MANE-4040 MECHANICAL SYSTEMS LABORATORY (MSL)
Lab Report Cover Sheet
Lab Number 2 and Title of Lab: Beam Bending Experiment and Analysis
Section (select 1): S2-W(9am)
Lab Bench (select 1): A
Submitted by Group (Bench) Leader: Maxwell Wethern
Group Member: Michael Ahn
Group Member: John Lockwood
Group Member: Joseph Trosa
Group Member: Kristi Kokthi
Lab Scheduled Dates:
1/24/2024; 1/31/2024
Lab Report Due Date:
2/14/2024
Lab Report Received Date (by TA):
________________________________________
Late Penalty Points (by TA): __________________________________________
Contributor(s)
(If multiple, indicate % of each)
Possible
Points
Abstract
Joseph Trosa
10
Introduction
Joseph Trosa
10
Experimental
Procedures
Michael Ahn
15
Max 50%, John 50%
25
Analysis and
Discussion
Kristi Kokthi
25
Conclusions
Michael Ahn
15
Section
Results
Total
100
Points Given
Beam Bending Experiment and Analysis
Kokthi, Lockwood, Ahn, Wethern, Trosa
Beam Bending Experiment and Analysis
Michael Ahn, Kristi Kokthi, John Lockwood, Joseph Trosa, Maxwell Wethern
ABSTRACT
This laboratory experiment explores beam bending phenomena through
three-point bending tests conducted on aluminum and polycarbonate samples using an
Instron machine. The experiment aims to understand fundamental principles of steady
stress beam loading, apply basic loading theory, and predict deformation behavior under
various conditions. Numerical analysis and experimental data integration facilitate
model development for extrapolating findings to complex geometries. Tests involved
measurements of cross-section dimensions, Instron machine stiffness determination,
and hand calculations for deflection and yield stress. Week 1 experiments revealed
discrepancies between observed and calculated deflections, attributed partly to Instron
machine effects. Week 2 experiments with varying cross-sections demonstrated material
and load placement impacts on deflection. Results suggest close agreement between
experimental and theoretical values, with differences likely due to testing errors. Overall,
the experiment underscores the importance of considering testing apparatus effects and
load placement in beam deflection analysis, providing valuable insights for engineering
applications.
INTRODUCTION
The purpose of this laboratory experiment is to gain a comprehensive understanding
of beam bending phenomena through the execution of three-point bending tests
utilizing the Instron machine. This investigation focuses on aluminum and polycarbonate
samples to discern their respective behaviors under stress. The primary objectives are
multi-faceted. Initially, the aim is to comprehend the foundational principles underlying
the steady stress beam loading process. Subsequently, the endeavor shifts towards the
practical application of basic beam loading theory in real-world scenarios. Furthermore,
numerical analysis is employed to predict the deformation behavior exhibited by beams
under varying conditions. Additionally, the exploration seeks to explain the dependence
of deflection on multiple factors including loading conditions, cross-sectional area, beam
material, and support separation distance. Finally, the investigation extends to the
development and validation of a model, integrating experimental data, to facilitate the
extrapolation of findings to intricate geometries.
A mechanical three-point bending test serves to evaluate material properties
such as modulus of elasticity, strength, and stiffness. This procedure entails subjecting a
beam to a load via the Instron machine, which measures key parameters including
bending moment of inertia, shear load, angular displacement, deflection, and curvature.
By analyzing these metrics, engineers gain valuable insights into how materials react to
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Kokthi, Lockwood, Ahn, Wethern, Trosa
stress and strain. Typically, the test involves positioning the beam on two supports and
applying a load at a designated point, allowing for thorough examination and
measurement of the material's response under these controlled conditions.
Numerical integration using the trapezoidal rule can be used to determine the
displacements in the beam. The Trapezoidal rule is:
(4)
where x is the axial position on the beam and I is the integrated value. Three integrations
need to be performed to find the displacements along the beam. To perform these
integrations, it is necessary to determine the area moment of inertia of the uniform
beam with a rectangular cross section:
𝐼 =
1
12
3
𝑏ℎ
(5)
where I is the area moment of inertia, b is the cross section width, and h is the cross
section height.
The theoretical maximum deflection in the 3 point beam with a centered
contracted load is
δ=
3
(6)
𝑃𝐿
48𝐸𝐼
where δ is the max deflection, P is the concentrated load, L is the length of the beam, E
is the Young’s Modulus, and I is the area moment of inertia found from equation 5.
