB BC 1 0.0860 A
COT 1 -0.2450 AB HM 1 0.0710 B
BA 1 -0.2640 B WA 2 0.0670 B
BC 1 -0.3105 C WA 1 0.0510 C
WAL -0.3370 CD COT 1 0.0435 CD
WA 2 -0.3440 CD BA 2 0.0340 DE
BA 2 -0.3605 D BA 1 0.0325 E

 

 

FPLSD = 0.0360

FPLSD = 0.0098

 

* means with the same letter within the same column are not
significantly different from each other at the 95%
probability level.

61

Fisher’s protected least significant difference

test of the mean values of the compliances,

modulus of elasticity, and Poisson’s ratio for
specimens loaded in the T direction and with the
lateral strain measured in the R direction.

Table 23.
TREE STT
___1___J}£B§£L_L_

BA2 23.4510*10‘6
BA 1 21.5000
COT 1 17.4260

BC 1 8.2640
WAL 8.2000

WA 2 7.1740

WA 1 6.3590

HM 1 6.0750

MMMUUOCD

HM 1
WA 1
WA 2
WAL
BC 1
COT 1
BA 1
BA 2

E.r

XPS£11._C_

164700
157300
139400
121950
121000
57300
46500
42650

"d'IJMUDOwV

 

FPLSD = 0.5959

 

FPLSD = 4961

 

TREE sRT

(l/psi)

 

HM 1 --2.1530=Ir10"6 .A WA 2 0.3805 A
WA 1 -2.1680 A BA 2 0.3580 B
8C 1 -2.3295 B HM 1 0.3545 BC
WAL -2.6280 C WA 1 0.3410 CD
WA 2 -2.7290 c BA 1 0.3340 DE
COT 1 -5.0310 D WAL 0.3205 E
BA 1 -7.1825 E COT 1 0.2885 F
BA 2 -8.3905 G BC 1 0.2820 F
FPLSD = 0.1095 FPLSD = 0.0138

 

 

* means with the same letter within the same column are not

significantly different from each other at the 95%
probability level.

62

Table 24. Fisher's protected least significant difference
test of the mean values of the compliances,
modulus of elasticity, and Poisson's ratio for
specimens loaded in the R direction and with the
lateral strain measured in the L direction.

 

 

 

 

 

 

BA 2 21.1950*10’5 .A * HM 1 162750 A
BA 1 20.2070 B WA 1 153400 B
COT 1 18.2460 C WA 2 140950 c
WAL 8.5070 D BC 1 124300 D
BC 1 8.0490 D WAL 117550 F
WA 2 7.0990 E COT 1 54800 G
WA 1 6.5180 EF BA 1 49500 GH
HM 1 6.1440 F BA 2 47150 H
FPLSD = 0.6375 FPLSD = 6294
TREE SLT TREE an
____1_1__11_1_111___111 _ 1 1 1 1 1
HM 1 -0.2705*10‘5 .A WA 1 0.0635 A
WA 2 -0.2805 A BC 1 0.0475 B
COT 1 -0.3425 B HM 1 0.0440 C
WAL -0.3635 BC WAL 0.0430 c
BC 1 -0.3835 CD WA 2 0.0395 D
BA 1 -0.4105 DE BA 2 0.0230 E
WA 1 -0.4125 E BA 1 0.0200 EF
BA 2 -0.4865 F COT 1 0.0190 F
FPLSD = 0.0345 FPLSD = 0.0032

 

* means with the same letter within the same column are not
significantly different from each other at the 95%
probability level.

63

Table 25. Analysis of variance and statistics of slope and
intercept constants for the compliance equations.

