The document describes a lab experiment to construct a cantilever beam with an attached strain gage. This setup is used to determine the weights of various objects by measuring changes in resistance from the strain gage. The beam is calibrated using two methods: 1) pure bending theory based on mechanics principles and 2) a calibration curve method using known weights. Results show the calibration curve method has lower uncertainty and is therefore more accurate for determining unknown weights.

1. Abstract—the goal of this lab is to construct a cantilever beam
with an attached strain gage that can determine the weight of
objects based on the change in resistance from the strain gage. In
order to obtain meaningful data, we had to calibrate the beam
using two different methods: 1) pure bending theory based on
Mechanics of Materials and2) calibration method which involved
finding a curve of best fit basedon the calibration weights obtained
in the lab.
Index Terms- pure bending, calibration, stress, strain
I. INTRODUCTION
HIS labs goal was to create a cantilever beam with an
attached strain gage in order to determine the weights of
various objects including a soda can, average gulp weight and
the weight of an object that the student chose.To achieve this,
we first had to create a LabView VI that could collect the
necessary data through the DAQ. Once complete, the students
had to construct the cantilever beam by following the provided
instructions and wire the strain gage to the Tauna Systems strain
gage amplifier which was wired to a Wheatstone bridge similar
to that in lab 1. Once everything was wired up, the students had
to adjust the strain gage amplifier using the zero screw to get a
Vg reading of approximately 2.5 V. This was performed in order
to get Vg into the correct sampling window and to balance the
Wheatstone bridge. Once this was complete the students could
begin weighing objects. The two methods for calculating the
weights of the objects that were used include 1) Pure Bending
Theory from Mechanics ofMaterials and 2) Use ofa calibration
curve. The Pure Bending theory from Mechanics of Materials
calculates the weight of the object based on the strain that
occurs and the beams dimensions.The calibration curve method
uses weights with known masses as well Vamp readings to create
a calibration curve that properly scales the beam to read the
correct weight values.
II. PROCEDURE
Attaching strain gage to the cantileverbeam
In part one of this lab, the students had attach the strain gage
the cantilever beam using the provided instructions. First off,
the cantilever beam was clean to provide a clean bonding
surface. After this, the strain gage was attached with glue
approximately 8 inches from the end of the cantilever beam and
0.5 inches away from the edge of the beam. After this step was
performed, markings were drawn onto the beam in order to
ensure that the calibration weights and the soda cans were place
approximately the same location each time data collection was
performed. Fig. 1. shows this illustration. After attaching the
strain gage, the cantilever beam was mounted in a provided
mounting bracket in order to properly the beam to obtain data.
Fig. 1. Cantilever beam illustration. [4]
Wiring
After securing the cantilever beam to the provided mount,
the strain gage has to be wired to obtain any readings. The
strain gage was first wired to the strain gage amplifier as
shown in Fig.2. Doing this is needed in order to make the
Wheatstone bridge work properly. After this was completed,
the strain gage amplifier was then wired to the DAQ using
the AI1 and AI0 ports on the DAQ.
Fig. 2. Strain Gage Amplifierwiringschematic [4]
Lab 2: Construction of Cantilever Beam Strain
Gage
Ballingham, Ryland
Section 3236 2/12/16
T