Young’s modulus is a measure of a material’s stiffness (Engineer’s Edge LLC, n.d).
Yield stress is the maximum stress that can be applied without permanent
deformation of the test specimen (Engineer’s Edge LLC, n.d.). The theoretical yield stress
in the three point beam with a centered concentrated load can be determined from
𝑆𝑦𝑝 =
𝑀𝑐
𝐼
(7)
where 𝑆𝑦𝑝is the yield stress, c is half the height of the beam, I is the area moment of
inertia (equation 5), and M is the bending moment. The theoretical bending moment in
the three point beam with a concentrated load is
𝑀=
𝐹𝐿
4
(8)
where M is the bending moment, F is the force applied, and L is the length of the beam.
When the beam is deformed by moments normal to its axis, it bends in a curved
shape (Trustees of Princeton University, n.d.). The theoretical radius of that curvature is
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Kokthi, Lockwood, Ahn, Wethern, Trosa
𝑟=
𝐸𝐼
𝑀
(9)
where r is the radius of curvature, E is the Young’s Modulus, M is the bending moment
(equation 8), and I is the area moment of inertia (equation 5).
In addition, beam bending produces concentrated stresses in fillets. A fillet is a
rounded corner or transition between two surfaces (Axsom, 2023), The fillet stress can
be found from
σ𝑓𝑖𝑙𝑙𝑒𝑡 = 𝐾𝑇 *
𝑀𝑧
𝐼
(10)
where σ𝑓𝑖𝑙𝑙𝑒𝑡 is the stress in the fillet, 𝐾𝑇 is the stress concentration factor, M is the
bending moment (equation 8), z is half the smaller surface height, and I is the area
moment of inertia (equation 5).
Lastly, the factor of safety for the fillet stress can be determined from
F.S =
𝑆𝑦𝑝
σ𝑓𝑖𝑙𝑙𝑒𝑡
(11)
where F.S is the factor of safety, Syp is yield stress, and σ𝑓𝑖𝑙𝑙𝑒𝑡 is the stress in the fillet.
EXPERIMENTAL PROCEDURE
Week 1
For the first step, 10 measurements for the cross section of both the aluminum
sample and the polycarbonate samples were taken. This was done using a Mitutoyo
caliper and measuring the base and the height of each sample. Then 6 tests were run on
the Instron Machine. The tests can be found in Table E.1. Each span was set using the
Instron Machine’s ruler to measure the distance between the supports. The supports
were tightened using an Alan wrench. For each test, an Instron extensometer and a
plunger was placed beneath the sample to measure deflection.
Table E.1 Test Conditions for Week 1
Test
Material
Cross Section
Height (mm)
Span (mm)
Max Load (N)
1
Polycarbonate
12.7
101.6
44.48
2
Polycarbonate
6.35
101.6
44.48
3
Aluminum
Alloy
6.35
101.6
44.48
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4
Aluminum
Alloy
6.35
101.6
356
5
Aluminum
Alloy
6.35
152.4
356
6
Aluminum
Alloy
12.7
152.4
356
After running tests 1-6 on the Instron machine, a 7th test was done in order to
determine the stiffness of the Instron machine. This was done by moving the lower
supports together and using the aluminum alloy sample with the 12.7mm dimension as
the height.
Hand calculations were then completed using measured cross-section dimensions
for beam deflection for tests 1-6. These calculated results were then compared to the
observed experimental results.
The next step was to complete hand calculations for the smallest radius of curvature
experienced by the beam’s neutral plane. These calculations were then used in order to
find the minimal yield strength for each test to remain elastic.
Using Google Sheets and data from test 6, vertical deflection, angular deflection,
bending moment, and stress were calculated and plotted against distance. For
calculating the bending moment, the trapezoidal rule was used. A comparison was then
made between the found deflection using test 6 data and the theoretical hand
calculation.
Week 2
In week 2, a long beam with variable cross section was used as the sample. 10
measurements were taken using a Mitutoyo caliper for both widths as well as the
sample’s thickness. The radius of the sample’s filet was found using a radius gauge set.
Using a caliper, the sample was marked at the center, an off center mark for test 2, as
well as support locations. The measurements for the marks can be found in Table E.2.
For each test, an Instron extensometer and a plunger was used in order to measure
deflection.
