Introduction to Strain Gage Lab
ME 125L: Measurement and Modeling of Dynamic Systems
Instructor: Professor Silvia Ferrari
TA: Chenghui Cai
November 5, 2006
The purpose of this laboratory is to calculate the amount of carbon dioxide put inside a soda
via measuring the strain change. Assuming the soda can is a thin-walled pressure vessel, a strain
gage is used to measure the strain on the soda can based on its own deformation. The strain value is
converted to electrical resistance, outputted through a strain indicator, and used to determine the
mass of carbon dioxide inside the can using the ideal gas law.
During the lab procedure, we will use a strain gage to find the strain due to an increase in
pressure within a soda can. This will enable us to determine the amount of carbon dioxide put into
the soda can to make it fizz when popped. To do so, one must assume the soda can to be a thin-
walled pressure vessel. This indicates that the thickness of the wall is no more than 10% of the
vessel’s diameter. The strain gage measures strain based on its own deformation during
Pressurized Soda in a Can
A strain gage, as shown in Figure 1, measures strain based on its own deformation during
experimentation and converts strain into electrical resistance. As equation (1) indicates, the
relationship between wire resistance, Rw, length of the wire, L, cross-sectional area of the wire, A,
and resistivity, , indicates that as the wire is stretched, L increases and A decreases.
Figure 1: Strain Gage 
strain direction R
foil Since also increases, resistance increases linearly with strain as follows:
where S is the strain gage factor with a value of 2.11 for this experiment. A strain indicator is used
to determine these miniscule changes in resistance through the use of an electric circuit, and outputs
a visual strain reading in units of microstrain .
Output voltage can be determined from Ohm’s Law as follows:
R 3 R1 R 4 R 2
( R 2 R 3)( R1 R 4)
where Vs is the supplied voltage, R1=R2=R4=120Ω, and the
value of R3 is a sum of the resistance of the strain gage and
the internal potentiometer. Adjusting the potentiometer
results in an initial R3 resistance (R3i) of 120Ω. When strain
occurs, R3i is increased by dR3. Since R1=R2=R3i=R4=120Ω, equation (3) becomes:
dR3 S (4)
Vo Vs Vs
4 R 3i 4
where dR3/R3i = R/R = S .
Figure 2 shows the quarter bridge circuit where we only need connect the strain gage as an
active resistance. We also can choose half bridge circuit, where we need make another strain gage
on a bar as an active compression and connect the strain gain on the can as R2 (or R3) and connect
the strain gain on the bar as R3 (or R2). The principle is the same, i.e., to measure the resistance
change and convert to voltage signal.
The pressure inside the soda can is calculated by first assuming
the soda can is a thin-walled pressure vessel whose wall thickness is no
more than 10% of the vessel’s diameter. Strain, , is defined as the
change in length over the initial length: L/Lo. Meanwhile, stress is
defined by the parameters in Figure (3) as follows:
h (5a) l (5b)
where di is the inner diameter of the soda can, do is the outer diameter, E is the Modulus of
Elasticity, Pi is the internal pressure, h is the wall hoop stress, l is the longitudinal stress and t is
the wall thickness .
Using Hooke’s Law below (according to the coordinate system in Figure 3) for
homogeneous isotropic materials, the strain of the material becomes:
x y z h l h
h , h (1 0.5 ) (6)
E E E E E E
where is poisson’s ratio and where the stress perpendicular to the surface is neglected.
Combining equation (6) with (5a) results in the following formula for Pg:
(1 0.5 )di
where Pi is equivalent to the absolute pressure, Pabs. To find gage pressure, Pg, atmospheric
pressure, Patm, must be subtracted from Pi as shown in equation (8).
Pg Patm Pabs (8)
where Patm is 101.33kPa . Here since h obtained by strain indicator is negative, the pressure change Pg is
negative. That means that the initial pressure inside the can, Pabs is greater than the final pressure Patm.
The Ideal Gas Law is used to approximate the mass of CO2 released from the soda can.
PV nRT (9)
where P is absolute pressure [N/m2], V is volume of CO2, n is number of moles of CO2, R is the gas
constant with a value of 8.31 J/(mol. K) for CO2, and T is temperature [K] . The mass of CO2 can
be determined by solving for n and converting the number of moles to mass as follows:
n moles of CO2 · m grams of CO2 = mass of CO2 (10)
1 mole of CO2
Finally, the arithmetic mean and standard deviation for the experimental data are calculated.
