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REIMANCIE OF BONDED WIPE
STRAIN GAGES ON WOOD
1
No. 2087
August 1957
MP'
UNITED STATES DEPARTMENT OF AGRICULTURE
FOREST PRODUCTS LABORATORY
MADISON 5. WISCONSIN
FOREST SERVICE
la Cooperation with the University of Wisconsin
CE.Z.4TER
FOREST RESEARCH CENTER
LIBRARY
(PERFORMANCE OF BONDED WIRE STRAIN GAGES ON WOOD
By
YOUNGQUIST, Engineer
1
Forest Products Laboratory, — Forest Service
U. S. Department of Agriculture
W. G.
Abstract
This report deals with the use of bonded wire strain gages on wood. The results of comparative tests using such gages and two types of mechanical gages
are presented. Methods for mounting bonded wire strain gages on wood and
special precautions_ that must be observed to obtain reliable data are also outlined and discussed.
Introduction
The extremely versatile bonded wire strain gage has been used for a number
of years at the U. S. Forest Products Laboratory for the determination of
strains in wood and wood-base materials and for the determination of stress
distribution patterns in wood structures. However, no report on the performance of these gages when used on wood has been issued. Wood is an anisotropic material with a cellular structure that varies widely in properties
with respect to grain direction, and it is therefore of interest to determine
the probable accuracy to be obtained with these gages when used on wood. It
is the purpose of this report to outline the methods used at the Forest Products
Laboratory for bonding these gages to wood, to indicate certain limitations on
the use of these gages, to present some comparative strain data obtained with
bonded strain gages and other types of strain gages commonly used with wood,
and to report the results of some limited special tests of these gages.
-Maintained at Madison, Wis. , in cooperation with the University of
Wisconsin.
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-1-
This work was not intended to determine the absolute accuracy that can be
obtained when using the bonded wire strain gages on wood, but rather to obtain an indication of the accuracy to be expected when normal testing techniques are used. The commercially available gages have about 4 percent of
the gage wire placed in a direction transverse to , the length of the gage. The
wire so placed responds only to strains in a transverse direction, such as
those caused by Poisson's ratio effect. The gage factor furnished by the
manufacturer corrects for this effect when the Poisson's ratio is 0.285. Only
a limited amount of information, however, is available on Poisson's ratio
for wood. As an example, the ratio for Douglas-fir (specific gravity 0.506,
moisture content 12.9 percent) is 0.292 in the longitudinal-radial direction
and 0.449 in the longitudinal-tangential direction. It is obvious that when
the actual values differ from 0.285 an error is introduced. For many applications these errors can be neglected, but corrections must be made when
more exact values are required. An indication of the magnitude of such
2
errors and a method of correction have been presented by B. M. Radcliffe. —
Correction factors have not been applied to the values presented in this report.
Test Materials and Strain Gages Used
Wood
Douglas-fir, white pine, and sugar maple, were used for these comparative
tests. Each set of compression specimens was obtained from one straightgrained, air-dry plank. The planks were 8 inches wide, 2 inches thick, and
48 inches long. The Douglas-fir tension specimens were obtained from a
section of plank that was end matched to the piece from which the compression
specimens were obtained. A single beam of southern yellow pine was used for
the repeated load tests.
Strain Gages
The bonded-wire strain gages were the commonly used commercial type
gages. The A-1-type gage has a resistance of 120 ± 1 ohm, a nominal gage
length of 13/16 inch, and a gage factor of 2.0. The gage consists essentially
of a grid of fine wires, all lying in one plane, cemented in place on a thin
2
—Radcliffe, B. M. "A Method for Determining the Elastic Constants of Wood
by Means of Electric Resistance Strain Gages. " Forest Products Journal,
Vol. 5, No. 1. Feb. 1955.
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FO2EST RESEARCH CENTER
111-i2ARY
paper backing, and covered by a piece of felt. Figure 1 shows the A-1-type
gages attached to a compression specimen.
A few A-7-type gages were also used. This is a wrap-around-type gage made
of a continuous length of wire wrapped in a tight helix pattern around a thin,
flat core of paper. This sensitive element is then sandwiched between two
paper covers for protection. The A-7-type gage has a resistance of 120
0.8 ohm, a nominal gage length of 1/4 inch, and a gage factor of 1.9.
