LAB #8: Measurement of Strain
Equipment:
Multimeter and DC power supply
Balance Unit
Strain Indicator (Vishay Micro-Measurements Model 2100)
Aluminum cantilever beam and tension specimne with two gages
DELL computer w/NI DAQ and Virtual Bench
Instron Model 3367 load frame and load cell
Objectives:
The purpose of this experiment is to acquaint you with the Wheatstone bridge
circuitry used in strain measurement and with commercial strain-measuring equipment.
Introduction
It is very important that resistance strain gages be mounted on the structure on
which measurements are to be made in such a manner that the gages are strained in
exactly the same manner that the structure is strained. To accomplish this, the gages are
bonded to the structure using an appropriate bonding agent (adhesive). The technique for
doing this is not complicated, but it requires very careful attention to details, meticulous
cleanliness, and a considerable amount of practice. After the gages are mounted, lead
wires must be connected to the gage tabs so the gages can be connected to a bridge
circuit for taking strain measurements. The gage leads are attached to the gage by
soldering, which is also an art that requires a great deal of skill.
Before starting to make measurements on either of the specimens on which strain
gages have been previously mounted, closely examine the gage installation and the
attached wires to make sure that the gage appears to be tightly bonded to the specimen,
there are no scratches across the gage, the leads are securely soldered to the strain-gage
tabs, etc. If you detect any possible difficulties with the specimen and gage, ask the TA if
a different specimen is available.
Always record in your lab notebook any information that appears on the
specimens (e.g., gage resistance, gage factor, etc.), on the load cell, etc.
1
1 Fundamentals of the Wheatstone Bridge Circuit and its Application
in Strain Measurement
1.1. Mount the aluminum beam with gages in the angle bracket on the load frame.
Figure 1. A cantilever beam with tip load. The strain gages designated as G1 and G2.
1.2. Make all physical measurements of the beam and loading weight that will be
necessary for calculating the strain in the beam at the location of the gages when the
weight is hung at the outer end of the beam. Record the data for future reference.
Beam:
Length
Width
Thickness
Material
_____________ in (moment arm to the center of gage)
_____________ in
_____________ in
_____________
Weight:
Weight
_____________ lb
1.3. Sketch (in your lab notebook) a bridge circuit in which the two gages can be used to
measure the strain in the beam when it is loaded as a cantilever beam. Use the
arrangement that produces the maximum sensitivity. See the attached supplement if you
don’t know.
1.4. Measure and record the resistance of each of the gages.
Gage #Gl _______________ Ω (top)
Gage #G2 _______________ Ω (bottom)
Hang the weight from the end of the beam and measure the resistances again:
Gage #Gl _______________ Ω (top)
Gage #G2 _______________ Ω (bottom)
Recall that from the definition of gage factor we have ε =
compute the microstrain for each gage:
2
∆R / R
. Use this relationship to
GF
Gage #Gl _______________ µε (top)
Gage #G2 _______________ µε (bottom)
1.5. Construct a 1/2-bridge for strain measurement by connecting the lead wires of the
gages to the balance unit. Complete the bridge using two of the three 120 Ω resistors that
are mounted in an aluminum box. Measure and record the input resistance to your bridge
(across the INPUT terminals). Input resistance: ______________ Ω. Measure and record
the output resistance of the bridge (across the OUTPUT terminals). Output resistance:
______________ Ω. These resistances should be about the same as the resistances of the
gages you measured in Step 1.4.
Balance Unit
P+
DVM
G2
G1
S+
S-
P10V
P+
S+
P-
SBalance
Potentiometer
+ -
Have your Instructor look at your setup before going further.
1.6. Turn on the DC power supply and use the multimeter to set the output voltage to
10V. Turn off the power supply, and then connect it to your bridge input terminals. Also,
connect the multimeter to the bridge output terminals. Set the multimeter to read DC
voltage on the 200 mV scale. Turn on the power supply.
1.7. Zero the output voltage of the bridge using the balance pot of the balance unit.
Observe the output for at least one minute. Does it drift off zero? With your hand, deflect
the end of beam about one inch. What change in the bridge output does this cause?
Deflect the beam approximately the same amount in the opposite direction. How does
this change the bridge output? When you allow the beam to return to its original position,
does the output of the bridge return to zero? Now, hang a weight of about 1 kg (2.2
pounds) on the end of the beam, and record the output voltage.
