This experiment tested tension and bending using strain gages attached to specimens. For tension, a beam with a 0.53" x 0.125" cross-section was loaded incrementally in a universal tester until maximum load. Strain readings were recorded and averaged. A similar procedure was used for a 1" x 1" bending beam in a four-point bend test. Stress-strain curves were plotted from the data. Young's modulus was calculated from the slopes as 26.7 Mpsi for tension and 55.5 Mpsi for bending, with 11% and 85% errors respectively, likely due to faulty equipment or human error. The goals of introducing strain gage concepts and expanding on Hooke's law and modulus of elastic

1. UNIVERSITY OF CALIFORNIA, MERCED
SCHOOL OF ENGINEERING
STRENGTH OF MATERIALS
ENGR 151
LABORATORY
EXPERIMENT: TENSION AND BENDING WITH STRAIN GAGES
Date of experiment: 10/12/15
Date of report submission: 10/19/15
Submitted by:
Derek Brigham

2. Introduction
This laboratory exercise intended to introduce tension and bending, Hooke’s Law,
modulus of elasticity determination, and strain gage knowledge and use thereof. Tension and
bending are important subjects to mechanical engineering. This is evidenced by a previous lab
having already been completed on tension and bending being a key subject to any strength of
materials course. These two topics require familiarity from any professional or studying
mechanical engineer.
Procedure
Two rectangular 1018 sheet metal specimens were prepared ahead of time for use in
tension and bending. The specimen for tension had a 0.530” x 0.125” cross-section and two
strain gages attached to it. The specimen for bending had a 1” x 1” cross-section and also had
two strain gages attached to it, one on top and one on the bottom (see Specimen section).
The beam for tension was tested first. The first step was to ensure that the strain gages
were properly attached and then connect them to the strain gage reader. Then, the beam was
secured into the Instron universal tester. After this, the use of the proper units was verified and
then the strain gages were zeroed. Now, the testing was performed. Stops were made at various
points and then the strain gage values were read. This continued until the load was nearing the
maximum load which was calculated in the pre-lab (see Appendix A: Pre-Lab Worksheet). Once
this point was reached, a final reading was taken and then the beam was removed and the
equipment was prepared for shutdown.
A similar procedure was followed for the bending specimen. The strain gages were
checked and then connected to the strain gage reader. Next, the beam was secured into the four-
point bend test equipment and then the units were verified and the strain gages were zeroed. The
testing was performed in the same manner as the tension testing; readings were taken in
increments of applied load up until the maximum load which was also calculated in the pre-lab
(see Appendix A: Pre-Lab Worksheet). After the final reading was taken, the equipment was
cleared of the specimen and shut down.
The governing equations for this experiment were:
𝜎𝑥 =
𝑀𝑦
𝐼
(Eq. 1)
Where M is the bending moment, y is the distance from the neutral axis, I is the area
moment of inertia, and 𝜎 is the bending stress.
𝜎 =
𝑃
𝐴
(Eq. 2)
Where P is the applied load, 𝐴 is the area, and 𝜎 is the stress.
𝐸 =
𝜎
𝜀
(Eq. 3)
Where 𝜎 is the stress, 𝜀 is the strain, and E is Young’s modulus.

3. 𝐼 =
𝑏ℎ^3
12
(Eq. 4)
Where b is the base, h is the height, and I is the area moment of inertia.
ε 𝑎𝑣𝑒𝑟 =
ε1+𝜀2
2
(Eq. 5)
Where ε1 is the reading from strain gage #1, 𝜀2 is the reading from strain gage #2,
and ε 𝑎𝑣𝑒𝑟 is the average strain.
ε 𝑎𝑣𝑒𝑟 =
|ε1|+| 𝜀2|
2
(Eq. 6)
Where ε1 is the reading from strain gage #1, 𝜀2 is the reading from strain gage #2,
and ε 𝑎𝑣𝑒𝑟 is the average strain.
Percent difference =
| 𝑎𝑐𝑡𝑢𝑎𝑙−𝑡ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙|
| 𝑡ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙|
∗ 100 (Eq. 7)
The raw data had now been collected from the experiment (see Appendix A: Data Sheet)
and now data analysis was conducted. From the tension data a stress vs. strain plot was prepared
(using Equation 2, also see Figure 1 and Table 1). The strain value used was an average strain
(Equation 5). As shown in Figure 1, a trendline was applied to then determine the value of the
slope of the data, which is Young’s modulus or E. This value could then be applied to the
published values. Next, a value of 30 Mpsi was assumed for Young’s modulus and expected
strain was calculated for the tension test (using Equation 3, also see Table 3 and Appendix A:
Pre-Lab Worksheet). These values were then included into Figure 1 as the Theoretical Stress
(psi) curve.
The same analysis was completed for the bending test as well, with two differences. The
stress vs. strain plot was obtained using Equation 6 instead of Equation 5 because values of
compression (Gage #2 Reading) were read as negative by the strain gage (see Appendix A: Data
Sheet). The second difference was that in Equation 3 a different area was used since the cross-
sections of the tension and bending specimens were different (see Specimen section).
Specimen

