ENGR 059
Strain Gage Laboratory
November 7, 2008
Ryan Carmichael
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Abstract:__________________________________________________________
In this laboratory, I successfully installed a CEA-13-240UZ-120 student strain gage onto
a 6061 Aluminum beam. My beam was then loaded with 4.984 lb and a P-3500 Portable Strain
Indicator was used to measure the strain indicated by my installed gage. The strain measured by
the P-3500 was 1352µ in/in compared to a theoretical value of 1347µ in/in for an error of 0.37%,
well within the 2% error limit.
Theory:___________________________________________________________
Normal strain in any given direction on the surface of a material can be determined by
scribing a line AB in the direction of interest and measuring the length of that line before and
after loading. The normal strain in this setup will equal the change in the length of AB divided
by the original length (εAB = ΔL / L). This method is fine for rough calculations, but for more
accurate and continuous results throughout static loading, an electric strain gage should be used
to measure surface strain.
In the most basic sense, a typical strain
gage, as shown in Figure 1, is comprised of a
length of folded wire adhered to some type of
suitable backing, often plastic. The backing is
A
B
then cemented to the surface of the test
material with the folds in the wire running
parallel to the direction in which strain is to be
measured in. For example, in Figure 1 strain
will be measured in the AB direction. When
Figure 1: Diagram of a Typical CEA Gage
the test material is then loaded, the surface to which the gage is attached will either elongate or
shorten in the AB direction. If the material elongates, then the wire in the gage will increase in
length and decrease in diameter, increasing the electrical resistance in the wire. Conversely, if
the material shortens, the wire in the gage will decrease in length and increase in diameter,
decreasing the electrical resistance in the wire. For a properly calibrated gage, a simple
measurement of this resistance will yield an accurate measure of normal strain.
This gage resistance is commonly measured using a P-3500 Strain Indicator. The P-3500,
which is used for static signals, is a portable, battery-operated, precision device that uses a
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Wheatstone bridge circuit to measure
resistance. The P-3500 will accept full-, half-,
or quarter-bridge strain gage inputs. The basic
Wheatstone bridge circuit in the P-3500
consists of four bridge arms (R1, R2, R3, and
R4) connected in a series-parallel arrangement
with a voltage source (Vin) as shown in Figure
Figure 2: Basic Wheatstone Bridge Circuit
2. The nodes that connect the power supply to the resistors are called the input corners of the
bridge and the nodes between which the differential output voltage (Vout) is measured are called
the output or signal corners of the bridge. The bridge is considered balanced if the differential
output voltage Vout = 0, regardless of the value of Vin. As shown mathematically below, this
Vout
R1 R3 ! R2 R4
=
Vin
(R1 + R2 )(R3 + R4 )
Vout = 0 ! R1 R3 = R2 R4
occurs when R1R3=R2R4. If the differential output voltage does
not equal zero then the bridge will be unbalanced and the
magnitude of the differential output voltage will be proportionally
to the magnitude of the unbalance.
For static strain measurements with a single strain gage, the quarter-bridge configuration
is used with either a two- or three-wire connection, although a two-wire connection is not
recommended for most cases. For the two-wire configuration, as shown in Figure 3, R1 from the
initially balanced Wheatstone
bridge in Figure 2 has been
replaced with a strain gage of
approximately the same resistance
in addition to two lead wires. If
these lead wires were to have no
resistance, then the Wheatstone
Figure 3: Two-wire Quarter-bridge Configuration
bridge would be balanced. However, in practice, lead wires do have a measurable resistance RL.
As the two lead wires are in series with the gage, this makes the resistance of the bridge arm RG
+ 2RL, which can result in a measurable lack of symmetry in the overall circuit and an initial
resistance offset. This initial resistance offset could potentially be accounted for by a sizeable
balance adjustment with the strain indicator, however if the temperature of the lead wires should
change during the measurement process, then the initial balancing will not prevent large errors.
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The change in wire temperature has the potential to greatly change the wires resistance and skew
results. For example, copper wire has a 22% difference in resistance between room temperature
and 100º F. Furthermore, the existence of the leads’ resistance in series with the strain gage act
as a parasitic resistance in the gage arm of the Wheatstone bridge, effectively reducing or
desensitizing the gage factor of the strain gage. During testing, the reduced gage factor results in
a reduced output signals, which gives an error approximately equal to the ratio of lead wire
resistance to gage resistance.