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Creating the Labview VI
In order for the VI to be able to successfully collect data, it
had to be able to determine the unknown weight of the object
placed onto the beam. To accomplish this, the VI calculated
the strain from the voltage measurement readings obtained
from the DAQ. After this, equations were used from
Mechanics of Materials in order to find the unknown object
weight.
The first equation used to calculate the strain at the gage
uses acquired voltage readings from the DAQ. Equation (1) is
as follows:
𝜀 =
4∆𝑉𝑔
𝑉𝑠 𝐺𝑓
(1)
After calculating the strain value, the stress (𝜎) can be found
using Hooke’s Law as follows:
𝜎 = 𝐸𝜀 (2)
Where E is the modulus of elasticity of the cantilever beam.
After solving for the stress,pure bending theory can be used to
solve for the unknown object weight.
𝜎 =
𝑀𝑐
𝐼
=
6𝑊𝐿
𝑏ℎ2
(3)
𝑐 =
1
2
ℎ (4)
𝑀 = 𝐿𝑊 (5)
Where M= bending moment, W=weight of the object,
L=length of the beam, h=height of the beam and b= width of
the beam. I=moment of inertia is given as follows by (6)
𝐼 =
1
12
𝑏ℎ3 (6)
From this, solving for the strain (𝜀) we get the following:
𝜀 =
6𝑊𝐿
𝐸𝑏ℎ2 (7)
𝑊 = 𝜎 (
𝑏ℎ2
6𝐿
) (8)
Data collection Procedure
Before collecting the data samples, the values for the h
(3.15mm), b (25mm), L (170mm) and E (69000 GPa). Also
Vamp had to be tared manually using the tare window located on
the LabView front panel. Furthermore, the sampling window
needed to be set for ±5 V to get an accurate reading of the
voltage measurements that are approximately 2.5 V.
A. Using Mechanics of Materials
The LabView written accomplishes this due to (1)-(8) which
are functions written into the LabView VI program.
B. Calibration method using calibration weights
This method uses calibration weights with known values to fit
a calibration curve using excel. In order to perform this
method, different weights were measured (50, 100, 200, 300
and 350 grams) using the scales in lab. The actual scale
reading of these weights were recorded then plotted versus
Vamp (Vamp is obtained by using the cantilever beam to weigh
the weights). From this, a trend line can be calculated from the
data in order to find the unknown weight using Vamp
C. Repeatability ofthe readings
To perform this step,the soda can was weighed 10 times with
the can being removed after each individual reading and
placed back on the beam in approximately the same location.
The data was recorded to excel.
D. Gulp test
In this test,the weight of a full can of soda was weighed on
the lab scale and recorded. After this, the can of soda was
placed onto the cantilever beam beginning at full weight.
During the data recording, gulps were taken at random
intervals and the can was placed back onto the beam after each
gulp. This was done until the can became empty.
E. Weight of student item
In this part of lab, the students were allowed to weigh
whatever item they had on them. First, the item was weighed
on the lab scale and then the cantilever beam. After this step,
the students placed a finger onto the beam in order see how
the data changed with the added load.
III. RESULTS

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Fig. 3. Vamp vs. time from thecalibration weights.
Fig. 4. Calibrationweights vs time plot.
TABLE I
CALIBRATION VALUES
#
Calibration Weight
(g)-Lab Scale
Vamp (V)
1 50 2.491
2 99.9 2.488
3 197.7 2.478
4 297.6 2.455
5 347.5 2.441
TABLE II
REPEATABILITY VALUES
Placement number
Weight (g)-MOM
Method
Vamp (V)
1 413.567 2.439
2 406.823 2.441
3 411.112 2.433
4 407.589 2.433
5 415.003 2.433
6 414.376 2.433
7 407.983 2.435
8 409.178 2.434
9 407.887 2.434
10 412.674 2.433
TABLE III
GULP TEST
Gulp number
Weight (g)- MoM
Method
Vamp (V)
0 413.567 2.432
1 371.223 2.442
2 322.563 2.450
3 276.238 2.459
4 237.887 2.466
5 201.457 2.475
6 161.112 2.483
7 101.987 2.490
8 41.223 2.511
9 14.997 2.514
TABLE IV
PHONE WEIGHT/ FINGER VALUES
Weight (g)-MOM
Method
Weight (g)-
Lab Scale
Vamp (V)
Finger Off gage 191.134 186 2.479
Finger On gage 161.122 - 2.485
IV. DISCUSSION
1. The maximum weight that the cantilever beam can
theoretically measure can be determined from (8). Since
we are using 6061 T6 aluminum which has a yield strength
(𝜎 𝑦) value of 241 MPa. Since we know what the
dimensions of the beam and the distance to the load, the
max weight can be solved for which is 58.61 N.
2. The full can weight was measured by using the calibration
curve method. A trendline was created by plotting the
actual calibration weight values vs their respective Vamp
values during the data collection in LabView. Using excel,
the calibration trendline equation was:
𝑦 = −4993.8 ∗ 𝑉𝑎𝑚𝑝 + 13323 (9)