A commercial type M strain indicator reading to the nearest 10 microinches
and estimated to half this amount was used to read the strains in these gages
(fig. 2).
The Tuckerman strain gage is of the optical type and is capable of measuring
strains as small as 0.000002 inch. The gage consists of two essential parts;
the autocollimator which contains the calibrated scale and the extensometer
which is attached to the test specimen. A 2-inch gage length extensometer
was used for the compression tests, and a 1-inch gage length extensometer
was used for the tension tests and one of the special tests. Figure 1 shows
two Tuckerman extensometers attached to opposite faces of a compression
specimen. Figure 3 shows a specimen ready for test with extensometers and
autocollimators in place. The extensometers were held in place with wire
spring clips. Simultaneous readings of load and strain for each extensometer
were obtained, the strains were averaged, and a load-strain curve was plotted.
The Lamb's roller extensometer is also of the optical type, and it is frequently
used to measure strains in wood specimens. The extensometer is shown attached to opposite faces of a compression specimen in figure 1. The gage
consists of three essential parts, the light source, the extensometer units
with rotating mirrors mounted on the specimen, and the drum holding the
graph paper for direct plotting of the stress-strain curve, as shown in figure
4. The gage is constructed so that the average strain of the two faces of the
specimen is obtained.
Both the Tuckerman and the Lamb's roller extensometers were calibrated by
means of precision gage blocks before these tests were started, and they were
accurate to within ± 0.2 percent.
Mounting of Bonded Strain Gages
The surfaces of the compression and the flexure specimens to which the gages
were to be mounted were produced with a sharp, hollow-ground saw and were
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very uniform and smooth. The test sections of the tension specimens were
produced by router knives and were also smooth. Before the gages were
mounted, the surfaces were sanded lightly with a fine grade of sandpaper. A
commercial nitrocellulose type of cement was used. A liberal amount of the
cement was spread over the area to receive the gage, and a straight edge
was used to remove the excess, leaving a thin, smooth coating of glue. After
this glue had dried (usually in 24 hours) a second coating of glue was spread
on the surface, and the gage was carefully placed in position. A 1/4-inchthick soft rubber pad was placed on the gage, and a 1-pound weight was placed
on top of the pad to provide glue pressure. It is sometimes necessary to
apply glue pressure with heavy rubber bands instead of weights. Gages were
allowed to dry for at least 24 hours before use. This general method of mounting gages on wood has been used successfully at the Laboratory for a wide
variety of applications.
Preparation of Test Specimens.
The compression test specimens consisted of rectangular prisms 1 inch by 1
inch in cross section and 4 inches long. Figure 5 shows the cutting method
used to obtain matched specimens from the Douglas-fir test plank. Specimens were obtained which were oriented with the long dimension parallel to
the grain, with the long dimension perpendicular to the grain, and at an angle
of 45 degrees to the grain. The specimens of maple and white pine were obtained in a similar manner, except that specimens oriented at 45 degrees to
the grain were not obtained. Only specimens 1 through 6 were used for these
tests. The eight tension specimens of Douglas-fir were obtained at random
locations in a section of plank, end matched to the one from which the compression specimens had been obtained. Figure 6 shows the dimensions of the
tensile specimens. The test planks had a moisture content of about 12 percent when the specimens were prepared. All specimens were conditioned to
constant weight before test at 75° F. and 64 percent relative humidity. These
conditions bring the average moisture content of wood to about 12,percent.
Methods of Test
Compression Tests
To provide the best possible comparative data, the modulus of elasticity of
each specimen was determined in turn with the Tuckerman gage, Lamb's
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roller gage, and finally with the bonded-wire gages. It was therefore necessary to stay well within the elastic limit of each specimen to avoid permanent
injury to the test piece. The maximum load applied to each specimen was
selected as less than one-half of the expected proportional limit value for the
species and loading condition. Load increments were chosen to provide about
20 equally spaced increments at which simultaneous values of load and strain
could be determined. All tests were made on the same testing machine. The
testing machine was not located in the conditioned room, therefore it was necessary to keep the specimen in an uncontrolled condition during the test period
of approximately 5 minutes. All three types of gages were attached to the
same two opposite faces. The radial faces of the compression-parallel-to-
grain specimens and end-grain faces of the other specimens were used for test.
