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TRANSCRIPT
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Beam Bending Lab Report
Submitted to:Dr. Annie Abell
&Miss MohiniDutt
Prepared By:Ian Hildebrandt
Engineering 1181The Ohio State University
College of EngineeringColumbus, OH
September 18, 2012
1Beam Bending Lab
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Table of Contents
List of Figures and Tables……………………………………………………………………...1
Executive Summary…………………………………………………………………………….2
Introduction………………………………………………………………………………………3
Content……………………………………………………………………………………….5-17
Task 2…………………………………………………………………………….5
Task 3-7………………………………………………………………………6-17
o Task 3………………………………….………………………………8-9
o Task 4……………………………………………………….………10-11
o Task 5………………………………………………………….……12-13
o Task 6…………………………………………………………….…14-15
o Task 7…………………………………………………………….…16-17
Deflection vs. Force Applied for 5 Beams…………………………………………………..18
Discussion Questions……………………………………………………………………..19-20
Conclusion………………………………………………………………………………….20-21
Appendices / Attachments……………………………………………………………………22
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Lists of Figures and Tables
Figure 1: Beam Bending Apparatus....………………………………………………………..3
Figure 2: Table and Graph of Task 3………………………………………………………….8
Figure 3: Table and Graph of Task 4……………………………………………………..…10
Figure 4: Table and Graph of Task 5………………………………………………………..12
Figure 5: Table and Graph of Task 6………………………………………………………..14
Figure 6: Table and Graph of Task 7………………………………………………………..16
Figure 7: Graph of Deflection vs. Force Applied for All Five Beams……………………..19
3Beam Bending Lab
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Executive Summary
The overall purpose of this lab was to explore the basic concepts that engineers use
to design economical and safe structures. In order to do this, students used the beam
bending apparatus shown below (Figure 1) to test the deflection of various materials.
The first step of this lab included assembling the beam bending apparatus. During the
building process, it was extremely important to make sure everything was aligned and
tightened properly. The next step of the lab was to begin taking measurement on the
five different beams. All the measurements were recorded in the excel lab worksheet
located on the class drive. Students started by measuring and recording the width and
thickness of each beam using the dial caliper. After, students measured the minimum
and maximum values with no weight on the weight holder. Lastly, students continued to
repeat measuring the minimum and maximum for each of the ten weights and recorded
all the values in the excel seed file. The first beam measured was the aluminum
cantilever beam. The second beam measured was the steel beam followed by the
aluminum box beam, the polystyrene beam, and the basswood beam. After the lab was
completed and the data was analyzed, the strongest beam was found to be the steel
beam and the weakest was found to be the polystyrene plastic.
Figure 1: Beam Bending Apparatus
4Beam Bending Lab
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Introduction
The overall goals of this lab were to:
Investigate and apply the concepts of stress, strain, and Young’s modulus
for structural materials.
Apply the stress-strain equation to calculate how applied forces deform
structures.
Calculate the moment of inertia of various beam geometries and
determine how beam geometry affects the stiffness and strength of beams
Use dial calipers and dial indicators to make accurate measurements of
the dimensions and deflections of structural beams.
Apply forces to cantilever beams and measure beam deflections.
This lab report contains multiple sections that explain the results of the beam
bending lab. In the first section, task 2, the lab worksheet is discussed in its entirety. In
task 3-7, the data and graph for each individual beam is discussed also. Following these
tasks, the four discussion questions are answered. Finally, the conclusion section is the
last part of the lab.
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Task 2
The beam bending lab worksheet on excel that was provided to the students was an
extremely useful tool. Students had to continuously record data throughout the entire
duration of the lab. Students were able to easily type in all the values into the excel
worksheet. This helped with time management and, as a result, efficiency during the
lab. The beam bending worksheet does the calculations for the students. It plots the
deflection vs. force and the theoretical deflection and applies a linear trend line to both.
The worksheet goes in order from task 3 to task 7. It has spaces for students to record
all the values measured during lab. Under the spaces designated for inputting data,
there is a graph for each task.
The number in cell H14 refers to the moment of inertia for the aluminum beam. It
uses the equation in cell G14 which takes the width of the beam multiplied by the
thickness of the beam cubed all divided by 12. This value is used to find the theoretical
deflection which is plotted on the graph for each beam as the red line. The moment of
inertia is calculated for all five beams using the same process as cell H14.
6Beam Bending Lab
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Task 3-7
The purpose of task 3-7 was to measure deflection for five different beams in order
to find out which one was the strongest. Students recorded values for ten different
weights that were applying forces on the beams. The amount of deflection that the
beam was experiencing was recorded using the dial indicator. The deflection vs. force
graph was plotted automatically by the lab worksheet for each beam and students were
able to immediately see the accuracy of their results by comparing their data to the
theoretical deflection line.
The function of the dial indicator was to measure the deflection in inches of each
beam. The dial indicator is very precise and can make accurate measurements to the
thousandths place in inches. The dial indicator is read in two steps. First, students read
a small dial which indicated the tens place and second, they read the large dial which
indicated the thousandths place.
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Figure 2: Table and Graph of Task 3
8Beam Bending Lab
Task 3 1 MPa = 145.038 lbf/in^21 lbf = 453.5924 gmf
Material: 6061 Extruded AluminumRectangular Beam
Young's Modulus E = 10,000,000 lbf/in^2 (psi) = 68,948 MPaDistance to Force L = 8.750 inDistance to Dial Ind S = 7.500 inWidth of beam w = 0.492 inThickness of beam t = 0.122 in
Moment of Inertia I = w * t^3 / 12 = 7.4450E-05 in^4
Theoretical Deflection δ = inch
Number of Weights (50 gm)
Total Weight (gmf)
Force (lbf)Incremental
Deflection, Δx (check this)
Force (lbf)Measured Deflection
(in)
Theoretical Deflection
(in)Error
min max avg ~ constant ? Force Measured TheoryNone 0 0.000 0.142 0.155 0.149 0 0 0.000
1 50 0.110 0.166 0.178 0.172 0.024 0.110 0.024 0.026 -10%2 100 0.220 0.193 0.208 0.201 0.029 0.220 0.052 0.052 0%3 150 0.331 0.223 0.228 0.226 0.025 0.331 0.077 0.078 -1%4 200 0.441 0.255 0.257 0.256 0.031 0.441 0.108 0.104 3%5 250 0.551 0.281 0.284 0.283 0.027 0.551 0.134 0.130 3%6 300 0.661 0.307 0.323 0.315 0.033 0.661 0.167 0.156 7%7 350 0.772 0.335 0.349 0.342 0.027 0.772 0.194 0.182 6%8 400 0.882 0.366 0.372 0.369 0.027 0.882 0.221 0.208 6%9 450 0.992 0.389 0.401 0.395 0.026 0.992 0.247 0.234 5%
10 500 1.102 0.414 0.435 0.425 0.030 1.102 0.276 0.260 6%
F * S^2 * (3L-S) / 6 E I
Dial Indicator Reading (in)
0.000
0.050
0.100
0.150
0.200
0.250
0.300
0.00 0.20 0.40 0.60 0.80 1.00 1.20
Abso
lute
Defl
ectio
n (In
ch)
Force (Weight) applied to Beam (lbf)
Deflection vs. Force for Aluminum Beam
Measured
Theory
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Task 3
In this task, the measurements were very accurate. It can be seen on the graph that
the red theory line runs almost through all the recorded data points in blue. There was
also very small percent error for these measurements with the highest percent error
reaching only 10%.