 

 

_ -6
EQUATION #1 SRL .- 0.0299*10 - 0.429 SLL
PREDICTOR COEF ST DEV T-RATIO P
m
CONSTANT 0.0299410"6 0.0291410‘6 1.03 < 0.4
SLOPE -0.429 0.04896 —8.77 < 0.002

“WIS 01'" VARLCE _ 1

 
 

     

SOURCE DF SS MS F P

 

REGRESSION 1 10.013549 0.013549 76.98 < 0.001
ERROR 6 0.001057 0.000176
TOTAL 7 0.014606
w
EQUATION #2 STL = 0.0152*10‘5 - 0.461 SLL
m
PREDICTOR COEF ST DEV T-RATIO P
a
CONSTANT 0.0152410‘6 0.03285*10'6 0.46 < 0.6

 

SLOPE _f0.461 0.05523 -8.35 < 0.002

 

 

SOURCE DF SS MS F P

w
REGRESSION 1 0.015645 0.015645 69.84 < 0.001
ERROR 6 0.001346 0.000224
TOTAL 7 0.016991

* Units for the compliances Sij are strain (inch/inch) per
unit stress (psi).

64

Table 25 (cont’d)

EQUATION #3 sTR := 1.79410"6 - 1.15 SRR

 

 

PREDICTOR COEF ST DEV _ T-RATIO P

   

CONSTANT 1.79810“6 0.5287*10'6 3.38 < 0.02

 

   

SOURCE DF SS MS F‘_ P
REGRESSION 1 49.766 49.766 152.19 < 0.001
ERROR 6 1.959 0.327

 

EQUATION #4 SLR = -0.247*10'6 - 0.00767 SRR

 

CONSTANT “0.24714076 0.05021"'10-6 -4.91 < 0.001

 

 

 

0.00262 0.00262 0.85 > 0.25

   

REGRESSION 1
ERROR 6 0.018852 0.003142
TOTAL 7 0.021515

 

* Units for the compliances Sij are strain (inch/inch) per
unit stress (psi).

65

Table 25 (cont’d)

 

 

EQUATION #5 SRT == 0.089*10‘5 - 0.338 ST.r
PREDICTOR COEF ST DEV T-RATIO P
m
CONSTANT 0.089*10'6 0.3332410‘6 0.27 < 0.8
SLOPE -0.338 0.02371 -14.27 _§ 0.001,

 

 

     

ANALYSIS OF VARIANCE

     

SOURCE DF SS MS F P

 

 

 

m
REGRESSION 1 42.233 42.233 204.02 < 0.001
ERROR 6 1.244 0.207
TOTAL 7 43.477

EQUATION #6 5LT = -0.291*10‘5 - 0.00648 STT
E _
PREDICTOR COEF ST DEV T-RATIO P

w

CONSTANT -0.291*10’5 0.04771810‘6 -6.10 < 0.001

 

 

   

SOURCE DF SS MS F P

m
REGRESSION 1 0.012889 0.012889 3.36 < 0.25
ERROR 6 0.023009 0.003835
TOTAL 7 0.035897

* Units for the compliances Sij are strain (inch/inch) per
unit stress (psi).

66

Table 26. Statistical analysis of the differences between
the slopes of compliance equations developed in
this study and those developed by Sliker, and Yu.

EQUATION #1 SRL = f(SLL)

   

SLOPE T DF T 80% T 90%

 

==============================I=fl====E=======E======I=E===IEII
WEIGEL “0.429

SLIKER “0.429 “0.193 22 1.321 1.717

YU “0.353 “0.551 13 1.350 1.771

           

 

EQUATION #2 STL = f(SLL)

 

SLOPE T DF T 80% T 90%

 

m
WEIGEL -0.461

SLIKER -0.500 0.402 22 1.321 1.717

YU -0.360 0.889 13 1.350 1.771

EQUATION #3 STR = f(SRR)

 

4.

 

SLOPE T DF T 80% T 90%
=========================================================HII
WEIGEL “1.150
SLIKER “0.887 2.414 15 1.341 1.753

YU -0.967 1.613 13 1.350 1.771

67

Table 26 (cont'd)

EQUATION #4 SRT = f(STT)

   

SLOPE T DF T 80% T 90%

 

w
WEIGEL “0.338
SLIKER “0.255 0.526 13 1.350 1.771

YU -0.288 0.332 13_ _1.350- _ 1.771

     

68

Table 27. Comparison of the reciprocal compliances.