Figure 3 shows one of the compression specimens in place in the testing machine with the Tuckerman gages in place. The gages are held in place on the
specimen with spring clips. Great care was taken to space the knife edges,
which were 2 inches apart, equidistant from the center of the length of the
specimen. Load was applied to the specimen at a uniform rate of 0.012 inch
per minute through a spherical head mounted in the head of the testing machine.
The two Tuckerman gages were read individually, an average was obtained,
and the resulting load-strain curve was plotted.
The Lamb's roller extensometer gage is shown in place in the testing machine
in figure 4. This gage permits the direct plotting of a stress-strain curve on
the drum holding the graph paper, as shown. The gage gives an average value
of strain for the two faces of the specimen.
The bonded electric strain gages, glued in position on opposite faces of the
test specimens, were spaced so that the active portion of each gage was distributed evenly about the perpendicular centerlines of the specimen faces.
For the A-1-type gages, only the strain in the central 13/16 inch of each
specimen was measured. The two gages on opposite faces of each specimen
were connected in series and thus served as a single averaging type gage. A
companion specimen, wired in the same manner, was used as a compensating gage. Figure 2 shows a compression specimen with bonded gages attached
ready for test. The indicator was graduated to the nearest 10 microinches,
and readings were estimated to the nearest 5 microinches.
Tension Tests
The dimensions of the specimen used for the tension-parallel-to-grain tests
are shown in figure 6. Load was applied to the notched shoulders through
metal grips at a rate of 0.02 inch per minute. Loads were kept well within
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the elastic limit of the material. All specimens were first tested by mounting the 1-inch gage length Tuckerman gages centrally on the two opposite
3/8-inch-wide faces and obtaining simultaneous readings of load and strain.
Following the completion of these tests, bonded strain gages were glued to
the same faces, and the test was repeated.
Special Tests
Following the completion of the major series of tests, a number of tests and
observations were made to check the stability and performance of the bonded
gages under varying conditions. The check on the stability of the gages under
supposedly constant conditions was made by using a compression specimen
with bonded gages attached as an active gage and using the gages on a closely
matched companion specimen as a compensating gage. The current to the
indicator was kept on at all times, and intermittent readings of time and indicated strain were taken. To check the behavior of the gages when both gages
were moved to a changed atmospheric condition, the gages and indicator were
placed on a cart and quickly moved to the desired conditioned room. Simultaneous readings of time and strain were taken at arbitrarily selected intervals. The check on the behavior of the gages when only the active gage was
moved to a different atmospheric condition was made as follows: Both of
the compression specimens to which the active and compensating gages were
attached were conditioned to a constant weight in a temperature-humidity controlled room. The compensating gage was then placed in a glass jar with a
tight-fitting metal screw-top cover. Sealed lead wires for the strain gages
were provided through the metal cover. After the compensating gage had
been sealed in the jar, the two gages and the indicating unit were quickly
moved to the desired conditioned room, and the time-strain readings were
taken.
To obtain information on the performance of the bonded gages attached to material with alternating bands of high and low density, such as formed by springwood and summerwood, a composite type of specimen was fabricated. One
white pine compression-perpendicular-to grain specimen and one similar
specimen of hard maple were selected for test. The modulus of elasticity
was first determined for each specimen with a Tuckerman strain gage. Each
specimen was next cut to a length of 2 inches and reassembled into a 1-inchsquare specimen 4 inches long, the top 2 inches being of white pine and the
bottom 2 inches of hard maple. A thin layer of polyvinyl glue was used to
bond the two pieces to each other. The modulus of elasticity of the central
1 inch of the composite specimen was now determined with Tuckerman strain
gages. The bonded strain gages were next glued in place on two opposite faces
of the test specimen. Each gage was accurately centered on the glue line with
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one-half of the active portion of each gage on the white pine portion of the
specimen and the other half on the maple. The specimen was again tested,
and the apparent modulus of elasticity as indicated by the bonded-wire gages
was determined.