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10Beam Bending Lab
Task 4 1 MPa = 145.038 lbf/in^21 lbf = 453.5924 gmf
Material: Mild SteelRectangular Beam
Young's Modulus E = 30,000,000 lbf/in^2 = 206,843 MPaLength of beam L = 8.750 inDistance to Dial Ind S = 7.500 inWidth of beam w = 0.500 inThickness of beam t = 0.125 in
Moment of Inertia I = w * t^3 / 12 = 8.1380E-05 in^4
Theoretical Deflection δ = inch
Number of Weights (50 gm)
Total Weight (gmf)
Force (lbf)Incremental
Deflection, Δx (check this)
Force (lbf)Measured Deflection
(in)
Theoretical Deflection
(in)Error
min max avg ~ constant ? Force Measured TheoryNone 0 0.000 0.190 0.195 0.193 0 0 0.000
1 50 0.110 0.200 0.205 0.203 0.010 0.110 0.010 0.008 26%2 100 0.220 0.210 0.215 0.213 0.010 0.220 0.020 0.016 26%3 150 0.331 0.218 0.222 0.220 0.008 0.331 0.028 0.024 15%4 200 0.441 0.230 0.234 0.232 0.012 0.441 0.040 0.032 24%5 250 0.551 0.239 0.244 0.242 0.009 0.551 0.049 0.040 23%6 300 0.661 0.250 0.257 0.254 0.012 0.661 0.061 0.048 28%7 350 0.772 0.261 0.270 0.266 0.012 0.772 0.073 0.056 31%8 400 0.882 0.270 0.275 0.273 0.007 0.882 0.080 0.063 26%9 450 0.992 0.283 0.286 0.285 0.012 0.992 0.092 0.071 29%
10 500 1.102 0.292 0.299 0.296 0.011 1.102 0.103 0.079 30%
Dial Indicator Reading (in)
F * S^2 * (3L-S) / 6 E I
0.000
0.020
0.040
0.060
0.080
0.100
0.120
0.00 0.20 0.40 0.60 0.80 1.00 1.20
Abso
lute
Defl
ectio
n (In
ch)
Force (Weight) Applied to Beam (lbf)
Deflection vs Force for a Steel Beam
Measured
Theory
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Figure 2: Table and Graph of Task 4
Task 4
For this task, the deflection of a steel beam was measured. The error in the
measurements was a little larger than the error for task 3. Regardless, the
measurements were still accurate and the data points stay relatively close to the theory
line as can be seen from the graph. The highest percent error was only 31%.
11Beam Bending Lab
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12Beam Bending Lab
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Figure 4: Table and Graph of Task 5
13Beam Bending Lab
Task 5 1 MPa = 145.038 lbf/in^21 lbf = 453.5924 gmf exact
Material: AluminumOpen Box Beam
Properties: Young's Modulus E = 10,000,000 lbf/in^2 (psi) = 22,046 MPaDistance to Force L = 8.750 inDistance to Dial Ind S = 7.500 inWidth of outside w1 = 0.250 inWidth of Inside w2 = 0.234 inThickness of Outside t1 = 0.250 inThickness of Inside t2 = 0.234 in
Moment of Inertia I = ( w1 * t1^3 - w2 * t2^3 )/ 12 = 7.5669E-05 in^4
Theoretical Deflection δ = inch
Number of Weights (50 gm)
Total Weight (gmf)
Force (lbf)Incremental
Deflection, Δx (check this)
Force (lbf)Absolute
Deflection (in)
Theoretical Deflection
(in)Error
min max avg ~ constant ? Force Measured Theorynone 0 0.000 0.184 0.187 0.186 0 0 0.000
1 50 0.110 0.198 0.209 0.204 0.018 0.110 0.018 0.026 -30%2 100 0.220 0.229 0.270 0.250 0.046 0.220 0.064 0.051 25%3 150 0.331 0.275 0.298 0.287 0.037 0.331 0.101 0.077 31%4 200 0.441 0.297 0.332 0.315 0.028 0.441 0.129 0.102 26%5 250 0.551 0.338 0.358 0.348 0.034 0.551 0.163 0.128 27%6 300 0.661 0.357 0.382 0.370 0.022 0.661 0.184 0.154 20%7 350 0.772 0.385 0.403 0.394 0.025 0.772 0.209 0.179 16%8 400 0.882 0.411 0.438 0.425 0.031 0.882 0.239 0.205 17%9 450 0.992 0.439 0.469 0.454 0.030 0.992 0.269 0.230 17%
10 500 1.102 0.466 0.485 0.476 0.022 1.102 0.290 0.256 13%
F * S^2 * (3L-S) / 6 E I
Dial Indicator Reading (in)
0.000
0.050
0.100
0.150
0.200
0.250
0.300
0.350
0.00 0.20 0.40 0.60 0.80 1.00 1.20
Abso
lute
Defl
ectio
n (In
ch)
Force (Weight) Applied to Beam (lbf)
Deflection vs. Force for Aluminum Box Beam
Measured
Theory
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Task 5
In task 5, the deflection of an aluminum box beam was measured. Once again, the
recorded values were accurate as can be seen by both the percent error and the graph.
The percent error values continuously grow smaller as the weight gets larger and the
values seem to be approaching a constant.