3
Output voltage at ( _____________ lb load) = _____________ mV.
Remove the weight. Does the output voltage return to zero?
1.8. Create a 1/4-bridge circuit by removing the lower gage from the bridge circuit and
replacing it by a resistor of approximately the same resistance. Re-balance the bridge.
Hang the weight on the beam again, and read the output voltage.
Output voltage at ( ____________ lb load) = ____________ mV.
Remove the weight from the end of the beam.
1.9. Hold your hand on the active gage (i.e., the one left connected to the bridge in Step
1.8) so as to warm it up; then observe the output voltage. What happens?
1.10. Turn off the power supply and un-wire your bridge circuit.
2. Use of the Vishay Micro-Measurements 2100 Strain Gage Conditioner and
Amplifier System
The wiring diagrams and instructions for using this system are in the Instruction Manual.
Very brief instructions are provided in this sheet.
2.1. First, study the bridge diagrams shown in Figure 1 on p.6. of the Instruction Manual.
There are three types of circuits, for a quarter-bridge, half-bridge and a full bridge. You
will use all three of these circuits in this lab.
2.2. Turn the amplifier box on; connect the METER output on 2110B to a voltmeter.
Select Channel 1 on the knob. With the adjusting screw in the first panel, bring the
Excitation Voltage to 2 V. Turn the amplifier box off.
2.3. Connect the strain gage on the top of the cantilever beam in a quarter-bridge
arrangement (Fig 1a on p.6; A1.INTERNAL DUMMY). The cable connected to the
amplifier has terminals A through H as identified in the figures below. Make sure you
pick the correct connection G or H depending on your strain gage. Connect the output
(terminal J2L on the back of the instrument) to a voltmeter. BEFORE turning the power
on, ask the TA to check your connections.
Yellow – E
To strain gage
amplifier
C
D
D
B
C
A
A
B
Blue – H (120Ω)
Orange – G (350Ω)
2.4. Balancing: Turn the amplifier power on. Balance the bridge: Use the balancing
potentiometer until the output is zero.
2.5. Calibration: The System 2000 has internal shunt resistors for calibration. Toggle the
CAL switch to position A and note down the output voltage. Note that this places an
equivalent strain of 1000 µε. Toggle the CAL switch to position B which places an
equivalent strain of -1000 µε in the active strain gage and note down the output voltage
again. These readings give you a calibration of the strain amplifier circuit. NOTE: If you
think the output is too low (sensitivity is too low), then you can increase the gain (the
potentiometer labeled GAIN and the MULTIPLIER switch). Return the CAL switch to
the middle position.
2.6. Apply a known load at the tip of the cantilever and measure the output of the strain
amplifier. Use these measurements for comparison of the theoretically expected strain at
the base of the cantilever.
2.7. Repeat this experiment with a half-bridge arrangement (see Fig 1a on p.6;
B2.ALTERNATE HALF BRIDGE).
3. Measurement of the elastic stress-strain curve in a tensile specimen
3.1. Obtain the prepared aluminum tensile specimen with two gages mounted on it. (This
specimen has a reduced cross section called the gage section. Measure and record the
cross-sectional dimensions of the bar.
3.2. Mount the specimen in the Instron Model 3367 loading frame. This machine has
wedge grips that clamp on to the specimen; you have to set the distance between the top
and the bottom wedge grips equal the total length of the specimen. Do this with the UPDOWN switch on the Instron. Once you have clamped the specimen in the grips DO
NOT use the UP-DOWN switch.
3.3. Strain Gages: Connect the two strain gages on the tensile specimens and the two
gages on the cantilever beam in a full-bridge arrangement (Fig 1a on p.6; C1.GAGES
FULL BRIDGE). Think about how you would arrange the four gages before you make
the connections. Ask the TA to check your connections. Balance the bridge and calibrate
as in Section 2.
3.4. Launch the Series IX software. This program controls the operation of the Instron
and collects data from the Load Cell and Extensometer. The program is set-up to run a
tensile test with a load limit of 1000 lb. Prior to running a test, you should balance and
calibrate the LOAD CELL and the EXTENSOMETER. Click on the BALANCE icon to
make the load display go to zero.