The effect of a large number of load repetitions on the bonded-wire strain
gages mounted on wood was investigated by the following means. A-1-type
gages were bonded to the top and bottom faces at the center of the length of a
southern pine beam 2 by 4 by 43 inches long. The beam was then placed in
a testing machine, supported on a span of 39 inches, and loaded at the third
points. The strain gage on the top of the beam was used as the active gage,
and the bottom strain gage was used as the compensating gage, and a loadstrain curve up to a total load of 1,500 pounds was obtained. Figure 7 shows
the beam in place in the testing machine. Following this initial calibration
of the gages, the beam was placed in a direct-stress fatigue machine, the loading method was duplicated, and repeated loads varying from a minimum of 150
pounds to a maximum of 1,500 pounds were applied at a rate of 550 repetitions
per minute. . The test was continued until 10,011,100 loads had been applied.
The beam was then replaced in the testing machine, and the stress-strain
curve up to a load of 1,500 pounds was again determined. Following this, the
beam was loaded to failure.
Figures 8 and 9 show an actual application of the bonded-wire strain gages in
a series of tests of laminated wood bow-string trusses.
Presentation of Data
The comparative modulus of elasticity values obtained by the Tuckerman gage,
Lamb's roller gage, and the bonded-wire strain gages for the three species of
wood are presented in tables 1, 2, and 3. Individual test values are presented
to permit direct comparisons between the three methods of test. The percentage of variation of each determination from the value obtained with the Tuckerman gage is also . shown. The data presented in tables 1, 2, and 3 are shown
graphically in figures 10 and 11.
The comparative values of the modulus of elasticity of Douglas-fir, tested in
tension parallel to the grain as measured by the Tuckerman gage and bondedwire strain gages, are presented in table 4 and shown graphically in figure 12.
Table 5 presents the results of compression tests of a composite specimen
fabricated from maple and white pine and also gives the stress-strain characteristics of the original pieces of wood from which the specimen was
Rept. No. 2087
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fabricated. The values in table 5 are shown graphically in figure 13. Figure
13 also presents the computed values of the modulus of elasticity for each test
made.
The results of tests to evaluate the effect of repeated loading on the performance of the bonded-wire strain gages are shown in table 6. Table 6 also presents the stress-strain data obtained in testing the beam to failure following
the completion of the comparative studies. The comparative stress-strain
curves obtained before and after the repeated load cycling are shown graphically in figure 14.
The comparison of the stress-strain characteristics of white pine in compression perpendicular to the grain as determined by the Tuckerman gage,
and 1-inch nominal and I/4-inch nominal gage length bonded-wire gages is
presented in table 7. Similar data for white pine in compression parallel to
the grain are presented in table 8. The information presented in tables 7 and
8 is presented graphically in figures 15 and 16.
Table 9 presents time-strain relationships that occur in bonded-wire strain
gages mounted on white pine when subjected to various exposure conditions.
Figure 17 shows a plot of the time-strain occurring in a parallel-to-grain
specimen. Similar data for specimens oriented perpendicular to the grain are
shown in figure 18.
Discussion of Results
Of primary interest in this study is the reliability of the strain data obtained
with bonded-wire gages mounted on wood. The Tuckerman and Lamb's roller
gages are both used to measure strain in wood and were thus chosen for comparative purposes. The Tuckerman values were arbitrarily selected as standards of comparison. In making comparisons in the data presented in tables 1, 2, 3,
and 4, certain important considerations must be kept in mind. The modulus
of elasticity values were obtained by plotting the stress-strain data for each
specimen, drawing a visually selected line of best fit and computing the modulus. The values obtained are thus not exact values, since two independent
operators would probably not arrive at exactly the same value in each instance.
To minimize these variations as much as possible, all of the slope lines were
fitted to the plotted data by one operator.
The bonded-wire gages and the two gages used for comparative purposes do
not measure the strains over identical portions of the specimens. The Tuckerman and Lamb's roller gages measure the strain over the central 2 inches
Rept. No. 20 87
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of a specimen 4 inches long. The A-1-type bonded strain gage, on the other
hand, measures the strain only over the central 13/16 inch of the specimen.
The test results show that some variation in modulus of elasticity occurs between individual specimens even though they are closely matched. It is logical to assume that variation also occurs along the length of each specimen.
This may be especially significant when obtaining a measure of the modulus
across a number of growth rings, which vary considerably in thickness and
composition.