14Beam Bending Lab
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Figure 5: Table and Graph of Task 6
15Beam Bending Lab
Task 6 1 MPa = 145.038 lbf/in^21 lbf = 453.5924 gmf exact
Material: Polystyrene PlasticRectangular Beam
Properties: Young's Modulus E = 928,242 lbf/in^2 (psi) = 6400 MPaDistance to Force L = 8.750 inDistance to Dial Ind S = 7.500 inWidth of beam w = 0.500 inThickness of beam t = 0.123 in
Moment of Inertia I = w * t^3 / 12 = 7.7536E-05 in^4
Theoretical Deflection δ = inch
Number of Weights (50 gm)
Total Weight (gmf)
Force (lbf)Incremental
Deflection, Δx (check this)
Force (lbf)Absolute
Deflection (in)
Theoretical Deflection
(in)Error
min max avg ~ constant ? Force Measured Theorynone 0 0.000 0.055 0.055 0.055 0 0 0.000
1 50.0 0.110 0.239 0.288 0.264 0.209 0.110 0.209 0.269 -23%2 100.0 0.220 0.486 0.600 0.543 0.280 0.220 0.488 0.538 -9%3 150.0 0.331 0.743 0.947 0.845 0.302 0.331 0.790 0.808 -2%
F * S^2 * (3L-S) / 6 E I
Dial Indicator Reading (in)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35
Abso
lute
Defl
ectio
n (in
ch)
Force (Weight) Applied to Beam (lbf)
Deflection vs. Force for Polystyrene
Measured
Theory
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Task 6
In this task, the deflection for a polystyrene plastic beam was measured. The
measurements for this beam were extremely accurate. The percent error is very small
and the theory line runs almost directly through all of the data points. The first data point
received a percent error of 23%. The second and third points received percent errors of
9% and 2%.
16Beam Bending Lab
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Figure 6: Table and Graph of Task 7
17Beam Bending Lab
Task 7 1 MPa = 145.038 lbf/in^21 lbf = 453.5924 gmf exact
Material: BasswoodRectangular Beam
Properties: Young's Modulus E = 2,200,000 lbf/in^2 (psi)Distance to Force L = 8.750 inDistance to Dial Ind S = 7.500 inWidth of beam w = 0.505 inThickness of beam t = 0.124 in
Moment of Inertia I = w * t^3 / 12 = 8.0237E-05 in^4
Theoretical Deflection δ = inch
Number of Weights (50 gm)
Total Weight (gmf)
Force (lbf)Incremental
Deflection, Δx (check this)
Force (lbf)Absolute
Deflection (in)
Theoretical Deflection
(in)Error
min max avg ~ constant ? Force Measured Theorynone 0 0.000 0.103 0.108 0.106 0 0 0
1 50.0 0.110 0.212 0.254 0.233 0.128 0.110 0.128 0.110 16%2 100.0 0.220 0.356 0.381 0.369 0.136 0.220 0.263 0.220 20%3 150.0 0.331 0.458 0.547 0.503 0.134 0.331 0.397 0.329 21%4 200.0 0.441 0.565 0.632 0.599 0.096 0.441 0.493 0.439 12%5 250.0 0.551 0.692 0.730 0.711 0.113 0.551 0.606 0.549 10%6 300.0 0.661 0.813 0.915 0.864 0.153 0.661 0.759 0.659 15%
F * S^2 * (3L-S) / 6 E I
Dial Indicator Reading (in)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70
Abso
lute
Defl
ectio
n (In
ch)
Force (Weight) Applied to Beam (lbf)
Deflection vs. Force for Basswood Beam
Measured
Theory
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Task 7
In the final task, the deflection for a basswood beam was measured. The
measurements for this beam were also accurate because once again there is small
percent error and the theory line runs very closely to all of the data points.
18Beam Bending Lab
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Figure 7: Graph of Deflection vs. Force Applied for All Five Beams
This graph shows the deflection vs. force applied for all five beams. It can easily
beam seen that the strongest beam is the steel beam. It deflects a very small amount at
the highest force applied. The second strongest beam is the aluminum cantilever beam
which deflects slightly less than the aluminum box beam which is the third strongest
beam. The fourth strongest beam is the basswood beam. It deflects at a very high rate
when only a small force is applied. Lastly, the polystyrene plastic beam deflects at an
immensely high rate at a very low force.