 

 

 

 

 

 

 

 

 

Ho SBI = 813
COMPLIANCE n MEAN ST DEV
w
SBI 16 -0.222*10‘5 0.0475410'6
SH 16 -0.2891*10'6 0.055410"6
t = 3.70 DF = 29.4 P = 0.0009

COMPLIANCE n MEAN ST DEV

STL 16 -0.2555410"6 0.0507410”6

 

- * ‘5 t ’5
SE: 16 0.3688 10 0.0702 10

 

69

Table 28. Statistical analysis of the difference between
the slope of the equation relating SRR and STT
developed in this study and the equat1on
developed by Sliker (1988).

 

WEIGEL 0.293
SLIKER 0.291 -0.066 _13 1.350 1.77}

 
 
 

 

 

70

Table 29. Analysis of variance of the regression equation
relating reciprocal compliances and t-test
comparing equations determined in this study with
their theoretical values.

*

Equation 1. sLR := -0.886*10'6 + 0.917 SRL

Analysis of Variance

   

 

 

Source DF SS MS F P

Regression 1 0.012156 0.012156 7.792 < 0.05
Error 6 0.009359 0.00156
Total 7 0.021515

   

t- test comparing predicted values and theoretical values

 

Predictor Coef Theoretical T 1525 T.1
value

Constant 0.0886*10'6 0 -1.1721 0.718

1.440 Slope 0.917 1 -0.268 0.718

1.440

   

71

Table 29 (cont’d)

Equation 2. SLT = -0.285*10’6 + 0.329 sTL

 

 

Source DF “_ SS MS F __ P

   

Regression 1 0.001842 0.001842 0.325 > 0.25
Error 6 0.034055 0.005676
Total 7 0.035897

       

 

Predictor Coef Theoretical T 1125 T 1

 

Constant -0.285*10'6 0 -1.8968 0.718
1.440

 

* Units for the compliances Sijrare strain (inch/inch) per
unit stress (psi).

72

Table 29 (cont’d)

Equation 3. SM = -0.279vlr10‘6 + 0.895 STR

Analysis of Variance

   

Source DF SS MS F P

L

41.402 41.402 119.659

 
   
 

 
 

 

< 0.001

 

Regression 1
Error 6 2.075 0.08177
Total 7 43.477

 

t- test comparing predicted values and theoretical values

 

       

 

Predictor Coef Theoretical T 1125 T.1
value _»_ f _
Constant -0.279avc10‘6 0 -0.7037 0.718
1.440
Slope 0.895 1 -1.298 0.718 1.440
E = —=—====-.—_-=——

 

* Units for the compliances Sij are strain (inch/inch) per
unit stress (psi).

73

 

L type specimen used for
loading in the L direction

 

 

 

 

R 1.25"
/L:‘

 

 

 

 

 

 

 

 

1.25"
R type specimen used for T type specimen used for
loading in the R direction loading in the T direction

Figure 1. Compression samples.

Type B strain gage
/ 1:
2:

 

 

Type A-l gage used
when loading in the

Type A-2 gage used
directions.

Type 8-2 gage used
when loading in the

Figure 2.

74

4"

Type A strain gage

[— ""1 2
l-mil constantan Wire

lZ-mil constantan leads

C. 25"

 

 

 

 

 

 

 

 

 

 

 

 

‘T ““Tn
u_1 11
/ / \

for measuring strains in the L direction
L direction.
the R and T

for measuring strains in

for measuring strains in the L direction
R and T directions.

Gage types and configurations.

75

, v.

4‘ \

 

3.5"

 

 

 

 

 

2" /

 

 

 

 

1: Type A-l gage
2: Type A-Z gage

Figure 3. Gage arrangement for measuring strains when
loading in the L direction.

76

l
I
Y
x

i
R
\HJ

:‘ W‘:

L, __‘_/ ’1

/
r
:1..\ /
.L‘A
A

 

 

 

 

 

 

 

B
1: Type A-2 gage
2: Type B-l gage
A: Used to measure strains in

the R and T directions when
loading in the R direction.

8: Used to measure strains in
the R and L directions when
loading in the R direction.

Figure 4. Gage arrangements for measuring strains when
loading in the R direction.