The modulus of elasticity of each specimen was obtained from the equation
E=—
(1)
E
where
E = modulus of elasticity
Cr = stress
e = strain
The stress was determined for each specimen by dividing the applied load by
the cross-sectional area of the specimen. The strain was obtained from the
Tuckerman and Lamb's roller data by dividing the total movement obtained
by the initial gage length (2 inches). The bonded-wire strain gages give direct
values of strain.
The data presented in tables 1, 2, and 3 show that a close correlation generally
exists between the values obtained by the three test methods. The coefficients
of variation obtained by the three methods are about of the same order of magnitude, but they are somewhat greater for the bonded-wire gages. It is interesting to note that the Tuckerman gage and Lamb's roller gage which measure
strains over the same gage length differ by more than 6 percent in several instances. No apparent reason for the occasional differences of 10 to 14 percent
between Tuckerman and bonded-wire gages was noted. The difference of 21.3
percent between the modulus values obtained with Tuckerman and bonded-wire
gages for the' maple specimen M-0-3 (table 2) requires further explanation.
The maple specimens cut parallel to the grain were obtained from a single
stick and are thus end matched. The two specimens on each end of the stick
were from material that was essentially straight grained. Specimen 3 and,
to a lesser extent, specimen 4 contained considerable curly grain, and this
is reflected in the low modulus values obtained for these specimens by all
three test methods. The deviation from straight grain was most pronounced
near the center of specimen 3, and this probably accounts for the fact that the
short gage length bonded gage gave the lowest modulus value. On this basis,
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it is not correct to consider the 21.3 percent difference between Tuckerman
gage values and bonded strain gage values as an actual error. To a lesser extent, this same consideration may account for some of the other larger differences noted. However, no apparent deviation from normal grain was observed in the remaining specimens.
Figure 10 shows that for all three species tested in compression parallel to
the grain, the differences between values obtained by Tuckerman and bondedwire gages are generally less than 10 percent, with an approximate normal
distribution above and below the comparative values. Figure 11 shows similar
data for specimens loaded at angles other than parallel to the grain. Again
the modulus values are generally within 10 percent of the comparative Tuckerman values. Most of the values determined by the bonded-wire gages, however,
are high. Such a result could be expected if the bonded-wire gage assembly is
itself stiffer than the material being tested.
The data in table 4 show that the modulus of elasticity of Douglas-fir in tension
parallel to the grain as determined by the bonded-wire gages gives values with
a lower coefficient of variation than the comparable Tuckerman values. The
maximum difference obtained between the two methods of test was 7.6 percent.
An approximate normal distribution above and below the standard of comparison was obtained as shown in figure 12.
The determination of the modulus of elasticity of wood in a direction perpendicular to the grain, that is, across a number of growth rings, is essentially
that of determining what might be called an apparent modulus of a composite
material. An examination of the end grain of such woods as Douglas-fir or
southern yellow pine often reveals a pattern of growth rings that vary considerably, in thickness, in the ratio of dense summerwood to the less dense springwood, and in the gradation between the two. It is known that the dense summerwood is stronger and stiffer than springwood, therefore, it is logical to
assume that a variation in Poisson's ratio also exists in the growth rings. A
strain gage, such as the Tuckerman or Lamb's roller gage measures the total
movement that occurs between knife edges. The bonded-wire gage, on the
other hand, measures the varying strains in the underlying material, and the
results may be affected by the varying lateral strains that occur. Table 5 and
figure 13 present the data obtained in tests of the composite white pine-maple
specimen. Since the maple and white pine differ significantly in modulus of
elasticity perpendicular to the grain, this composite specimen simulates conditions that exist in one growth ring.
Figure 13 indicates that the modulus of elasticity of the maple in the composite specimen was 147,000 pounds per square inch. Similarly, the modulus
of the white pine was 91,800 pounds per square inch. The apparent modulus
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of elasticity of the composite specimen as determined by both the bondedwire strain gages and the Tuckerman gages was 108,300 pounds per square
inch. It is of interest to examine the relationship which exists between this
apparent modulus and the modulus of elasticity of the individual pieces of
maple and white pine.
