MET211 Lab 10 Report
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MET 21100 Memo Lab Report Grading Sheet
Expectations:
The complete draft lab report was read/reviewed by ALL group members. Suggestions and
corrections were considered, and incorporated where appropriate. The final version of the
complete lab report was then reviewed by ALL group members prior to submission.
Names :
Peter Catizone M,W,F 11:30-12:20
Nate Montanari M,W,F 11:30-12:20
Quinn Steinkamp M,W,F 11:30-12:20
Lab Date - 11/16/2023 Lab Div# - 211000-008
Format/Grammar/Spelling
6 points
Title Information
2 points
Executive Summary
10 points
Results
40 points
Conclusions
10 points
Data Sheet(s); references
2 points
Subtotal:
Attendance:
Total score:
To: Dr. Sunghwan Lee
From: Peter Catizone, Nate Montanari, and Quinn Steinkamp
Cc: Shuning Yin
Date: November, 30, 2023
Re: MET 211 3 Point Bending & Beam Deflection
Executive summary
This lab was completed as part of the MET 211 Lab curriculum. It was conducted to
show the lab groups the effects that material, size, and quantity have on deformation while
conducting a 3 point bending test. To conduct the experiment the lab group was given access to a
United Electromechanical Test Machine (UTM), a 500 lb
f
capacity load cell, a Vishay
Measurements Group P 3500 Strain Indicator, a 24 inch steel scale, dial caliper, micrometer,
digital multimeter, screwdriver, Lab view software with computer and connection box, and 6
different specimens including : 7 - ¼ in x 1 in x 36 in 6061-T6511 Aluminum bar, ½ in x 1 in x
36 in 6061-T6511 Aluminum bar, ¾ in x 1 in x 36 in 6061-T6511 Aluminum bar, 1-¾ in x 1 in x
36 in 6061-T6511 Aluminum bar, ¼ in x 1 in x 36 in AISI 1018 Steel, and ¼ in x 1 in x 36 in CA
260 Brass. Within this lab the group set up the UTM with the 3 point bending apparatus to test
the given samples. The group was given a few elected samples from the list to test while other
lab groups collected the other data. To start the bar of choice was put into the 3 point bending
apparatus. Then the data acquisition equipment was zeroed in preparation for the test. To conduct
the test the group set the setting on the UTM machine in accordance with a data table that was
provided in lab. Then one person started the test while another filmed bot the strain indicator and
the screen on the UTM to collect the deformation of the beam in inches and the strain that the
UTM applied in lb
f
. The data acquired from the lab was then analyzed by the group and
determined that materials known for their stiffness such as steel, deformed less than materials
that are known to be more flexible such as brass or aluminum. The test of 7 stacked pieces of
aluminum compared to a bar of the same thickness yielded interesting results. The bar mode up
of 7 different bars deformed more than that of the one which was one solid piece.
Results
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Table 1: Modulus of Elasticity Using Deflection From Three-Point Bending
Specimen
b
(in)
h (in)
I (in
4
)
L
(in)
M
py
(lb
f
/in)
E
exp
(psi)
E
pub
(psi)
%
Diff
¼” Steel
1
0.25
0.001
30
70.311
39.55*10^6
29*10^6
36.4
¼” Brass
1
0.25
0.001
30
20.909
11.76*10^6
16*10^6
26.5
¼” Al
1
0.25
0.001
30
24.089
13.55*10^6
10*10^6
35.5
½” Al
1
0.5
0.010
30
1807.9
10.1*10^6
10*10^6
1
¾” Al
1
0.75
0.035
30
6632.5
10.6*10^6
10*10^6
6
1-¾” in
Al
1
1.75
0.447
30
5182
6.52*10^6
10*10^6
34.8
7 Al Stack
1
1.75
0.009
30
157.57
9.84*10^6
10*10^6
1.6
Table 2: Area Moment of Inertia Using Deflection From Three-Point Bending
Specimen
E
pub
(psi)
L (in)
M
py
(lb
f
/in)
I
EXP
(in
4
)
I
THEO
(in
4
)
% Diff
Al Stack
10*10^6
30.0
157.57
0.008
0.009
11.1
Sample Calculations:
E
exp
: (M*L^3)/(48*I) = [70.311*(30^3)]/[48*(0.001)] = 39.55*10^6 psi
I
EXP
: (b*(h^3))/12 = [1*(0.25^3)]/12 = 0.001 in^4
I
THEO
: (M*L^3)/(48*E) = [157.57*(30^3)]/[48*(10*10^6)] = 0.008 in^4
% Diff Between I or E: (Iexp-Itheo)/Etheo *100% = (0.008-0.009)/0.009 *100 = 11.1%
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Conclusion
In conclusion the results yielded in the lab provided great insight on how material
properties such as size, shape, stiffness are affected at different loads. The data that was acquired
proved the group's theories correct. Using the tests of bars of different materials showed that
materials of different stiffness deform differently under the same load. Using the test of a stack
of bars and one solid bar yielded results that show how a solid bar will deform less than a stack
of bars totaling the same thickness. This showed that choosing different materials of different
sizes is important to consider when designing different products, structures, or anything that
involves bending forces.