Table E.2 Test Conditions for Week 2
Test
Location of Load
(from left support)
Span
Max load (N)
1
6.35cm
12.7cm
1334.5
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Kokthi, Lockwood, Ahn, Wethern, Trosa
2
4.572cm
12.7cm
1334.5
Modifying the Google Sheet used to calculate deflections, stress, and bending
moments for Test 6 from Week 1, angular deflection, vertical deflection, shear, and
moment were then calculated and plotted for Test 1 and Test 2 from Week 2. These
results were then compared to the experimental results. Beam overhang was neglected
during this analysis.
RESULTS
In (Appendix B1.1), the mean base, height, and area are specified for both the
aluminum and polycarbonate samples, derived from a total of 10 measurements for
each sample (see Appendix B.1, B.2). Also documented in (Appendix B1.1) are the
moments of inertia for each sample for two different orientations; the cross-section for
Ix is rotated by 90 degrees to determine the value for Iy. Additionally, this table includes
the span of the beam, maximum load, and Young’s modulus for each test.
Below, in (Appendix B1.2), the crosshead displacement, corrected crosshead
displacement, and deflectometer displacement are presented for each test. These values
were directly obtained from the raw data received from the Instron test for each sample
at the maximum force. The corrected crosshead displacement was calculated by
subtracting an adjustment factor determined in the compliance test for week 1. For tests
1-3, the adjustment factor subtracted from the crosshead displacement was 0.102108
mm, while for tests 4-6, it was 0.259334.
Hand-calculated maximum deflections for each test are provided in (Appendix
B1.3) below. These deflections were determined at the halfway point of the total span of
the beam where the point load was applied, using the beam deflection equation for a
simple beam with a concentrated load P at the center. Details of the calculations can be
found in (Appendix C1.1, C1.2). The spring constant of the data for the compliance test
was measured to be k = 4415 N/mm. This value represents the slope of the linear
portion of the data in Fig.1 below. The initial portion of the data, up to the point marked
as (0.18669, 15.25045728), was excluded from the linear regression equation due to
possible errors in the completion of the compliance test leading to a nonlinear
relationship.
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Fig.1: Force vs. Crosshead Displacement of Compliance Test Data
The smallest radius of curvature for each test was computed, as detailed in
(Appendix B1.4). The bending-moment diagram used to find the radius for each test,
along with further hand-calculations, can be found in (Appendix C2.1, C2.2). Table-2
below displays the calculated minimum yield stresses required for polycarbonate and
aluminum to ensure all the deflections of the tests conducted during the first week
remain elastic. For the specifics of the calculations, refer to (Appendix C3.1).
Table-2: Minimum Yield Stresses for Each Material
Material
Calculated Minimum Yield Stress
(Tensile) (MPa)
Polycarbonate (Tests 1-2)
18.15
Aluminum (Tests 3-6)
148.86
The trapezoidal numerical integration of test 6, utilizing the cross-section
measurements found earlier in (Appendix B1.1), was employed to determine the
theoretical deflection of the beam. Displacement vs. distance along the beam, slope vs.
distance along the beam, and maximum tensile stress vs. distance along the beam were
plotted from the numerical integration spreadsheet (see Appendix A1.1, A1.2, A1.3).
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Kokthi, Lockwood, Ahn, Wethern, Trosa
(Appendix B1.5) documents the mean height of both the smaller and middle
bases, as well as the mean width of the sample, obtained from the measurements of the
stepped shaft (see Appendix B.3). Additionally, the mean fillet radius of the fillet
between the smaller base (referred to as Base 1 in the table) and the middle base is
recorded. Test parameters such as the span of the beam and the maximum load applied
are also noted, along with the cross-sectional areas and moments of inertia of each
section of the stepped shaft.
Table-3 presents the crosshead displacement, corrected crosshead
displacement, and the deflectometer displacement for each of the two tests from week
2. Similar to the values in (Appendix B1.2), these were derived from the raw data of each
test from the Instron. The adjustment factor subtracted from the crosshead
displacement was determined using the equation from Fig.1, y =4415x, where y = 1334.5
N, resulting in x = 0.30224 as the adjustment factor for both tests.
Table-3: Recorded Instron Displacements of Stepped Shaft for Week 2
Stepped Shafts Test
Type (at 1334.5 N)
Crosshead
Displacement
(mm)
Corrected
Crosshead
Displacement (mm)
Deflectometer
Displacement (mm)
Symmetric Loading
0.36068
0.05844
0.1843532
Asymmetric Loading
0.332486
0.03025
0.1669542
For the symmetric loading test of week 2, shear, moment, slope, and deflection
vs. the distance along the beam were plotted from the trapezoidal numerical integration
data used to determine the theoretical deflection of the beam (see Appendices A2.1,
A2.2, A2.3, A2.4). Similarly, shear, moment, corrected slope, and corrected deflection vs.
the distance along the beam for the asymmetrical loading case were plotted (see
Appendices A3.1, A3.2, A3.3, A3.4).
