AEROSPACE 305W STRUCTURES & DYNAMICS
LABORATORY
Laboratory Experiment #1
Bending of Selectively Reinforced Beams
March 19, 2012
Devin O’Connor
Section Number: 12
Lab Partners:
Mikhail Abaimov
Rebecca Frey
Shannon Hagarty
Nicholas Svirbely
Course Instructor: Dr. Stephen Conlon
Lab TA: Kevin Brennan
Abstract
The primary objective of this lab is to observe and analyze the flexural behavior of
structural beam elements. This analysis is necessary in determining important characteristics of
materials used for aerospace structures. The most important characteristics considered are
strength, weight, and cost. Desirable materials weigh the least, are cheap to implement in
industry, and are the strongest. The lab tested three irregular T-beam specimens: one
unreinforced aluminum, one aluminum reinforced with aluminum caps, and one aluminum
reinforced with graphite/epoxy composite caps. Strain and displacement measurements were
taken as the beams were placed in a fixed clamp, mimicking cantilevered condition, as
incremental loads were applied from 0 to 5 pounds. Data was collected and recorded by strain
gages located on the web and flange, and a linear variable differential transformer at the tip.
The strain gages measured normal strains, which are important for determining stiffness
characteristics of the samples. The linear variable differential transformer measured
displacement of the tip of the beam. Gathering displacement data is important because minimal
displacement is desired in the members of structures in industry. It was found that the
composite reinforced beams generally exhibited less tip displacement and less max strain
values, followed by the aluminum reinforced beam, and then lastly, the unreinforced
aluminum. Also, it was experimentally determined that beams exhibit stiffer properties when
they are in H-orientation as opposed to I-orientation, due to the change in the moment of
inertia.
2
I.
Introduction
Structural design for aerospace application revolves around three key principles: the structure
must be as strong as possible, weigh as little as possible, and must cost a reasonable amount to
produce. Weight is such an important constraint in the aerospace industry because the structures must
obviously be able to fly, and the more it weighs, the more fuel is necessary to keep it flying. Efficient
designs balance the constraints efficiently by using the minimum amount of material needed to
satisfy performance, without violating stability, strength, producibility, and ease of use. One method
for balancing these constraints is known as selective reinforcement, which is explored in this
experiment. The addition of small layers of material can increase the stiffness of a member, which is
especially necessary when it is known that a bending load will have to be resisted.
The experiment is conducted in order to observe and analyze the flexural behavior of structural
beam elements. In addition, the experiment is meant to assess the utility of composite materials in
reinforcement of the beam elements, known as selective reinforcement. Three beam specimens are
tested: baseline aluminum, aluminum reinforced with aluminum caps, and aluminum reinforced with
graphite/epoxy (composite) caps. Composite materials are beneficial in the aerospace industry
because they are light-weight and have the same, if not stronger, section stiffness characteristics than
their metal counterparts. This is a non-destructive test, which means that the stresses are limited to
well below the levels that could result in the specimen yielding or failing.
In the experiment, the beam elements are cantilevered and a known load is applied at the tip. This
is conducted in order to record the displacement of the tip and the presence of strain. Strain gages are
used to measure the deflections near the root of the beam and a Linear Variable Differential
Transformer is used to measure displacement near the tip. These characteristics are directly related to
the modulus of elasticity of the materials and the area moments of inertia. The comparison among the
different reinforced and unreinforced beams is important because it shows how the various materials
react differently to the same applied load. This experimental data can then be used to determine what
material would be most effective and efficient for a given real-world structure. It is expected that the
unreinforced aluminum will have the most deflection and strain, followed by the aluminum
reinforced aluminum, and finally the composite reinforced aluminum should have the least
deflection. It is also expected that the H-orientation will experience less strain and displacement than
the I-orientation because it has great stiffness properties due to the change in the area moment of
inertia.
3
The theoretical displacement at any point along the beam is calculated using Equation 1, which
related the applied load, P, to the material properties, including modulus of elasticity, E, area moment
of inertia, I, and the axial distance along the beam, x as compared to the length of the beam, L. This
equation is derived from the governing differential equation for transverse loaded cantilevered beams
and the boundary conditions at the wall and the tip.