The lab manual for MET 211 poses some questions for the lab group to think about to
further their understanding of the lab. The first question the lab manual asks is “Do the empirical
values for modulus of elasticity support the validity of the formula for deflection of a simply
supported beam experiencing three-point bending?” The group's data do support the validity of
the formula to an extent. To have the values be perfect you have to have the perfect condition
which the group found the the lab equipment and specimens was not exact so there will be some
variance from the modulus of elasticity. The second question the lab manual poses is “Do the
empirical values for area moment of inertia support the validity of the formula for deflection of a
simply supported beam experiencing three-point bending?” To answer this question the group
answered in the same manner as before, the results showed that the empirical values helped
prove the validity of the equation to an extent but due to the lab equipment and specimens not
being perfect the results will be slightly different. The final question the lab manual poses is
“Comment your observations, similarities, and differences, regarding the area moment of inertia
of a stacked beam and a solid beam made of the same material.” According to the group's
calculations both beams have a moi of .447. The group found this interesting because they had
the same moi but differing amounts of deformation at the same loads.
So in conclusion the group has a deeper understanding of deformation under load
utilizing a 3 point bending test. The group found that factors such as material, size, and load
applied affect the amount of deformation an object such as the beam tested within the lab
experiences and can now relate these findings to other real life applications.
Sources
Roach, Thelen;
MET 21100 Laboratory Manual
, Purdue University: West Lafayette, IN, 2023
“Aisi 1018 Steel, Cold Drawn - Matweb.”
MatWeb
,
www.matweb.com/search/DataSheet.aspx?MatGUID=3a9cc570fbb24d119f08db22a53e2
421. Accessed 29 Nov. 2023.
“Aluminum 6061-T6; 6061-T651.”
MatWeb
,
www.matweb.com/search/DataSheet.aspx?MatGUID=b8d536e0b9b54bd7b69e4124d8f1
d20a. Accessed 29 Nov. 2023.
“Cartridge Brass, UNS C26000 (260 Brass), Os070 Temper Flat Products.”
MatWeb
,
www.matweb.com/search/datasheet_print.aspx?matguid=83677ae92338456da4dafe8fe4b
815c5. Accessed 29 Nov. 2023.
Data Sheet
¼” 1018 Steel
¼” Al
¼” Brass
Load, P (lb)
Def, y (in)
Load, P
(lb)
Def, y (in)
Load, P (lb)
Def, y (in)
1
3
0.034
3
0.127
3
0.178
2
6
0.087
6
0.248
6
0.338
3
9
0.123
9
0.369
9
0.469
4
12
0.170
12
0.499
12
0.588
5
15
0.208
15
0.619
15
0.768
6
18
0.250
18
0.750
18
0.898
½” Al
¾” Al
Load, P (lb)
Def, y (in)
Load, P (lb)
Def, y (in)
1
16
0.008
30
0.005
2
32
0.017
60
0.01
3
48
0.027
90
0.014
4
64
0.033
120
0.018
5
80
0.044
150
0.023
6
96
0.052
180
0.028
7 Stack ¼” Al
1-¾” Al
Load, P (lb)
Def, y (in)
Load, P (lb)
Def, y (in)
1
25
0.182
25
0.007
2
50
0.348
50
0.014
3
75
0.509
75
0.018
4
100
0.669
100
0.023
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5
125
0.819
125
0.028
6
150
0.978
150
0.031
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Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
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Engineering Mechanics: Statics
Mechanical Engineering
ISBN:9781118807330
Author:James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:WILEY