Clearly for most static testing the two-wire configuration is not optimal. As a result, the
most common configuration used for static testing is the three-wire configuration (shown in
Figure 4). For this configuration, there is one lead wire in series with R2 and one lead wire in
series with the strain gage. We
know that for the circuit to be
balance R1R3=R2R4, where R1 in
this case is the resistance of the
gage arm. Furthermore, in the
P3500 and in most commercial
strain indicators R3 is set equal to
Figure 4: Three-wire Quarter-bridge Configuration
R4. As such R1 must equal R2 to
preserve the balance of the circuit. In the three-wire configuration R1’=Rg + RL = R2 + RL = R2’,
which preserves the balance in the circuit. This is based on the assumption that the resistance in
each wire is the same, which is a fair assumption to make if the lead wires are made out of the
same material, are about the same length and shape, and are at approximately the same
temperature. Thus, the three-wire configuration avoids both the initial offset error due to an
unbalanced bridge of the two-wire configuration as well as lead wire temperature error.
Furthermore, only one lead wire is in series with the strain gage, which results in approximately
half of the leadwire desensitization compared to the two-wire configuration. As shown, the threewire configuration reduces or eliminates the three major sources of error for the two-wire
configuration, making it the clear choice for static measurements. It should also be noted that the
third lead wire connecting the strain gage to the negative terminal of the output voltage is a
voltage-sensing wire only, and has no bearing on bridge balance or temperature stability.
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R1 R3 ! R2 Rconfiguration
For the three-wire
we can do the following calculations to determine the
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Vout =
Vin
3 + R4 )specific to the resistances.
∆Vout. Note: (R
C 1=+toR2a)(R
constant
Vout = 0 " R1 R3 = R2 R4
(R + #R1 )(R3 + #R3 ) ! (R2 + #R2 )(R4 + #R4 )
Vout + #Vout = 1
Vin
(R1 + #R1 + R2 + #R2 )(R3 + #R3 + R4 + #R4 )
#R #R2 #R3 #R4
#Vout = ( 1 +
+
+
)(C)(Vin )
R1
R2
R3
R4
#R1 = (#Rg )$ + (#Rg )#%
R1 = Rg + RL = R2 = R3 = R4
#Vout = [(
#Vout = (
#Rg
Rg + RL
#Rg
Rg + RL
)$ + (
#Rg
Rg + RL
)#% + (
#Rg
#RL
#RL
)#% + (
)#% + (
)#% ](C)(Vin )
Rg + RL
Rg + RL
Rg + RL
)$ (c)(Vin )
If we assume RL to be negligible (this will create a small error) then we can easily convert this
formula to determine the strain at the surface of the beam by plugging into the formula
where G.F. is the gage factor of the strain gages used. This is the
strain value calculated for us by the P-3500.
Procedure:_________________________________________________________
The following was adapted from Bulletin 309D Student Manual for Strain Gage Technology
and View MM Videotech Library Vol. 1 CEA Gages/MBond 200. For a more detailed procedure
one or both of these sources should be consulted.
1. Prepared Beam and Work Surface: obtained a 0.1255 in thick, 0.750 in wide beam made
of 6061 Aluminum (E = 10.0 * 106 psi), cleaned the beam and glass work surface,
degreased and abraded the surface of the beam with the suitable chemicals, burnished a
layout line on the beam, and neutralized the surface of the beam.
2. Adhered Gage to Beam: arranged a CEA-13-240UZ-120 student strain gage and two
terminals on the work surface, attached the gage and terminals to a piece of cellophane
tape, arranged the tape over the beam in the suitable location so that one end of the tape
was on the beam and the gage was held off the beam, applied catalyst and cyanoacrylate
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glue to the beam over the layout line, under the gage, brought gage into contact with the
glue with a single wiping stroke with a gauze sponge, pressed thumb firmly against tape
and gage for more than one minute, and removed the tape leaving the gage and terminals
adhered to the beam.