Px 2 (3L  x)
w( x) 
6 EI
(1)
The theoretical strain at any point along the beam is calculated using Equation 2. The equation
is derived from Hooke’s Law, which relates the strain of the member to the stress and modulus of the
material. The z in Equation 2 is the distance from the neutral axis to the strain gauge, and the other
variables are the same as in Equation 1.
∈𝑥𝑥 =
−𝑃𝑧(𝑥−𝐿)
𝐸𝐼
(2)
These equations are essential for comparing theoretical data to the experimental data gathered from
the experiment. The main goal of this experiment is to come to a valid conclusion about the strength
and effectiveness of the various beam specimens. The hypotheses made earlier hopefully will be
bolstered by the gathered experimental data.
4
II.
Experimental Procedure
The experiment began by ensuring proper connection among all of the measuring instruments and
fixtures. Figure 1 illustrates the set-up and orientation of the experimental apparatus.
Figure 1. The Experimental Apparatus
Two strain gages were located on each test specimen; one was meant for measuring in the Iorientation and the other for H-orientation. The strain gage was connected to the strain gage box,
which was set for a gage factor of 2.125 and a nominal resistance of 350 ohms. The structural beam
was inserted into the fixture to mimic a cantilevered condition. To ensure that the specimen was not
damaged by the clamp of the fixture, filler blocks were inserted along the web of the part of the beam
that was in the fixture. A stopper was located at the end of the fixture to ensure that the beam was not
inserted too far, and it also ensured a relatively constant gage length for each experiment run. Figure
2 indicates important dimensions of the specimen and Table 1 provides the values of these
dimensions.
Figure 2. Important Specimen Dimensions.
5
Table 1. Relevant Specimen Properties
Specimen
Beam,
Cap
1
2
3
Al, Al, Al
Al ,G/E
Gage
h
b1
tf
Length
(in)
(in)
b2
(in)
(L, in)
(i)
8.750
0.500
1.250
0.625
0.063
8.750
0.500
1.250
0.625
0.063
8.750
0.500
1.250
0.625
0.063
(All dimensions ±0.001 unless otherwise specified.)
tc
(in)
tr
(in)
0.063
0.063
0.063
0.063
0.063
Once the beam was set in place, the load hanger was placed at a point near the tip of the beam and
the LVDT was mounted on the fixture and positioned so that the tip was perpendicular to the beam.
The strain gage box and the LVDT were zeroed in order to produce more accurate data recordings.
The LVDT was connected to the LabView program, which gathered displacement data as the load
hanger was loaded in increments of half a pound up to five pounds. At every increment the “take
sample” button was clicked to record both strain and displacement readings in LabView. The beam
was then unloaded in increments of one pound in order to gather data on the residual stress and strain
that hadn’t relaxed yet, also known as hysteresis. This process was repeated a total of six times
because there were three different beam specimens and they were tested in two different orientations.
6
III.
Results and Discussion
Data was processed for all three samples and for both orientations of the beam, orientations
referring to the I-configuration and the H-configuration. The data that was gathered reduced into
some very valuable information regarding the response of the beam to various loads, and the role that
various materials play in structural design. Displacements and strains were present in all of the
samples. Table 2 reports the theoretical and experimental values for strain and displacement of the
unreinforced aluminum beam for I-orientation. In addition, Table 2 shows the percentage error
between the previously mentioned results.