The mean, χ, is the average of the gathered values and can be calculated as follows:
where N is the number of gathered values. Finally, the standard deviation, σ, tells us how close the
data is gathered around the means and is calculated as follows:
N i 1
In addition, the most common value is the mode and when the values are listed from smallest to
largest, the median is the value in the center of the list if N is odd or the average of the two middle
values if N is even .
The procedure for part I was completed through the use of the following materials: stain
gage, solder, and a Vishay 3800 Strain Indicator. Figure 4 shows the functional diagram:
Figure 4: Instrument Functional Diagram
Fluid Strain Gage Strain Gage Wiring
Strain Primary Variable Data
Medium Conversion Transmission
Element Element Circuit Element
Variable Variable Data
Manipulation Presentation Observer
Element Signal Element Signal Element
Strain Indicator Strain Indicator Digital Display
In addition, Figure 5 shows a visual representation of the strain indicator.
Figure 5: Vishay 3800 Strain Indicator 
Digital display of
strain and voltage Wires from strain
to these ports
Knob to set
voltage to ~0
A soda can is lightly sanded with 320-grade sandpaper to reveal a sanded surface of
approximate 2cm by 2cm. The surface is then cleared running a gauze sponge in one direction
along the surface of the can to avoid contamination. Sanding and properly cleaning the surface
allows the gage to better attach to the can. The strain gage is then placed on a piece of tape with
the copper side (shiniest face) of the gage facing the sticky side of the tape. The opposite side of the
gage is then lightly coated with a catalyst to allow it to better attach to the can .
Next, the tape is placed vertically on the surface of the can so that the strain gage is
accurately positioned on the sanded area with the middle strain gage running along the can’s
circumference. One end of the tape is attached to the can and a drop of superglue is added to the
interior surface of the hanging tape. The remainder of the tape is pressed onto the surface of the
can by running a gauze sponge from bottom to top along the outer surface of the tape. This step
must be completed rapidly because the catalyst helps the superglue harden at a faster rate. Pressure
is then applied with your thumb to the surface of the strain gage for one minute. Finally, the tape is
removed carefully from the surface of the can, leaving the gage firmly attached to the can .
When the can is ready for experimentation, two wire leads are soldered onto the gage’s
contact pads. If a quarter bridge circuit is employed, these wires are then plugged into the strain
indicator by connecting one wire to the top port, and the other to both the third and fifth ports. If a
half bridge circuit is used, the connection is different. The connections can be found in the manual
of Vishay 3800. The gage factor is set at 2.11 and the displayed strain is set at zero. To conclude
this procedure, one of the things is to be done: the top of the soda can is popped or the can is shaken
and the strain reading is recorded .
Results for this laboratory are to be calculated using the material specifications listed in
(1) This is an introduction to the lab. The only purpose of this handout is to explain the principle of
how to calculate the amount of carbon dioxide put inside a soda can. You should understand and
derive EVERY equation on your own.
(2) In Lab 4, you may just do the experiment once. In other words, in Equation 11, N=1 and ignore
 Crews, Kelli. T.A. Thermal Anemometer Slides. ME125L, Professor Silvia Ferrari. February
 Crews, Kelli. T.A. Voltage, Velocity Conversion Table (Handout). ME125L, Professor Silvia
Ferrari. February 2004.
 Crews, Kelli. T.A. Wind Tunnel Handout. ME125L, Professor Silvia Ferrari. February 2004.
 Ferrari, Silvia. ME125L: Classnotes. Spring 2004.
 Jensenius, Mark, T.A. ME125L: Pressurized Soda in a Can (Handout). ME125L, Professor
Silvia Ferrari. February 2004.
 Munson, Bruce R. Fundamentals of Fluid Mechanics (4th Edition). John Wily & Sons, Inc.,
2002. pg 14 and inside cover.
 Olivari, D. & Carbonaro, M. Chapter 5: Hot Wire Measurements (Handout). ME125L,
Professor Silvia Ferrari. February 2004.
 InterTechnology, Inc. Wide Range Strain Indicator Vishay 3800 Model.