4. Results
Equations 1-7 were used to obtain the results of this experiment. Tables 1-3 show the data
obtained from the experiment and also the data analysis such as average and expected strain, in
με, by using Equations 3, 5, and 6. The stress, in psi, was calculated using Equations 1 and 2.
Figures 1 and 2 show the data from Tables 1 and 2 plotted as two curves for actual and
theoretical values along with trendlines which give the value of Young’s modulus from its slope.
As shown in Tables 1 and 2 and in Figures 1 and 2, it can be seen that the average strain
increases proportionally with the increase in actual load and stress. This is to be expected due to
Hooke’s Law (Equation 3), which predicts that stress and strain are linearly proportional. This is
indeed verified by the data of the experiment. In a similar manner, expected strain for both
tension and bending (Tables 1 and 2) increased proportionally to actual load and stress as well.
Table 3 reveals some interesting information; the percent difference of the theoretical and
actual Young’s modulus for tension and bending were both greater than 5%. This was expected,
and seen by a larger difference, for the bending test because the teaching assistant warned that
one of the strain gages for the bending test had malfunctioned and therefore would give
inaccurate readings. However, the tension test was expected to perform well, and it did relative
to bending, but was still outside of the 5% error range. The actual values of Young’s modulus for
tension and bending were 26.7 and 55.5 Mpsi, respectively.
Table 1: Tension – Stress and Average and Expected Strain
Actual
load (lbs) Stress (psi)
Average
Strain (με)
Expected
Strain
(με)
134 2,107 73.5 67.402
250 3,931 142 125.75
367 5,770 210.5 184.601
492 7,736 283.5 247.476
594 9,340 345 298.782
724 11,384 421.5 364.172
Table 2: Bending – Stress and Average and Expected Strain
Actual
load (lbs) Stress(psi)
Average
Strain
(με)
Expected
Strain
(με)
54 875 13.5 29.2
102 1,652 26.5 55.1
153 2,479 41 82.6
205 3,321 56 110.7

5. 256 4,147 71.5 138.2
327 5,297 93 176.6
Table 3: Tension and Bending – Young’s Modulus and Percent Difference
𝐸 𝑇𝑒𝑛𝑠𝑖𝑜𝑛 (Mpsi) 𝐸 𝑇𝑒𝑛𝑠𝑖𝑜𝑛 % Error 𝐸 𝐵𝑒𝑛𝑑𝑖𝑛𝑔 (Mpsi) 𝐸 𝐵𝑒𝑛𝑑𝑖𝑛𝑔 % Error
26.7 11 55.5 85
Figure 1: Tension – Stress vs. Strain
Figure 2: Bending – Stress vs. Strain
y = 26.664x + 151.91
0
2,000
4,000
6,000
8,000
10,000
12,000
0 100 200 300 400 500
Stress(psi)
Strain (με)
Stress vs. Strain in Tension
Stress (psi)
Theoretical Stress (psi)
Linear (Stress (psi))

6. Discussion
The calculatedYoung’smodulusforthe tensiontestwas relatively accurate.The Young’s
moduluscalculatedforthe bendingtest,however,was farlessaccurate.The Young’sfromthe tension
testdeviatedfromthe publishedresultsbyonly 11% (see Table 3 and Equation7) while the bendingtest
had an error of 85% (see Table 3and Equation 7). These resultscouldbe due inpartto faultyequipment
ineitherof the straingages forboth the tensionandbendingtests,butcertainlymore sointhe bending
testdue to faultyequipment.Also,the specimenmayhave slippedwhile underloadineithercase of
tensionorbending,whichwill resultininaccurate readingsfromthe straingages;since the errorwas
higherinthe bendingtest,thiswas more likelythe case inthe bendingtest. Humanerrorcertainly
occurredwhenwritingdownthe readings givenbythe straingages;thisis because the numbersusually
shiftarounda bit,but thiswill be averyminimal effect.
Straingage loadcellsare small instruments thatdetectaloadof eithertensionorcompression
by measuringthe increase ordecrease inelectrical resistance throughthe loadcell.Thisistypicallya
verysmall change,butit isstill detectablewithaccuracybyusingan amplifier.Straingage loadcellsare
typicallyusedinsetsof fourforloadtesting,twointensionandtwoin compression.A straingage load
cell couldbe designedusingaWheatstone bridgecircuitconfiguration,whichisanelectrical circuit
configuration knownforbeingextremelyaccurate thatallowsone tosolve foran unknownelectrical
resistance.Itisdone bybalancingtwolegsof a bridge circuit,withone legcontainingthe unknown
electrical resistance.Fourof these straingage loadcells constructedthiswaycouldthenbe bondedto a
beam,twoin tensionandtwoincompression. Afterconnectingthe straingagestoa device like the one
usedinthisexperimentwouldthenbe readytotesttensionandcompressioninabeam.
Conclusion
This experiment sought to introduce strain gage load cells and their use in determining
strain in beams under tension and bending stresses. It also sought to further expand upon the
concepts of Hooke’s Law and Young’s modulus of elasticity. This goal was accomplished
y = 55.502x + 172.87
0
1,000
2,000
3,000
4,000
5,000
6,000
0 50 100 150 200
Stress(psi)
Strain (με)
Stress vs. Strain in Bending
Stress(psi)
Theoretical Stress (psi)
Linear (Stress(psi))

7. through the data collection and analysis that this experiment required. Skills developed through
this laboratory exercise will be very useful for this class and also further on in professional life.