The apparent modulus of elasticity may be computed from the previously presented equation (1)
oEa = e
(2)
The Tuckerman gage measures the total deformation that occurs between
knife edges. This deformation is composed of two parts, namely the movement in the maple spanned by one-half of the gage and the movement in the
white pine spanned by the other half of the gage. This can be written
e = em + ep
(3)
where
e = total deformation
e = deformation in maple
e = deformation in pine
also
crh
e-
m
Em
crh
p
(4)
where
hm = height of maple block within gage length
h = height of pine block within gage length
Em = modulus of elasticity of maple
E = modulus of elasticity of pine
Under the conditions used in this test h
= hp= 1/2 inch and e = E (1 inch
m
gage length). Therefore from equation 4,
e=e=
cr
2E m 2E
p
(5)
Then from equation 2,
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E
2E E
o-
a
0-
= e = u-
2.E
-1- m
a-
2E
p
Em+ E p
(6)
1)
where
E a = apparent modulus of elasticity
Substituting the values for Ern and ED obtained from the Tuckerman test date
in this equation, we obtain E a = 113,b00 pounds per square inch. This compares with the 108,300 pounds per square inch value obtained directly from
the data of the actual test of the composite specimen. This can be considered
as a reasonable agreement, since the separate modulus determinations of the
pine and maple were made on portions of the specimens not identical to those
included in the gage length of the composite specimen.
The bonded-wire gages give values of strain directly. The relationship between the apparent modulus obtained and the modulus of each individual piece,
however, is as previously described and given by equation (6).
The data presented in table 6 and shown graphically in figure 14 indicate that
the bonded-wire gages were not affected by a large number of repeated loads.
The strains shown are the additive compression and tension strains in the top
and bottom faces of the beam. A plot of the load-strain data obtained in the
final test of the beam to failure showed the proportional limit load to be 5,200
pounds. The maximum load was 8,580 pounds. The 1,500 pound maximum
repeated load was thus about 29 percent of the proportional limit load and 17
percent of the maximum load or somewhat lower than the normal design range
for a wood beam.
Figure 15 permits a comparison of the modulus of elasticity of white pine in
compression perpendicular to the grain as determined by Tuckerman gages
and by bonded-wire strain gages of nominal 1-inch and 1/4-inch gage lengths.
Based on the average of the two specimens tested, the 1-inch gage length
bonded gages gave values that were 5.7 percent higher than the Tuckerman
values. The 1/4-inch gage length gages gave values that were 68.6 percent
higher than the comparable Tuckerman values. This confirmed the results
of some previous tests made at the Laboratory in which 1/4-inch gage length
bonded gages were used in an attempt to determine the stress distribution on
the face of a loaded wood beam.
Figure 16 presents similar data except that strains were measured parallel
to the grain. The average modulus of elasticity for the two test specimens
as determined by the 1-inch gage length bonded gages was 2.2 percent lower
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than the comparable Tuckerman values. The 1/4-inch gage length bondedwire gages gave values 11.7 percent higher than the Tuckerman values. It
is possible that the actual construction used in the manufacture of the 1/4inch gage length gage which employs 3 thicknesses of paper and 2 layers of
wire might result in a component stiff enough to resist through a reinforcing
action the movement of the material to which it is attached. This would be
of most significance in determining the modulus of elasticity perpendicular
to the grain.
It is a well known fact that wood shrinks as it loses moisture and swells 'as it
absorbs moisture. A piece of wood will give off or take on moisture from the
surrounding atmosphere until the amount of moisture in the wood balances that
in the atmosphere. Thus, wood is almost always changing dimensions, at
least slightly, because of atmospheric changes. The total shrinkage that
occurs in wood in a direction parallel to the grain is small and usually ranges
from 0.1 to 0.3 percent when green wood is dried to 0 percent moisture (ovendry). The amount of shrinkage that occurs in directions across the grain in
drying the three species of wood tested from the green to the ovendry condition is shown in the following tabulation:
Species
Pine (eastern white)
Maple (sugar)
Douglas -fir
Radial
shrinkage
(Across the
Tangential
shrinkage
(Tangent to
growth rings)
growth rings)
Percent
Percent
2.3
4.9
5.0
6.0
9.5
7.8
The rate at which these changes occur depends on many factors, but most important in the present connection is the size of the piece and the amount of end
grain exposed, because a large piece comes to equilibrium at a much slower
rate than a small piece, and end grain is much more permeable to moisture
than side grain. In selecting a piece of wood on which to mount a compensating gage, it is very important that the piece match the actual test piece as
closely as possible. If the compensating gage were placed on a small, thin
wood member and the active gage on a large beam, erroneous readings could
easily occur. This would be of special importance in tests of long duration.
