Exp 8 Lab Report
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School
University of Alabama, Huntsville *
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Course
375
Subject
Aerospace Engineering
Date
Dec 6, 2023
Type
Pages
8
Uploaded by PresidentAtomHedgehog21
1
MAE 375 Section
(08)
Experiment
(8): (Modulus of Elasticity Flexure Test)
Experiment Conducted:
(09/15/2023)
Report Submitted:
(09/15/2023)
Author:
(John Holland)
Group Team:
(A3)
2
I.
Objective and Expectations:
The goal of this experiment was for us to calculate the modulus of elasticity based on measured values of stress
and strain, and compare it to the standard value of the modulus of elasticity for that type of metal. I expect that
the calculated value of modulus of elasticity will be close to the standard value.
II.
Experimental Procedure:
1.
Schematic of the Specimen:
Figure 1: Full schematic of the full set-up of the
experiment’s equipment
.
3
Figure 2: Top and side view drawings of the aluminum cantilever beam with attached strain gauge used in this
experiment. Le represents distance between center line of strain gauge and the place where load is applied. P is
the applied load.
)
2.
Description of Equipment:
•
Cantilever flexure frame
•
Aluminum cantilever beam with strain gauge attached
•
P-3 strain indicator
•
Calipers
•
Ruler
•
Scale
•
Weights and weight hanger
3.
Procedure:
First, use the calipers and tape measurer to record the effective length (Le), thickness (t), and width (b), and record
the gauge factor (Sg) indicated on the beam. Using the recorded values, calculate the maximum load (Pmax) for
the beam using a stress of 15,000 psi with the given equation 7.3-3.
Next, secure the beam into the flexure frame and connect the wires of the strain gauge into the strain indicator,
and set up the strain indicator by activating the correct channel, selecting the gauge factor, and zeroing the strain
indicator.
Next, determine the 10 different loads that will be applied to the beam, making sure to not exceed Pmax, and then
apply these loads onto the beam in 10 increments, recording the load and strain for each increment, before
unloading them in 10 decrements, recording load and strain again for each. At
–
at
Finally, using the given formula 7.3-3, calculate the stress for each load increment and decrement.
4.
Introduction of Equation/s:
? =
Δσ
Δε
𝜎 =
6𝑃 × 𝐿
𝑒
? × ?
2
(7.3-1)
(7.3-3)
where:
E
= modulus of elasticity, in psi
σ
= stress measured in psi
𝛥𝜎
= change in stress
ε = strain in in
./in.
𝛥
ε
= change in strain
P
= applied load
L
e
= effective length, between gauge center point and point where load is applied, in in.
b
= width in in.
t
= thickness in in.
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4
5.
Reference:
“The experiment was performed following the steps listed in Chapter
7, Section 4
in the laboratory manual [1].”
6.
Deviation:
The only deviation was from steps 6-7, where instead of plugging the strain gauge wires into the flexure frame,
then into the stain indicator, we plugged the strain gauge wires into the strain indicator directly.
III.
Data Summary:
Measured Data from Worksheet:
Guage Factor Sg = 2.110
Width b = 1.0065 in.
Thickness t = 0.1285 in.
Effective length Le = 10.25 in.
Tables from Worksheet:
Table 1: Tabulation of Loads, Strains, and Stresses
Load (lb)
Strain (με)
(increasing)
Stress (psi)
(increasing)
Strain (με)
(decreasing)
Stress (psi)
(decreasing)
0
0
0
0
0
0.22
82
814.1
82
814.1
0.44
165
1628.2
164
1628.2
0.66
248
2442.3
247
2442.3
0.88
330
3256.4
328
3256.4
1.10
411
4070.5
409
4070.5
1.32
493
4884.6
491
4884.6
1.54
575
5698.7
574
5698.7
1.76
660
6512.8
654
6512.8
1.98
740
7326.9
739
7326.9
2.20
824
8141.0
824
8141.0
IV.
Calculations:
𝜎𝑚?𝑥 =
6𝑃𝑚?𝑥 × 𝐿
𝑒
? × ?
2
𝑃𝑚?𝑥 =
15,000𝑝?𝑖 × 1.0065 × 0.1285
2
6 × 10.25
= 4.054
5
𝜎 =
6𝑃 × 𝐿
𝑒
? × ?
2
𝜎
𝑛
=
6𝑃
𝑛
× 𝐿
𝑒
? × ?
2
= 𝑃
𝑛
(
6 × 10.25
1.0065 × (0.1285)
2
)
𝜎
𝑛
= 𝑃
𝑛
(3700.45)𝑝?𝑖
? =
Δσ
Δε
=
8141.0
0.000824
𝑝?𝑖 = 9879842 𝑝?𝑖
%?𝑖𝑓𝑓 = |
10500000 − 9879842
10500000
| ∗ 100% = 5.91%
6
Graph/s:
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7
V.
Discussion:
1.
Comparison of Results:
Table 2: Results table
Standard value of modulus of
elasticity for 2024-T6 aluminum (psi)
Experimental results for
modulus of elasticity (psi)
% Difference
1050000 psi
9879842
psi
5.91 %
2.
Results Discussion:
The results show that, compared to the expected standard value for the modulus of elasticity, the experiment’s
results had an error of 5.91 %. This shows that the results are fairly accurate to the standard value, and are well
within reasonable limits.
3.
Sources of Errors:
The likely sources for the difference are the inaccuracies in measurements of width, thickness, and effective
length, inaccuracies in recording the strain from the strain indicator, and the effects of impurities of the aluminum
beam.
VI.
Conclusion:
The experiment overall went well. The biggest problems my group had were measuring the length, as the tape
measure was a bit awkward for measuring the effective length, and recording the values from the strain indicator,
as it would take a while for the weights to settle enough to get accurate measurements. The strain indicator was
somewhat complicated to use at first, and my group had to set up the strain indicator twice due to the first one
having a low battery.
8
VII.
References:
1. MAE/CE 375 - Mechanics of Materials- Laboratory Manual, University of Alabama in Huntsville, Version 8.0,
August 2022.
VIII.
Appendix: