MEE 324 Lab 2
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Lab 2: Material Characterization
Fabian Ameen
Lab Number: Thursday 10:30 - 11:35 AM
Date of Experiment: 2/8/2024
Due Date: 2/23/2024
Abstract:
This lab experiment focused on conducting bending tests on 7075 Aluminum beams in cantilever configurations equipped with strain gauges. The objective was to obtain load-strain data for beams of uniform and variable cross-sections, analyze the effects of variable geometry on stress, strain, and curvature, and compare experimental results with theoretical expectations. Load-strain data was collected for beams with strain gauges mounted at various positions, ensuring elastic behavior. For the sample with constant cross-section, axial and transverse strains were measured, while for
variable cross-section beam, strain measurements focused on the upper fibers to calculate stress and curvature. The experiment utilized a specially designed rig for load measurement. Through this experiment, Young’s modulus and Poisson’s ratio were determined for uniform cross-section beams, and the validity of beam theory regarding variable cross-sections was
tested.
Data Analysis:
A)
Shear force and Bending moment diagram of load 4
Shear Force
3.565 N
R
y
x3
x2
x1
P = 3.565 N
Bending Moment
x3
x2
x1
P -0.94116 N-m
P
=
I
∗
E
y
max
∗
x
gauge
ε
axial
(3)
B)
After plotting the data of microstrain 1 vs the load (Figure 1) a linear regression can be performed, the slope of which (44906) is equal to the
I
∗
E
y
max
∗
x
gauge
term from equation 3 that was provided in the lab handout (shown
above). Plugging in the known variables y, x, and I, E can be solved for giving
the calculated elastic modulus
44906
=
I
∗
E
y
max
∗
x
gauge
44906
=
20.54
∗
6.27
3
12
∗
E
3.135
∗
264
E
=
88
GPa
This value of Young’s Modulus is above the literature value of 71 GPA
[1]
. This discrepancy is most likely due to a measuring inaccuracy as a small error can
largely impact the calculated value.
0
0
0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
f(x) = 44906.22 x
R² = 1
Load vs Axial Strain
Strain
Load
C)
Poisson’s ratio can be calculated by dividing the lateral strain by axial strain. By calculating the Poisson’s ratio for each loading the average and standard deviation can be determined through excel. Mean: 0.403 STD: 0.00963. This value is also slightly higher than the literature value of 0.33, which could also
be due to measurement errors.
D)
Based on the data collected theory of the constant stress beam is valid. Based on the data collected both pairs of segments (1 with 2 and 3 with 4) have a constant strain at both points. This supports the idea that the stress is
constant as well because stress is related linearly with strain. (Figure 2)
Index
Force (N)
microstrain
1
microstrain
2
microstrain
3
microstrain
4
1
0.721
20.037
20.595
11.331
12.49
2
1.44
38.754
40.424
21.938
23.971
3
1.983
57.472
59.99
33.045
36.122
4
2.798
77.706
80.268
44.579
49.4
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5
3.615
96.387
100.044
55.447
61.551
Figure 2 (Data collected from constant stress beam)
Conclusion
In conclusion, the bending tests conducted on 7075 Aluminum provided important insight into the theory behind Young’s Modulus and beam
theory. The first experiment gave proof of the theory that stress and strain can be linearly related with a constant (E). Also, the second experiment’s results proved that by varying the cantilever width a constant stress can be applied to a beam. The calculated values of the modulus of Elasticity and Poisson’s ratio were both slightly higher than the literature values. This is most likely due to a measurement error when the dimensions of the beam were taken, as a change in dimension can have a large impact on the calculation.
References
ASM Material Data Sheet
, asm.matweb.com/search/SpecificMaterial.asp?bassnum=MA7075T6. Accessed 23 Feb. 2024.
[1]
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