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Fig. 5. Plot of weight vs. Vamp with thecalculatedtrendline
Using (2) as well as the measurements of Vamp, the mean
weight of the 10 different calculated weights was determined
to be 385.7 g. Using the mechanics of materials method, the
mean weight of the 10 weight measurements from table II is
equal to 410.6 g.
3. The uncertainties of both cases (mechanics of materials
and calibration methods) were found using (14) and (15).
The mechanics of materials method had an uncertainty of
±17.6 g. The calibration method had an uncertainty of 5.5
g. Because the calibration method has a smaller
magnitude of uncertainty, it was the better method.
4. Calculations for the standard deviation and the mean for
the repeatability test were found using
𝑆𝐷 = √
1
𝑁
∑( 𝑥 𝑖 − 𝑥̅)2
𝑁
𝑖=1
(10)
𝑥̅ =
∑ 𝑥𝑖
𝑁 (11)
Using (10) and (11), the standard deviation was 3.10 g and the
average was 410.6 g.
5. A confidence interval can be calculated using the
following:
𝑥 𝑖 = 𝜇 𝑓 +
𝑡𝜎𝑓
√𝑁
(12)
Using (9) as well as a t-table in [3] and the measurements
obtain for 𝜎𝑓, 𝜇 𝑓, 𝑎𝑛𝑑 𝑁 that are located in table V, the 95%
confidence interval was calculated to be 385.7±3.81 g. Due to
the fact that we are 95% confident that the following can
placement will have a reading of ±3.81 g within the mean
shouldn’t cause any problems due to repeatability.
6. The standard deviation and mean for gulp size were
calculated using (10) and (11). Since the calibration
method had a lower uncertainty value, it was method
used.Doing this yielded a mean of 38.6 g and standard
deviation of 7.55 g.
7. The weight of the empty can on the lab scale yielded a
value of 15.9 g. The cantilever beam scale yielded a value
of 12.874 g. The differences in weight of the two values
comes from the uncertainties calculated for each case.
The values for uncertainty are located in the appendix.
8. In order to reduce the uncertainty associated with using
the cantilever beam we must improve the accuracy of the
dimension values of the beam measured. This can be done
by using better instruments to find these values. Also, use
a better more sensitive strain gage will lower the
uncertainty associated with the cantilever beam. Lastly,
minimizing outside vibrations will cause the uncertainty
value to decrease.
9. The weight of the beam affects the calibration of the
beam. The weight of the beam causes a slight amount of
strain that can be detected by the strain gage. The way we
remove this problem is by taring Vamp at the start of data
collection. Doing this gets rid of changes in resistance that
would be detected as strain by the strain gage.
V. CONCLUSION
This lab taught students that there are many possible
methods to calculate the weight of an object. The main
emphasis is that while there may be many ways to measure the
weight of an object, methods with lower uncertainty values are
preferred as lower uncertainty values yield more accurate
measurements. Since using the calibration method yielded
lower uncertainty values, it was the method used.The can of
soda that weighed 388.7 g on the lab scale weighed 410.6 g
using the mechanics of materials method and 385.7 g using the
calibration method. This data can be found in the appendix.
APPENDIX
TABLE V
UNCERTAINTY VALUES
Parameter Calculated Uncertainty
Vamp ±4.51 V
VS ±4.52 V
VG ±0.025 V
𝜎 ±6.6 GPa
𝜖 ±0.0287
W ±16.4g
WC ±5.1 g
h ±0.0008 in.
𝑏 ±0.00007 in.
L ±0.3 mm

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Gf ±0.5%
Calibration Weight ±0.2 g
Uncertainty equations [2][3]:
𝑈 𝑉𝑎𝑚𝑝
= 0.22 ∗
𝑉𝑎𝑚𝑝
220
+ 𝑈 𝐷𝐴𝑄 (11)
𝑈∆𝑉 𝑔
= ((
𝑑∆𝑉𝐺
𝑑∆𝑉𝑎𝑚𝑝
)
2
(𝑈 𝑉 𝑎𝑚𝑝
)
2
)
1/2
(12)
𝑈𝜖 = √(
𝑑𝜖
𝑑∆𝑉𝐺
)
2
( 𝑈∆𝑉 𝐺
)
2
+ (
𝑑𝜖
𝑑𝑉𝑠
)
2
( 𝑈 𝑉𝑠
)
2
+ (
𝑑𝜖
𝑑𝐺𝑓
)
2
( 𝑈 𝐺 𝑓
)
2
(13)
𝑈 𝜎 = ((
𝑑𝜎
𝑑𝜖
)
2
( 𝑈 𝜖)2
+ (
𝑑𝜎
𝑑𝐸
)
2
( 𝑈 𝐸)2
)
1/2
(14)
𝑈 𝑊
= √(
𝑑𝑊
𝑑𝑏
)
2
( 𝑈𝑏
)2 + (
𝑑𝑊
𝑑ℎ
)
2
( 𝑈ℎ
)2 + (
𝑑𝑊
𝑑𝐿
)
2
( 𝑈𝐿
)2 + (
𝑑𝑊
𝑑𝜎
)
2
( 𝑈𝜎
)2 (15)
𝑈 𝑊 𝐶
= √(
𝑑𝑊
𝑑 𝑉 𝑎𝑚𝑝
)
2
(𝑈 𝑉 𝑎𝑚𝑝
)
2
+ (
𝑑𝑊
𝑑𝑚
)
2
( 𝑈 𝑚)2 (16)
REFERENCES