In Table-4, the maximum fillet stresses for the upper left fillet of both loading cases were
recorded. From these maximum stresses and the given value of yield strength for
aluminum alloy T-61 of Sy = 262 MPa, the factor of safety was determined and recorded
below.
Table-4: Fillet Stresses and Factor of Safety
Test
Maximum Fillet Stress
(MPa)
Factor of Safety
Symmetric
109.347
2.40
Asymmetric
139.96
1.87
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ANALYSIS AND DISCUSSION
Appendix D1.1 shows the accuracy of the deflectometer as opposed to the
corrected crosshead displacement. The deflectometer is on average about twice as
accurate as the data received by looking at the crosshead displacement despite the
corrections. That could be due to human error and it is most likely that data collection
was performed correctly with the deflectometer but not with the crosshead
displacement. The measurements on the BlueHill program might have been zeroed
slightly early or late after the beam started bending.
The stiffness of the Instron testing machine was determined by looking at the
slope of the force graphed with respect to crosshead displacement. The displacement
correction for tests 1-3, with a maximum load of 44.48 N, was determined to be
0.102108 mm, while for tests 4-6 with a maximum load of 356 N, it was 0.259334 mm.
One can already notice the direct positive relationship between the Instron’s load and
the needed data correction. That conclusion would be consistent with theory. The
mechanics of machines such as Instrons aren’t “ideal” as in they often still have
relatively significant errors in output with respect to parameters such as friction or
stiffness coefficients. In our case, the crosshead displacement measurements are shifted
by a factor of “k”. In the results section, we detailed how stiffness was determined
through a compliance test for which the force/strain graph slope was calculated (shown
in Fig.1). The larger the “k” value, the larger the error and therefore the needed
crosshead displacement correction. This error will vary depending on the load. When
performing a test under relatively low loads, there isn’t much risk of data being affected
by the Instron’s stiffness absorbing load but more so that the load displayed on the
software will be different from the true force we are looking to achieve. That can be
considered instrumental error. When performing tests under high loads, the stiffness of
the Instron “k” will sustain a larger fraction of the load that is supposed to be applied on
the beam and thus increasing error.
In order to calculate the yield strengths of each material required for tests 1-6 (as
shown in Appendix C3.1), one can apply the following equation which was derived from
the Euler-Bernoulli formula for beam deflection [3]:
𝑆𝑦𝑝 = σ𝑚𝑎𝑥 = 𝑀𝑐/𝐼
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Beam Bending Experiment and Analysis
Kokthi, Lockwood, Ahn, Wethern, Trosa
, where 𝑆𝑦𝑝 is the yield strength of the material, 𝑐 is the distance from the centerline of
the thickness of the sample to each edge, σ𝑚𝑎𝑥 is the maximum stress at a point in the
beam, 𝑀 is the moment, and 𝐼 is its moment of inertia at that point. It is important to
mention that in practical applications the yield strength will not be set equivalent to
maximum stress as engineers usually apply a safety factor to the maximum stress based
on different failure conditions, function/production constraints, etc. This number will
usually be a few times higher than 1 but, for our experimental purposes, it is 1. The
minimum yield strengths of the polycarbonate and aluminum were calculated to be
18.15 MPa and 148.86 MPa respectively as shown in Table-2.
The samples used during the second week of the experiments had varying
cross-sections. Considering that, we can’t derive an expression from the Euler-Bernoulli
equation by simply integrating as we did before. In order to predict the maximum
deflection for such a load case, we used numerical methods to convert a simple shear
stress graph into the beam deflection. We pick this approach because the shear stress
curve can be easily defined using our knowledge of physics. Due to the simple nature of
our setup, two supports and a single point negative load (pointing perpendicularly
downwards to the top face of the beam), the shear stress will be a constant value which
will be positive along the first and negative along the second half of the length of the
beam. Using a spreadsheet or an alternative computational program one can integrate
that curve appropriately by taking into account its Young’s modulus.