Table 2. Beam Bending Test and Theory Data (Aluminum Only; I-Orientation)
Displacement(in)
Theoretical Strain(µs)
Percent Error in Strain (%)
Theoretical Displacement (in)
0
0.728485
0.000001
0
n/a
0
n/a
0.5
11.158173
0.000711
30.71634704
-63.67350263
0.00124464
-42.87503378
Force (lbs) Strain(us)
Percent Error in Displacement (%)
1
22.03883
0.001469
61.43269408
-64.12524254
0.002489279
-40.98693714
1.5
33.034279
0.002206
92.14904112
-64.15125041
0.003733919
-40.91998336
2
45.292442
0.002965
122.8653882
-63.13653285
0.004978559
-40.44461152
2.5
56.648666
0.00376
153.5817352
-63.11497202
0.006223198
-39.58090774
3
68.373866
0.004393
184.2980822
-62.90039203
0.007467838
-41.17440773
3.5
80.189259
0.00526
215.0144293
-62.7051732
0.008712478
-39.6268189
4
92.660607
0.005982
245.7307763
-62.29181855
0.009957117
-39.92237202
4.5
104.99257
0.006758
276.4471233
-62.02074244
0.011201757
-39.67017945
5
116.00441
0.007508
307.1634704
-62.23365596
0.012446397
-39.67732118
4
94.702268
0.005976
245.7307763
-61.46096577
0.009957117
-39.98263042
3
72.85076
0.004717
184.2980822
-60.47123273
0.007467838
-36.8358027
2
52.229168
0.003186
122.8653882
-57.49073943
0.004978559
-36.00557581
1
29.123146
0.001652
61.43269408
-52.59340904
0.002489279
-33.63541196
0
6.96006
0.000147
0
n/a
0
n/a
Figures 3 and 4 graphically show the relationship between displacement and load, and strain and
load, respectively. Notice that the experimental has a much shallower slope than the theoretical data
for both types of data. Evidence of hysteresis is observed in Figure 4 because the slopes of the
loading and unloading cases differ, indicating residual strain in the sample. They also do not have the
same zero load values. For this configuration the percent error was consistent for both the strain and
the displacement. There was no steady trend of the error increasing or decreasing as the load
increased. The average error for strain was about 63% and for displacement it was about 40.5%. A
maximum displacement of 0.007508in was recorded. A maximum strain of 116µs was recorded at
the maximum load value of 5 pounds. The theoretical max strain was much great, calculated to be
307µs. The maximum displacement was also expected to be larger, theoretically calculated to be
0.012446in. The data was not accurate; however, it was precise because the data produces a strong
7
linear relationship for both strain and displacement versus the applied load, as shown in Figures 3
and 4.
Displacement vs. Load
0.014
0.012
Theoretical
Loading
Displacement (in.)
0.01
Unloading
(Loading)
y = 0.0015x - 4E-05
0.008
0.006
0.004
(Unloading)
y = 0.0015x + 0.0002
0.002
0
0
-0.002
1
2
3
4
5
6
Load (lbs)
Figure 3. Displacement vs. Load (Aluminum Only; I-Orientation)
Strain vs. Load
350
300
Theoretical
Strain (μs)
250
Loading
200
Unloading
150
(Loading)
y = 23.29x - 0.8514
100
(Unloading)
y = 21.788x + 7.5083
50
0
-50
0
1
2
3
4
5
6
Load (lbs)
Figure 4. Strain vs. Load (Aluminum Only; I-Orientation)
8
Table 3 reports the experimental and theoretical data for the unreinforced aluminum beam tested
in H-orientation. The percentage error for strain was very inconsistent; it had a wide range of values.
At small load values the percent error was generally larger than at higher load values; however, there
were still some inconsistencies at higher loads. The displacement percent error was generally high for
this configuration, averaging at about 47%. Potential reason for this error may be the fact that the
moment of inertia increased as compared to the other configuration because there is more mass
further away from the neutral axis. This resulted in smaller displacements, which are harder to
measure and lead to greater error. The experimental max displacement for this configuration was
0.0054in, whereas the theoretical value was 0.0094in. The recorded maximum strain was 10.52µs,
which matches closely to the theoretical value of 11.47µs.
Table 3. Beam Bending Test and Theory Data (Aluminum Only; H-Orientation)
Force (lbs)
Strain(us)
Displacement(in)
Theoretical Strain(µs)Percent Error in Strain (%)
Theoretical Displacement (in)
0 n/a
Percent Error in Displacement (%)
0
-0.239049
0.000001
0 n/a
0.5
0.416907
0.000319
1.14701087
-63.652742
0.000943257
-66.18102595
1
1.204053
0.000892
2.294021739
-47.51344421
0.001886515
-52.71704568
1.5
2.073194
0.001585
3.441032609
-39.75081797
0.002829772
-43.98842855
2
2.925935
0.001962
4.588043478
-36.2269557
0.00377303
-47.99935181
2.5
4.926599
0.002662
5.735054348
-14.09673385
0.004716287
-43.55729847
3
6.689478
0.003214
6.882065217
-2.798392798
0.005659545
-43.21098087
3.5
6.697678
0.003725
8.029076087
-16.58220787
0.006602802
-43.58455963
4
7.624214
0.004366
9.176086957
-16.91214309
0.00754606
-42.14199031
4.5
8.739338
0.004658
10.32309783
-15.34190466
0.008489317
-45.13104105
5
10.526816
0.005417
11.4701087
-8.223921156
0.009432575
-42.57135346
4
8.066984
0.004352
9.176086957
-12.08688368
0.00754606
-42.3275176
3
5.910532
0.00324
6.882065217
-14.11688478
0.005659545
-42.75157997
2
4.729812
0.002284
4.588043478
3.089955935
0.00377303
-39.4650966
1
1.720618
0.001258
2.294021739
-24.99556693
0.001886515
-33.31619223
0
-0.558827
0.000117
0 n/a
0 n/a
Figure 5 displays the linear relationship between displacement and load, and also shows the
differences in the slopes between theoretical and experimental data.