Figures 17 and 18 indicate the possible magnitude of errors caused by changing moisture conditions. Wood will reach an equilibrium moisture content of
about 12 percent at 75° F. and 65 percent relative humidity and a moisture
content of about 6 percent at 75° F. and 30 percent relative humidity. The
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data in figure 17 indicate that under this rather severe moisture differential
for the two matched blocks, the longitudinal strain was very small during the
first 3 hours and amounted to only about 0.06 percent after 40 hours.
Figure 18 indicates that under similar differential moisture conditions, the
shrinkage across the growth rings amounted to about 0.27 percent after only
2-1/2 hours. Using an average modulus of elasticity of 79,000 pounds per
square inch for these specimens, the movement of 0.0027 which occurred is
equivalent to that resulting from a load of 213 pounds on the specimen. It is
significant that these specimens were loaded only to 160 pounds in determining the modulus of elasticity. Figure 18 also indicates that small but measurable strains occur when both active and compensating specimens remain in
the same controlled condition or are both moved to a changed condition. This
indicates that careful selection of a compensating-gage specimen and care in
exposing both active and compensating gages to the same atmospheric conditions can greatly minimize errors due to differential shrinking and swelling
of the test piece. The effect of temperature is also an important consideration in using bonded-wire strain gages. However, no data on temperature
effects were obtained in this study.
In many instances, it is desirable to use the bonded-wire strain gages to indirectly obtain stresses in a structure or member. If the modulus of elasticity
of the material is known, the strains can readily be converted to stresses.
For metal structures, an adequate modulus of elasticity value can often be
assumed. For wood structures, such a procedure cannot be used. The modulus of elasticity of wood varies between species, and within a species due to
such factors as a variation in density, moisture content, and grain orientation.
The magnitude that variations between species can assume is indicated by the
data in tables 1 and 3 which show the average modulus of elasticity parallel
to the grain of Douglas-fir to be 2,056,000 pounds per square inch and that of
white pine to be 1,219,000 pounds per square inch. The test data in tables 1,
2, 3, and 4 show that some variation in modulus of elasticity occurs in closely
matched material. The most significant differences occurred in the maple
specimens cut parallel to the grain because of grain deviation.
It is recommended that, whenever possible, a separate determination of the
modulus of elasticity of the wood in a test structure be made. The determination can be made on some of the excess material from the test structure or on
material salvaged from the structure after completion of the test. Figure 8
shows a test in progress in which this latter method was used. The test structure is a laminated bow-string truss of 32-foot span being loaded at 12 points
through a cable-pulley system. Bonded-wire strain gages were attached to
the top, bottom, and sides of the top and bottom chords at various points along
the length of the truss. Figure 9 shows the strain gages in greater detail.
Rept. No. 2087
-14-
Following the test of the structure to failure, undamaged sections of the
chords six inches long that contained the strain gages were removed for calibration. These sections were loaded in compression parallel to the grain,
and stress-strain data were obtained for each gage. The individual modulus
of elasticity values thus obtained were used to analyze the results obtained in
the test of the truss.
Conclusions and. Observations
The following conclusions and observations are based on the results of these
tests and on the experience gained at the Forest Products Laboratory in using
the bonded-wire strain gages on wood..
1. The bonding technique described in this report, using nitrocellulose cement
as a bonding agent, is a simple and satisfactory method of attaching gages to
wood maintained in the dry condition. The maximum moisture content in the
wood used in these tests was 12 percent. It can be assumed, however, that
the same bonding techniques would be satisfactory on wood with a moisture
content of 15 to 18 percent. At moisture contents above this level, or where
the gages are exposed to adverse atmospheric conditions, special gages and
moisture-proofing techniques should be used.