3.5. Clip-Gage Extensometer: Click on the CALIBRATE icon (this is a scale with a
needle pointer). Squeeze on the two buttons of the extensometer with your fingers and
then hit OK. Hold on to the buttons until the calibration is finished. Then connect the
extensometer on the specimen, just below the strain gages using the spring clips. Make
sure the knife-edges on the extensometer do not damage the strain gages. Now click the
BALANCE button to zero out the extensometer.
3.6. Go to the Windows Start button and launch the Virtual Bench – Logger. Open Edit
>Settings and input filename and timing configurations. Make sure Enable Logging
button is checked. Sey the input voltage range for Ch0 based on what you expect for the
strain gage output. You need to estimate the strain in the specimen for a load of 1000 lb
and use this to determine the expected voltage output. After the settings are done, toggle
radio button: “Logging on” and the press “Start” on the Virtual Bench – Logger. The data
from the strain gage amplifier will be sampled at 1 per second and written to the file you
specified.
3.7. Switch back to the Series IX software and click on the Play button. Follow the dialog
boxes. You specify the filename for two types of files (the *.mrd is an internal format for
Instron and the *.txt file is a simple text file) and then enter the correct specimen
dimensions. When these dialog boxes are finished, the test runs automatically. The crosshead of the Instron will move until the load increases to 1000 lb and then stop. Ask the
TA to return the cross-head manually. Click on the OK button. A graphical display of the
collected data in the form of a stress-strain curve will be shown.
3.8. Switch back to the Virtual Bench – Logger from the Task Bar and stop data
acquisition.
3.9. Make copies of the data files saved by the Logger and the Series IX for analysis of
the stress and strain.
Formal Report Instructions:
Discuss the theory of strain gages, Wheatstone bridge circuits, cantilever beam bending
and the tension test in the introductory section. In the section on results, discuss your
measurements on the cantilever beam bending experiment performed with the bridge
circuit that you constructed as well as the one obtained from the Vishay instrument. For
the tension test, you have the load cell output for the force and three different
measurements of the strain: first, the cross-head moves at a constant speed and so you get
a displacement as a function of time that can be converted to strain. Second, the clip-gage
extensometer output provides a measurement of strain in the specimen. Finally, the strain
gage output that was logged provides another measurement of the strain as a function of
time. Compare these through a plot of stress vs strain and discuss what you observe and
given that the Young’s modulus is ~10 million psi for the aluminum alloy. For all
calculations based on measurements, discuss errors quantitatively.
Laboratory 8 Supplement
Measurement of Strain
Fundamentals of the Bridge Circuit
P+
1
2
S-
S+
4
Vex
3
P-
Vo
Note: the bridge boxes used in lab do not correspond exactly to the above schematic.
How are they different? Discuss your hypothesis with the TA.
When identical gages are used in each arm of the bridge circuit, the output voltage is
given by
V  ∆R
∆R 2 ∆R 3 ∆R 4 
V o = ex  1 −
+
−

4  R1
R2
R3
R4 
In the case of strain gages, the gage factor is defined as
∆R R
G=
ε
and thus, the voltage across the Bridge Circuit can be written in terms of strain
G ⋅ V ex
[ε 1 − ε 2 + ε 3 − ε 4 ]
Vo =
4
8
Calibration Resistance
Shunt gage 2 with a known resistance (Rs) as a
means of simulating
a strain in gage 2.
Rs
1
4
simulated strain = ε 2 =
2
where ∆R 2 can be
found by adding
resistances in
parallel.
3
R2 Rs
R 22
∆R 2 = − R 2 +
=−
R2 + Rs
R2 + Rs
Because we can simulate a strain, shunting a gage with a known resistance provides us a
means of finding the sensitivity of the bridge arrangement. We define the sensitivity as
the ratio of output voltage to strain and then use the above equations to relate the strain to
known quantities.
V
G ⋅ V ex [− ε 2 ] G ⋅ V ex
Sε2 ≡ o =
=
ε2
ε2
4
Measurement of Strain in a Cantilever Beam and a Tensile
Specimen
P
Rt
Rb
You can use strain gages on the cantilever beam as dummy resistors when putting
together the full bridge circuit for the tensile test.
9
1 ∆R 2
⋅
G R2