9
Displacement vs. Load
0.01
Theoretical
Displacement (in.)
0.008
Loading
Unloading
0.006
(Loading)
y = 0.0011x - 0.0001
0.004
0.002
(Unloading)
y = 0.001x + 0.0002
0
0
1
2
-0.002
3
4
5
6
Load (lbs)
Figure 5. Displacement vs. Load (Aluminum Only; H-Orientation)
The slope values match closely; however, the intercepts vary among all three data groupings in
Figure 6.
Strain vs. Load
14
12
Theoretical
Strain (με)
10
Loading
8
Unloading
6
(Loading)
y = 2.1708x - 0.7374
4
2
(Unloading)
y = 2.1614x - 0.3374
0
-2
0
1
2
3
4
5
6
Load (lbs)
Figure 6. Strain vs. Load (Aluminum Only; H-Orientation)
Data for the aluminum reinforced beam in the I-orientation is displayed in Table 4. The data
presents many useful patterns and trends that can be compared and contrasted with the other
materials, as well as the other configurations. These comparisons are addressed later on in the results
section. Percent error for the experimental strain values averaged around 34.9%. The percent error
for strain as compared to displacement was generally much higher for this material and
10
configuration. The average percent error for displacement was about 6.67%. It was noticed that the
percent error for displacement, again, decreased as the load increased. This may be an indication of
the threshold of the instruments measuring the displacement data. This is relatively low error, and is
displayed visually in Figure 7 since the lines of theoretical and experimental data match. The
maximum displacement was 0.0056in, and the maximum strain was 58.47µs. This data makes sense
and matches the prediction that the aluminum reinforced beam would have less displacement and
strain than the unreinforced beam in the same I-configuration, because the reinforced beam exhibits
higher stiffness properties.
Table 4. Beam Bending Test and Theory Data (Aluminum Reinforced; I-Orientation)
Displacement(in) Theoretical Strain(µs)
Force (lbs)
Strain(us)
Percent Error in Strain (%)
Theoretical Displacement (in)
0
0.334912
-0.000001
0
n/a
0
Percent Error in Displacement (%)
n/a
0.5
7.304436
0.000447
5.846776962
24.93098416
0.000508254
-12.05180795
1
15.840053
0.000926
11.69355392
35.45969945
0.001016508
-8.903774232
1.5
22.350409
0.001424
17.54033088
27.4229611
0.001524761
-6.608332978
2
31.820762
0.001895
23.38710785
36.06112483
0.002033015
-6.788689076
2.5
38.937876
0.002415
29.23388481
33.19432657
0.002541269
-4.968732082
3
47.858867
0.002995
35.08066177
36.42521146
0.003049523
-1.787906344
3.5
56.468279
0.003621
40.92743873
37.97169027
0.003557776
1.777054461
4
64.479132
0.004266
46.77421569
37.85187212
0.00406603
4.918061319
4.5
73.359125
0.004955
52.62099265
39.41037844
0.004574284
8.322965846
5
82.042332
0.005621
58.46776962
40.32061175
0.005082538
10.59435962
4
65.782843
0.004549
46.77421569
40.639115
0.00406603
11.87816712
3
49.105182
0.003483
35.08066177
39.9779238
0.003049523
14.2145984
2
33.419653
0.002439
23.38710785
42.89775897
0.002033015
19.96959754
1
16.159832
0.001351
11.69355392
38.19435995
0.001016508
32.90604861
0
0.359511
0.000205
0
n/a
0
n/a
Displacement (in.)