For the symmetrical loading experiment, the graph of deflection over distance
along the beam (shown in appendix A2.4) displays a maximum deflection of 0.17125
mm. The experimental data from Table-3 indicate the maximum corrected crosshead
displacement to be 0.05844 mm and the maximum deflectometer displacement to be
0.1843532 mm. This result mirrors the previous results in Tests #1-6 that the
deflectometer is much more accurate than the crosshead displacement measurements.
For the asymmetrical loading experiment, the graph of deflection over distance along
the beam (shown in appendix A3.4) displays a maximum deflection of -0.342064 mm.
The experimental data from Table-3 indicate the maximum corrected crosshead
displacement to be 0.03025 mm and the maximum deflectometer displacement to be
0.1669542 mm. Again, the deflectometer is more accurate, however the difference in
this case is much larger. The error for the deflectometer was much larger in the
asymmetric loading experiment. This is most likely due to human error on our part in
placement of the deflectometer.
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Kokthi, Lockwood, Ahn, Wethern, Trosa
As mentioned previously, the factor of safety is applied to a stress value in order
to account for cases of extensive but still reasonable use where a member/section might
sustain larger than predicted or/and cyclical loads under circumstances that can’t be
accounted for as precisely. These can include different levels of operator skill, defects in
manufacturing, transportation/installation methods, etc. In essence, the factor of safety
reduces the risk of design failure and it is calculated using the equation below:
𝐹𝑂𝑆 = 𝑆𝑦𝑝/σ𝑚𝑎𝑥
, where 𝐹𝑂𝑆 is the factor of safety, 𝑆𝑦𝑝 is the yield strength of the subject material, and
σ𝑚𝑎𝑥 is the maximum load stress at the point/section of interest. Engineers in different
industries pick different safety factors to suit their needs.
A large majority of the error that we predict to have occurred during our
experiment was in the setup of the instruments rather than extraction of the data from
the software. The distance measured to set the deflectometer could have been
incorrect. There were difficulties in adjusting the upper jaw height prior to each
experiment due to high fluctuations in the load indicated on-screen at even a light press
of the buttons that move it. As a result, the software measurements may have been
zeroed inappropriately. In addition, the values we took to be “theoretical” were actually
manually approximated from line graphs that were created in a spreadsheet application.
The resolution of the data in that graph would then limit how accurate the theoretical
displacement could be. It is also possible that we made errors in our cross-sectional area
measurements.
CONCLUSIONS
Reflecting upon the results of this experiment, the importance of keeping in mind
the Instron machine’s effect on the experiment becomes apparent. In comparing Week 1
observed deflections against the hand calculated deflections, there are noticeable
variations between the measured cross-head displacement and the deflectometer
displacement, which can be seen in Appendix B1.2. However, upon taking into account
the stiffness of the Instron machine, the corrected cross-head displacement agrees
much better with the measured deflectometer displacement.
In addition to understanding the importance of accounting for the Instron machine
itself, it is clear that the placement of the load on a beam is important in determining
the deflection a beam will have. Comparing results for the symmetric loading and the
asymmetric loading for an aluminum beam, the symmetric loaded beam had a
maximum observed deflection of 0.0635m while the asymmetric loaded beam had a
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Kokthi, Lockwood, Ahn, Wethern, Trosa
maximum observed deflection of 0.08128m, which shows how a more symmetric loaded
beam system will deflect less than an asymmetric load.
The material and cross-sectional area also plays a strong role in determining the
deflection of a beam. The polycarbonate material deflected much more than the
aluminum material, which can be seen in Appendix B1.2. In addition, comparing
deflections from test 1 and 2, it is clear that having a higher height in a cross-sectional
area reduces deflection as well as deflection in test 1 was observed to be 0.318mm and
in test 2, deflection was observed to be 2.06mm.
The experimental observed values and the theoretical hand calculations are close to
each other, but not the same. The difference of these values is most likely due to testing
errors. For this experiment, vertical loading tests were conducted; however, it is likely
that the span between the supports were not exactly as intended as the supports were
placed using the ruler on the Instron machine. In addition, it is likely that there was
some fatigue in the samples for Week 1 as many of the tests needed to be redone during
experimentation.
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REFERENCES
[1] MSL Lab 2 Beam Bending Instructions, LMS, Cagliari
[2] Collins, J. A., Busby, H. R., & Staab, G. H. (2010). Mechanical design of machine
elements and machines: A failure prevention perspective. John Wiley & Sons, Inc.