2. Tests of Douglas-fir, sugar maple, and white pine compression specimens
parallel to grain indicate that the modulus of elasticity values obtained with
the nominal 1-inch gage length (bonded-wire gages) are in good agreement
with values obtained with Tuckerman and Lamb's roller gages of 2-inch gage
length. The bonded-wire gages give values generally well within 10 percent
of and normally distributed about the Tuckerman values chosen for comparison. A comparison between the Tuckerman gage values and Lamb's roller
gage values shows differences of the same order but of slightly less magnitude. A much closer correlation would probably be obtained if the same gage
length were used for both the Tuckerman and bonded-wire gages.
3. Tests of Douglas-fir, sugar maple, and white pine compression specimens
perpendicular to the grain and Douglas-fir specimens at 45,° to the grain give
modulus of elasticity values obtained with bonded-wire gages and Lamb's roller
gages that are in most instances within 10 percent of the comparable Tuckerman values. In all instances, the modulus of elasticity values obtained with
the bonded gages are higher than the Tuckerman values. The reason for this
is not known. Such a result could be expected, however, if the bonded-wire
gage assembly is itself stiffer than the material being tested.
Rept. No. 2087
-15-
4. The modulus of elasticity values for Douglas-fir in tension parallel to the
grain as determined by Tuckerman gages of 1-inch gage length and nominal
1-inch gage length bonded-wire gages are in good agreement with an approximate normal distribution of differences and a maximum difference of 7.6 percent.
5. Tests of a single composite compression specimen composed of equal
lengths of maple and white pine perpendicular to grain gave identical apparent
modulus of elasticity values with both the Tuckerman and bonded-wire gages.
The values so determined agreed closely with the modulus values computed
from the measured modulus of elasticity values for the individual sections of
maple and white pine.
6. Two bonded-wire gages mounted on a southern yellow pine beam were apparently unaffected by more than 10,000,000 flexural load cycles.
7. Comparative compression tests of white pine, both parallel and perpendicular to the grain, indicate that the bonded-wire strain gages of nominal 1/4inch gage length give modulus of elasticity values significantly higher than
those obtained with Tuckerman gages or bonded gages of nominal 1-inch gage
length. The average differences between the Tuckerman values and the values
obtained with the 1/4-inch gage length bonded gages were 11.7 percent for ,
specimens parallel to the grain and 68.6 percent for specimens perpendicular
to the grain. These results generally confirm those obtained in previous tests
made at the Laboratory.
8. These tests confirm the fact that a deviation from straight grain in a wood
specimen may significantly affect the measured modulus of elasticity of the
piece. A drop in modulus of elasticity of maple from 2,320,000 to 1,070,000
pounds per square inch was obtained in a distance of only 4 inches along the
grain. Care must be taken to mount each bonded-wire gage on wood representative of the piece and in proper orientation with respect to the desired
direction.
9. Highly significant apparent strains can be obtained in strain gages mounted
on wood caused only by differential moisture exposure of the wood samples on
which the measuring and compensating gages are mounted. These apparent
strains are greatest when measured in compression across the grain, but they
cannot be ignored in tests parallel to the grain when the tests are of long duration. The results show that careful selection of a compensating-gage specimen and care in exposing both active and compensating gages to the same atmospheric conditions can greatly minimize errors due to differential shrinking and swelling.
Rept. No. 2087
-16-
10. The use of an assumed modulus of elasticity for wood in converting
measured strains to stresses is not satisfactory and maylead to sizable
errors. It is recommended that whenever. possible a separate determination of the modulus of elasticity of the wood in a test structure should be
made.
Rept. No. 2087
-17-
1. -45
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Table 5.--Comparison of the stress-strain relationships of a
composite maple-white pine compression specimen
as determined by Tuckerman and bonded-wire strain
gages
Maple specimen :
White pine
specimen
: Composite maple-white pine
specimen
Load: Strain
: Load : Strain
Strain
: Load :
:(Tuckerman :
:(Tuckerman :
:gage value):
:gage value):
:(Tuckerman :Bonded-wire
:gage value):gage value
Pounds: In./in. :Pounds:
0 :
:
0
20 : 0.000000 : 10
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20
6o :
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8o :
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100 :
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120 :
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In./in. :Pounds:
: 0.000000 :
0
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:
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:
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:
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: .000445 : 50
: .00054o : 6o
In./in. :
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