Displacement vs. Load
0.006
Theoretical
0.005
Loading
0.004
Unloading
0.003
0.002
(Loading)
y = 0.0011x - 0.0002
0.001
0
-0.001
0
1
2
3
4
5
6
(Unloading)
y = 0.0011x + 0.0002
Load (lbs)
Figure 7. Displacement vs. Load (Aluminum Reinforced; I-Orientation)
11
Strain (με)
Strain vs. Load
90
80
70
60
50
40
30
20
10
0
-10 0
Theoretic
al
Loading
Unloadin
g
1
2
3
4
5
(Loading)
y = 16.417x - 0.9707
(Unloading)
y = 16.371x + 0.2186
6
Load (lbs)
Figure 8. Strain vs. Load (Aluminum Reinforced; I-Orientation)
Table 5 shows the data for the aluminum reinforced aluminum beam. The trends in this data align
with the predicted values and the hypothesis that displacement and strain decrease in the Horientation as compared to the I-orientation due to increased moment of inertia. A max displacement
of 0.003in was recorded, and a max strain of 5.76µs was recorded. The percent error for strain and
displacement were generally high for this material and configuration. The displacement percent area
was steady around an average of 37.5%. The strain percent error reached a maximum of about 108%.
This occurred for small load conditions. A possible source of this apparent error is the fact that the
theoretical values are already very small, so any inconsistencies result in a mushroomed percent
error. Another reason for error in strain measurement was the fact that the placement of strain gages
for H-configuration is generally poor because the strain gage is so close to the neutral axis, which
results in lower strain values.
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Table 5. Beam Bending Test and Theory Data (Aluminum Reinforced; H-Orientation)
Displacement(in) Theoretical Strain(µs)
Force (lbs)
Strain(us)
Percent Error in Strain (%)
Theoretical Displacement (in)
0
0.679289
-0.000002
0
n/a
0
Percent Error in Displacement (%)
n/a
0.5
1.179455
0.000303
0.575740197
104.8588941
0.000480225
-36.90461188
1
2.327376
0.000595
1.151480394
102.1203325
0.000960451
-38.04990771
1.5
2.827542
0.000908
1.72722059
63.70474135
0.001440676
-36.97402375
2
4.065658
0.001198
2.302960787
76.54047879
0.001920901
-37.6334365
2.5
4.123054
0.001485
2.878700984
43.22619901
0.002401126
-38.15402551
3
5.041391
0.001797
3.454441181
45.93940775
0.002881352
-37.6334365
3.5
5.812138
0.002105
4.030181377
44.21529593
0.003361577
-37.38057898
4
6.591085
0.002397
4.605921574
43.10024376
0.003841802
-37.60740705
4.5
6.509091
0.002692
5.181661771
25.61782856
0.004322027
-37.71441701
5
7.419228
0.003016
5.757401968
28.8641655
0.004802253
-37.19614173
4
5.93513
0.00241
4.605921574
28.85868559
0.003841802
-37.26902419
3
4.967596
0.001845
3.454441181
43.80317221
0.002881352
-35.96755167
2
2.893138
0.001248
2.302960787
25.62688936
0.001920901
-35.03049145
1
2.401171
0.000663
1.151480394
108.5290391
0.000960451
-30.96989716
0
1.220452
7.11E-05
0
n/a
0
n/a
Displacement vs. Load
0.006
Theoretical
0.005
Displacement (in.)
Loading
0.004
Unloading
0.003
(Loading)
y = 0.0006x - 3E-06
0.002
0.001
(Unloading)
y = 0.0006x + 7E-05
0
-0.001
0
1
2
3
4
5
6
Load (lbs)
Figure 9. Displacement vs. Load (Aluminum Reinforced; H-Orientation)
13
Strain vs. Load
9
Theoretical
8
7
Loading
Strain µε)
6
Unloading
5
4
(Loading)
y = 1.3592x + 0.8362
3
2
(Unloading)
y = 1.2477x + 1.0202
1
0
0
1
2
3
4
5
6
Load (lbs)
Figure 10. Strain vs. Load (Aluminum Reinforced; H-Orientation)
Table 6 displays the theoretical and experimental data for the composite reinforced beam in Iorientation. Maximum displacement for this specimen was 0.0049in. This specimen underwent the
least tip displacement for the I-orientation samples. This matches well with the prediction that the
composite material would exhibit higher stiffness properties. The maximum strain was 36.97µs,
which was also the least for the I-orientation. The error was generally higher for the displacement as
compared to the strain. Strain average percent error was about 19% and remained especially low
during the loading condition. The average percent error for displacement was about 55%.