[3] Cagliari, L. V. R. (n.d.). LAB# 2 – BEAM BENDING NON-UNIFORM CROSS
SECTION RPI LMS - Rensselaer Polytechnic Institute. https://lms.rpi.edu/
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Kokthi, Lockwood, Ahn, Wethern, Trosa
APPENDIX
A1.1: Deflection vs. distance along beam - Week 1 Test 6
A1.2: Corrected slope vs. distance along beam - Week 1 Test 6
A1.3: Tensile stress vs. distance along beam - Week 1 Test 6
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A2.1: Shear force vs. distance along beam - Week 2 Symmetric
A2.2: Bending moment vs. distance along beam - Week 2 Symmetric
A2.3: Corrected slope vs. distance along beam - Week 2 Symmetric
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A2.4: Deflection vs. distance along beam - Week 2 Symmetric
A3.1: Shear force vs. distance along beam - Week 2 Asymmetric
A3.2: Bending moment vs. distance along beam - Week 2 Asymmetric
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A3.3: Corrected slope vs. distance along beam - Week 2 Asymmetric
A3.4: Corrected deflection vs. distance along beam - Week 2 Asymmetric
B1.1: Measurements and Given Information of Each Test Sample for Week 1
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Kokthi, Lockwood, Ahn, Wethern, Trosa
Material
μ Base
(mm)
μ Height
(mm)
Area
(mm^2)
Ix
(mm^4)
Iy (mm^4)
Young’s
Modulus
(GPa)
Aluminum
6.38
12.644
80.75
274.46
1075.919
68.9
12.785
69.653
172.29
948.71
2.41
Polycarbonate 5.448
Span of Tests
1-4 (mm)
101.6
Max Load
Tests 1-3
(N)
44.48
Span of Tests
5-6 (mm)
152.4
Max Load
Tests 4-6
(N)
356
B1.2: Recorded Instron Displacements for Tests in Week 1
Test #
Crosshead
Displacement (mm)
Corrected
Crosshead
Displacement (mm)
Deflectometer
Displacement (mm)
1 (at 44.48 N)
0.420878
0.31877
0.3967226
2 (at 44.48 N)
2.161794
2.059686
2.1171662
3 (at 44.48 N)
0.067056
-0.035052
0.0540766
4 (at 356 N)
0.691388
0.432054
0.4017518
5 (at 356 N)
1.821688
1.562354
1.44145
6 (at 356 N)
0.726948
0.467614
0.3755898
7 (at 44.48 N)
0.102108
N/A
0.0013208
7 (at 356 N)
0.259334
N/A
-0.0034798
B1.3: Hand calculated deflection
Test #
Hand Calculated Deflection
(mm)
1
0.4314
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2
2.394
3
0.04767
4
0.3815
5
1.2876
6
0.3233
B1.4: Smallest Radius of Curvature
Test #
Smallest Radius of Curvature, r
(mm)
1
1994.034
2
359.378
3
18046.037
4
2254.741
5
1503.161
6
5986.380
B1.5: Dimensions of Stepped Shaft and Week 2 Test Information
μ Base 1
(mm)
μ Middle Base
(mm)
Width (mm)
μ Fillet Radius
(mm)
Aluminum
12.86
19.05
12.66
3.175
Area of Base 1
(mm^2)
162.74
Ix of Base 1
(mm^4)
2242.36
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Area of Middle
(mm^2)
241.11
Ix of Middle
(mm^2)
7292.77
Span (mm)
127
Max Load (N)
1334.5
C1.1: Beam deflections tests 1-3
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C1.2: Beam deflections tests 4-6
C2.1: Radius of curvature tests 1-3
C2.2: Radius of curvature tests 4-6
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C3.1: Yield Stresses
C4.1: Fillet Stresses
21
Beam Bending Experiment and Analysis
Kokthi, Lockwood, Ahn, Wethern, Trosa
D1.1: Table showing percent error of corrected crosshead displacement and deflectometer
measurements, both compared to calculated test deflections (found in Appendix B1.3)
respectively.
Test #
1 (at 44.48 N)
2 (at 44.48 N)
3 (at 44.48 N)
4 (at 356 N)
5 (at 356 N)
Δ Corrected (%)
Δ Deflectometer
(%)
-26.108
-8.03834
-13.9647
-11.5637
-173.531
13.43948
13.25138
5.308467
21.33846
11.94859
22
Beam Bending Experiment and Analysis
Kokthi, Lockwood, Ahn, Wethern, Trosa
6 (at 356 N)
44.6378
16.17377
23