19Beam Bending Lab
0.00 0.20 0.40 0.60 0.80 1.00 1.200.000
0.100
0.200
0.300
0.400
0.500
0.600
0.700
0.800
0.900Deflection vs. Force Applied for All Five Beams
Steel Beam
Aluminum Box Beam
Polystryene Plastic Beam
Basswood Beam
Aluminum Cantileaver Beam
Force (Weight) Applied to Beam (lbf)
Abso
lute
Defl
ectio
n (in
ch)
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Discussion Questions
1. The strength of materials and structures is extremely important in our everyday
lives because almost everywhere we go or look we see many things that are built
with strong materials in order to maximize efficiency. Cars, buildings, planes, and
bridges are just a few of the things that we see every day that rely completely on
the strength of their materials. Since the strength of the materials used to build
these things is known, the safety of these structures is maximized.
2. Engineers use a great deal of factors in order to design safe structures. They
make sure that the material being used can easily withstand forces that would
happen to certain structures. For example, a building in Wisconsin would be built
to withstand the greatest possible wind gust that would take place. Materials
being used are always tested beforehand and the strongest/safest ones are
always chosen according to the specific thing being built. Engineers are always
extremely careful when they design structures because they do not want any
error in their design, which could potentially lead to a defect in the future. In all,
engineers always test every structure before it is built to make sure the correct
materials are being used and that the materials are strong enough to withstand
any force.
3. The strongest beam I tested was the steel beam. I came to this conclusion
because when I plotted all five beams on one graph it was clear that the steel
beam deflected the least when the greatest amount of force was applied to it.
The polystyrene plastic was the weakest I measured because, once again, on
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the graph it was clear that the plastic deflected the most at the lowest force
applied.
Material Used Relative Strength
(1-10)
Strongest Steel Beam 9.5
Aluminum Cantilever Beam 8.8
Aluminum Box Beam 8.5
Basswood Beam 4.1
Weakest Polystyrene Plastic Beam 2.0
4.
Conclusion
Throughout the duration of this lab, the students were exposed to stress, strain,
Young’s modulus, moment of inertia, force, and deflection. After making use of these
concepts during lab, a conclusion was drawn about the strongest and weakest beams
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tested. The strongest beam was found to be the steel beam. The weakest was found to
be the polystyrene plastic. This was verified when the force vs. deflection for all five
beams was plotted on one graph.
During the lab, not many difficulties were faced. However, one difficulty was
making sure that the minimum and maximum values were accurate because if the
weight was not adjusted properly, then the dial indicator would not produce the same
reading. Another difficulty that was faced was measuring the width and thickness of
each beam. The dial caliper is extremely precise and at times it was a little bit difficult to
get the exact reading. Other than those two, there were no other difficulties experienced
during the lab.
22Beam Bending Lab
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Beam Bending Lab Report Grading Guidelines (100 pts)
Contents Points Worth
Point Value
Report Formatting 5 pts
1. Cover Sheet with proper formatting, Table of Contents, and List of Illustrations
2
2. Executive Summary 3
Introductory Paragraphs (3-5 lines) 5 pts
1.Brief introduction of objectives/goals of the lab. 3
2.Brief introduction to the contents of the Lab Report. 2
Task 2 – Beam Bending Lab Worksheet 10 pts
1.Describe the contents of the Beam Bending Lab Worksheet and describe how it is organized.
4
2.Describe the Excel formula in Cell H14 of the Worksheet. To which Equation Number in the Preparation Document does it refer? And which other calculations in the Worksheet use the number in Cell H14?
6
Tasks 3-7 – Measure the characteristics of all of the cantilever beams 30 pts
1.Briefly state the purpose of Tasks 3-7. 5
2.What was the function of the Dial Indicator? How did you read the dial? 5
23Beam Bending Lab
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3.Copy and paste the data tables and graphs from Tasks 3 - 7 into your Lab Report and discuss each graph. Were your measurements accurate? If not, why not?
15
4.Plot Deflection versus Applied Force for all five beams on the same graph. Place this graph in your report and discuss the results.
5
Discussion Questions 1 – 4. These are to be answered in your report. 40 pts
Discussion Question 1 10
Discussion Question 2 10
Discussion Question 3 10
Discussion Question 4 10
LAB Report Conclusion 10 pts
Total 100 pts
24Beam Bending Lab