Table 6. Beam Bending Test and Theory Data (Composite Reinforced; I-Orientation)
Force (lbs)
Strain(us)
Displacement(in)
Theoretical Strain(µs)
Percent Error in Strain (%)
Theoretical Displacement (in)
0
-0.107857
-0.000004
0
n/a
0
n/a
0.5
4.483829
0.000398
5.126881762
-12.54276559
0.000302561
31.54375032
Percent Error in Displacement (%)
1
10.002052
0.000814
10.25376352
-2.454820834
0.000605122
34.51835774
1.5
14.511744
0.001258
15.38064528
-5.649316194
0.000907683
38.59467161
2
19.775785
0.00171
20.50752705
-3.568163264
0.001210244
41.29385242
2.5
22.579993
0.002193
25.63440881
-11.91529647
0.001512805
44.9625349
3
27.89323
0.002689
30.76129057
-9.323602868
0.001815366
48.12443242
3.5
31.082812
0.003194
35.88817233
-13.38981625
0.002117927
50.80787456
4
33.911619
0.003747
41.01505409
-17.31909234
0.002420487
54.80352778
4.5
35.551507
0.004351
46.14193585
-22.95185206
0.002723048
59.78415903
5
36.97001
0.004935
51.26881762
-27.88987201
0.003025609
63.10764016
4
29.22154
0.004087
41.01505409
-28.75411079
0.002420487
68.85028504
3
20.858111
0.003181
30.76129057
-32.19364138
0.001815366
75.22641113
2
14.437949
0.002144
20.50752705
-29.59683063
0.001210244
77.15439742
1
5.172582
0.00116
10.25376352
-49.55430766
0.000605122
91.69692258
0
-2.165917
0.000171
0
n/a
0
n/a
14
Displacement vs. Load
Displacement (in.)
0.006
Theoretical Displacement
0.005
Loading
0.004
Unloading
0.003
(Loading)
y = 0.001x - 0.0002
0.002
0.001
(Unloading)
y = 0.001x + 0.0002
0
0
1
2
3
4
5
6
Load (lbs)
Figure 11. Displacement vs. Load (Composite Reinforced; I-Orientation)
Strain vs. Load
60
Theoretical
Strain (με)
50
40
Loading
30
Unloading
20
(Loading)
y = 7.6845x + 2.3028
10
0
-10
0
1
2
3
4
5
6
Load (lbs)
Figure 12. Strain vs. Load (Composite Reinforced; I-Orientation)
15
(Unloading)
y = 7.8356x - 2.1733
Table 7 provides the theoretical and experimental data for the final configuration and material of
the experiment. The composite reinforced beam in H-orientation exhibited the highest stiffness
characteristics out of every configuration and material. The maximum displacement was 0.0032in
and the maximum strain was about 13µs. The experimental displacement data matched the
theoretical data very well, averaging only about 10% error. Much of this error came during the
loading phase, whereas the unloading data was very accurate. This may be a result of displacement
being more sensitive to the boundary conditions since it is dependent on four boundary conditions,
whereas strain only has two boundary conditions. Since the clamp is not ideal, meaning it is not
immovable and could possibly have twist and displacement, error during the loading process
occurred. The percent error for strain was very large, averaging about 152%. This is due to the fact
that the range of strain values for this material and configuration was very small, so small
inconsistencies resulted in large percent errors.