77

 

 

 

 

 

 

1: Type A—Z gage
2: Type B—l gage

A: Used to measure strains in
the T and R directions when
loading in the T direction.

8: Used to measure strains in
the T and L directions when
loading in the T direction.

Figure 5. Gage arrangements for measuring strains when
loading in the T direction.

78

 

Figure 6. Test specimen A in the compression cage. B is
end block. C is end bearing block. D is
centering guide. E is hole for metal dowel
connection to universal joint. Ball bearing is
centered between B and C at each end (Sliker
1989).

79

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Figure 8.

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REFERENCES

Bodig, J. and J. R. Goodman. 1969. A new apparatus for
compression testing of wood. Wood and Fiber, 1(2):146-
153.

. 1973. Prediction of elastic parameters for
wood. Wood Science, 5(4):249-264.

 

Bodig, J. and B. A. Jayne. 1982. Mechanics of Wood and
Wood Composites. Van Nostrand Reinhold Company. 712p.

Bucur, V. 1983. An ultrasonic method of measuring the
elastic constants of wood increment cores bored from
living trees. Ultrasonics, May: 116-126.

Goodman, J. R., and J. Bodig. 1970. Orthotropic elastic
properties of wood. J. of the struct. Div., ASCE
96(ST 11): 2301-2319.

Guitard, D., and F. EL Amri. 1987. Modeles previsionnets
de comportement elastique tridimensionnel pour les bois
feuillus et bois resineux. Ann. Sci. For., 44(3): 335-
358

Hoadley, B. R. 1980. Understanding Wood: A craftsman’s
guide to wood technology. The Taunton Press. 256p.

. 1990. Identifying Wood: Accurate results
with simple tools. The Taunton Press. 223p.

 

Kollmann, F. F. P., and W. A. Cote. 1968. Principles of
Wood Science and Technology: vol. 1 Solid wood.
Springer-Verlug. 592p.

Ott, L. 1988. An introduction to statistical methods and
data analysis. Third edition. PWS-Kent Publishing
Company. 945p.

Panshin, A. J., and C. De Zeeuw. 1980. Textbook of Wood
Technology. Fourth edition. Structure, Identification,
Properties, and Uses of the Commercial Woods of the
United States and Canada. McGraw-Hill Book company.
722p.

91

Perry, C. C. 1984. The resistance strain gage revisited.
Experimental Mechanics 24(4): 286-299.

Petersen, R. G. 1985. Design and analysis of experiments.
Marcel Dekker, Inc. 429p.

Radcliffe, B. M. 1955. A method for determining the
elastic constants of wood by means of electric
resistance strain gages. Forest Prod. J., 5(1): 77-88.

Sliker, A. 1967. Making bonded wire electrical resistance
strain gages for use on wood. Forest Prod. J., 17(4):
53-55.

. 1971. Resistance strain gages and adhesives
for wood. Forest Prod. J., 21(12):40-43.

 

. 1973. Young's modulus parallel to the grain in
wood as a function of strain rate, stress level, and
mode of loading. Wood and Fiber, 4(4): 325-333.

 

. 1985. Orthotropic strains in compression
parallel to the grain test. Forest Prod. J.,
35(11/12): 19-25.

 

. 1988. A method for predicting non-shear
compliances in the RT plane of wood. Wood and Fiber,
20(1): 44-55.

 

. 1989. Measurements of the smaller Poisson's
ratios and related compliances for wood. Wood and
Fiber Science, 21(3): 252-262.

 

Sliker, A., J. Vincent, W. J. Zhang, and Y. Yu.
Unpublished. Compliance equations for wood at three
moisture content conditions.

Steel, G. D., Fobert and James H. Torrie. 1980. Principles
and procedures of statistics. second edition. McGraw-
Hill Book company. 633p.

U. S. Forest Products Laboratory. 1974. Wood Handbook:
Wood as an engineering material. (USDA Agr. Handb. 72,
rev.). U. S. Gov. Print. Off., Washington, D.C..

Yu, Y. 1990. Non-shear compliances and elastic constants
measured for nine hardwood trees. Masters Thesis.
Michigan State University.