3. Attached Leads: obtained a piece of three-conductor lead-in wire, separated an individual
wire from each of the two outside strands of wire to serve as jumper wires, tinned
remaining strands, cut the strands to size, masked the gage grid with masking tape,
soldered the lead wires to the terminals, created stress relief loops in the leads, soldered
the leads to the gage
4. Protected the Gage: created another stress relief loop in the main body of the threeconductor wire, attached the main body of wire to the beam with electrical tape, cleaned
the gage area with rosin solvent, tested the soldered connections, and applied two
protective coats of polyurethane to the gage area
5. Testing: attached beam with two c-clamps to a classroom table in a cantilever formation
with the gage overhanging the table, attached the P-3500 Portable Strain Indicator, set the
gage factor, balanced the unloaded reading, applied 4.984 lb to the free end of the beam,
5.125 in away from the layout line and the gage, and used the P-3500 to measure the
strain
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Manually attached page here
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Results:___________________________________________________________
Experimental Strain
Theoretical Strain
Percent Error
1352µ in/in
1347µ in/in
0.37%
Discussion:_________________________________________________________
As the experimental results for strain was well within the allowed 2% error, no major
installation errors occurred. In addition, selecting a strain gage appropriate for this laboratory
also reduced potential error. For this lab, CEA-13-240UZ-120 student gages manufactured by
Vishay Micro-Measurements were used. This strain gage sufficiently met the selection criteria
necessary for this laboratory, namely, the gage needed to be low cost as it was being used to
practice installation skills, easy to install so novices could install it, and the gage had to work
with both the chemicals used in
cleaning and bonding as well as
conform to geometric limitations and
other details such as the setup having a
fairly low strain gradient. By
examining the components of the name
CEA-13-240UZ-120 (using Figure 5)
we can learn how each part of the gage
contributes to making the CEA-13240UZ-120 student gage the proper
Figure 5: Strain Gage Selection Steps
gage selection for this laboratory.
As per Figure 5, the first step to gage selection involves picking a gage length. Our gage
length is .240 in, which is a relatively large value. Large size gages in general provide the
advantages of better heat dissipation, improved strain averaging for inhomogeneous materials,
and easier handling and installation. They however are not optimal for situations where a peak
strain value is needed and for installation in very small areas. For our lab, we were not concerned
with a peak strain value and were not working with a very small area so the larger gage was
chosen because of its relative ease of installation.
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The second step to gage selection is choosing an appropriate gage pattern. The pattern
selected for our laboratory was a UZ pattern, which specifies a single rectangular gage, with a
specific aspect ratio and tab placement. The UZ pattern is sufficient for our simple installation
because we only needed a single gage and the aspect ratio and tab placement do not cause any
problems with our setup.
Step three dictates the choice of a gage series. For our laboratory CEA-Series Student
Gages were used. This series is the preferred choice for routine strain-measurement situations
that don’t require any extreme temperature or size considerations. CEA-Series gages are
polyimide-encapsulated A-alloy gages, which work with the chemicals used in this lab. In
addition, CEA-Series gages have large copper-coated tabs, which make soldering easier.
Step four was unnecessary for our simple installation and was skipped. Step five involves
selecting a resistance. This criterion is largely based on price and availability. The 120Ω
resistance for our gage is sufficient for our basic purposes. A larger resistance is usually
preferable, but not worth the extra money for our simple installation and test. Finally, step six
involves selecting a self-temperature compensation number. Our gage has a S-T-C Number of
13. This is approximately equal to the thermal expansion coefficient of the material on which the
gage will exhibit minimum thermal output. A value of 13 is sufficient for our lab because we are
not very concerned with temperature and thermal output. In all, the CEA-13-240UZ-120 strain
gage was a suitable gage for our installation for its ease of use, affordability, and compatibility
with our undemanding setup.
Conclusion:________________________________________________________
In conclusion, I was able to install a CEA-13-240UZ-120 student strain gage onto a 6061
Aluminum beam with only 0.37% error, well within the 2% limit. This success can be attributed
both to careful installation and testing as well as to proper strain gage selection.
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References:________________________________________________________
Beer, Ferdinand P., and E. Russell Johnston. Mechanics of Materials. New York: McGraw-Hill,
2008.
Siddiqui, Faruq. “Mechanics of Solids: Installing an Electric Resistance Strain Gage &
Measuring Strain with it.” Swarthmore College, 2008.
"Strain Gages - Vishay." Vishay - manufacturer of discrete semiconductors and passive
components. 6 Nov. 2008 <http://www.vishay.com/strain-gages/>.
View MM Videotech Library Vol. 1 CEA Gages/MBond 200
Vishay Measurements Group, Inc. “Bulletin 309D: Student Manual for Strain Gage
Technology,” 1992.
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