Table 7. Beam Bending Test and Theory Data (Composite Reinforced; H-Orientation)
Displacement(in)
Theoretical Strain(µs)
Percent Error in Strain (%)
Theoretical Displacement (in)
0
-0.091459
-0.000007
0
n/a
0
n/a
0.5
0.351311
0.000206
0.412224529
-14.77678425
0.000299645
-31.25192198
Force (lbs) Strain(us)
Percent Error in Displacement (%)
1
2.663553
0.000419
0.824449059
223.0706582
0.000599289
-30.08387211
1.5
3.4507
0.00031
1.236673588
179.0307834
0.000898934
-65.51471815
2
4.688815
0.001008
1.648898117
184.3605042
0.001198579
-15.90040941
2.5
5.557956
0.00142
2.061122647
169.6567334
0.001498224
-5.221096322
3
6.902664
0.001704
2.473347176
179.0818882
0.001797868
-5.221096322
3.5
7.8292
0.002098
2.885571705
171.3223167
0.002097513
0.023209213
4
7.017456
0.002423
3.297796235
112.7922861
0.002397158
1.078029758
4.5
8.058785
0.002715
3.710020764
117.2167088
0.002696803
0.674774446
5
12.994848
0.003191
4.122245293
215.237136
0.002996447
6.492775224
4
10.346429
0.002489
3.297796235
213.7376679
0.002397158
3.831290164
3
6.000725
0.001855
2.473347176
142.6155559
0.001797868
3.177738452
2
3.688483
0.001181
1.648898117
123.6938087
0.001198579
-1.466650314
1
1.761615
0.0006
0.824449059
113.6717826
0.000599289
0.118560223
0
0.416907
-0.000219
0
n/a
0
n/a
16
Displacement vs. Load
0.0035
Theoretical Displacement
Displacement (in.)
0.003
Loading
0.0025
Unloading
0.002
(Loading)
y = 0.0007x - 0.0002
0.0015
0.001
(Unloading)
y = 0.0007x - 0.0002
0.0005
0
-0.0005
0
1
2
3
4
5
6
Load (lbs)
Figure 13. Displacement vs. Load (Composite Reinforced; H-Orientation)
Strain vs. Load
Strain (με)
14
12
Theoretical
10
Loading
8
Unloading
6
(Loading)
y = 2.1872x - 0.0657
4
2
(Unloading)
y = 2.5988x - 0.6287
0
-2
0
1
2
3
4
5
6
Load (lbs)
Figure 14. Strain vs. Load (Composite Reinforced; H-Orientation)
17
IV.
Conclusions
The experiment was conducted using three beam samples, in order to determine flexural
properties of the various materials including: baseline aluminum, aluminum reinforced with
aluminum caps, and aluminum reinforced with composite caps. The instruments used were strain
gages, a LVDT and the LabView program. The physical response of the samples, the displacement
and strain data, collected helped lead to a number of conclusions in relation to strength and weight of
the material. It was evident that the composite reinforced aluminum beam exhibited the highest
strength properties because the stiffness value was the greatest and in the experiment it had the least
strain and displacement when the maximum load was applied. Another critical result was the fact that
all the beam samples exhibited higher strength behaviors when they were in H-orientation because
that increased the area moment of inertia, which increased stiffness. These conclusions are important
because they indicate what materials best maximize efficiency when designing aerospace structures.
Composite materials are beneficial because they are lighter and have greater stiffness properties than
just plain aluminum. The downside to composites is that they are expensive to produce and
implement in industry.
Overall, the lab goals were met. Strain and displacement were successfully measured and
recorded using LabView. The specimens reacted the way that was expected. Cogent data was
compiled and organized to provide linear relationships between strain and load, and displacement
and load. Also, hysteresis was evident for all of the specimens. This was expected because it is a
natural phenomenon that occurs in all materials because of residual stress and strain. Since there is
residual stress and strain in the beams, the final values of strain and displacement did not match the
initial values. The difference can be accounted for on a more scientific level, due to energy
dissipation from the material plasticity. Hysteresis is more easily observed in highly elastic materials;
however, it was found that the reinforced and unreinforced aluminum beams all experienced
hysteresis.
Error could have resulted in poor set-up of the LVDT. Since there was such a small window to
work with, about 0.75 of a millimeter, it was difficult to set the zero value for the instrument. It was a
very sensitive instrument that could also have picked up noise from the surroundings; therefore,
resulting in flawed data. Another potential source of error was the fact that the specimens were used
for several years in the same experiment. The specimens may have been fatigued, which would result
in flawed strain and displacement data; however, this error is minimal as compared to other potential
18
sources. The clamp may also have caused a stress point in the specimens. Filler blocks were inserted
along the webs of the specimens to lessen this effect, but it may still have affected it.
Recommendations for the future would be to have a mechanical way of zeroing the LVDT instead
of inaccurately fumbling around with hands to set the initial LVDT position. Another
recommendation would be to use new samples, instead of reusing older fatigued samples. New
samples would help eliminate error from the weakening of the stiffness properties of the material due
to cyclical loading and unloading for several years. A stronger clamp could also be used to avoid
possible error from the theoretical assumption of an immovable clamp.
19