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Mechanical Engineering Sample Experiment including Experimental Data
Typology: Assignments
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New Jersey Institute of Technology
Strength of Materials Laboratory - Spring 2020
Experiment # 3: Stresses, Strains, and Deflection of Steel Beams in Pure Bending
Group Number: 6
Experiment Number: 3
Course & Section: Mech 237-
Date Submitted: April 9, 2020
Instructor: Celina Semaan
TA: Hasan Tareq
Group Members:
Zacchaeus Amante
Joseph Roberto
Chinua McDonald
Material: Steel Beam
Format Checklist
Overall Format/Organization
Abstract
Analysis
Discussion/Conclusion
References
The analysis section of this lab report includes raw data values given, which are then used
to create the graphs shown below. The lab groups then calculate the necessary theoretical values
and compare them to the experimental values, which can be obtained by looking at the graphs.
All five graphs are Depth (inches) vs Strain ( × 10
− 6
inches )
, but they are in different
loading/unloading increments. The first graph is 2000lb loading, the second graph is 4000lb
loading, the third graph is 6000lb loading, the fourth graph is 4000lb unloading, and the fifth
graph is 2000lb unloading.
The equations outlined in the lab manual must then be used to determine the necessary
theoretical values. The values being compared in the tables below are strain measurements,
location of the neutral axis, and deflections. Once these theoretical and experimental values are
compared, it will be possible to obtain a percent error based on the difference in the values.
Important Equations:
ε
t ( bottom )
=− ε
c ( top )
P ∗ a ∗ c
y =
P ∗ a
2
− 4 a
2
P = the load
a = distance away from the support
c = distance from Neutral Axis to the top of the beam
E = Modulus of Elasticity
I = cross-sectional moment of inertia
ε
t
= maximum tensile strain
ε
c
= maximum compressive strain
EI = flexural rigidity
L = length of the beam
Given Data:
d = 8 inches
● Below is the graph for 6000lbs loading:
● Below is the graph for 4000lbs unloading:
● Below is the graph for 2000lbs unloading:
A table for the theoretical and experimental values of the location of the neutral axis is shown
below:
Loading 2000 lbs 4000 lbs 6000 lbs 4000 lbs 2000 lbs
Average Value 2.
Standard Deviation 1.
Then, the lab group must compare the theoretical and experimental compressive (top) strain
values, as well as the theoretical and tensile (bottom) strain values, as shown in the table below:
Load, P (lbs) Strain at bottom (tension) Strain at top (compression)
Theoretical Electrical
Strain Gauge
Theoretical Electrical Strain
Gauge
Loading 2000 229.8850575 219 -229.8850575 -
Unloading 4000 459.7701149 433 -459.7701149 -
Discussion:
This week’s lab introduced the concept of stresses, strains, and deflections of steel beams in pure
bending. Pure bending occurs when a constant bending moment is applied to a typically straight
beam without any axial, shear, or torsional forces simultaneously affecting said beam. However,
pure bending does not actually exist, as it requires a weightless member to be tangible in real
life, so it is mainly used as a concept.
The first objective of this lab was to compare theoretical and experimental calculations of strain
upon multiple degrees of loading. Experimental values were given in lab data sent to us, while
theoretical values could be found by manipulating the flexure formula as well as those derived
from Hooke’s law. For the 2000 lb loading case, the electrical strain was theoretically found to
be 229.885 while the experimental value for the same scenario was dictated as 219. Like all the
other loadings and unloadings applied in this lab, the difference between theoretical and
experimental values are very slim, showing the accuracy in methodology our group applied to
find said values. It is important to realize that when loading and unloading, the amount of strain
(whether theoretical or experimental) was found to be equal and opposite. This is because the
amount of force that was applied to the beam was within the elastic range of the material.
Conceptually, the beam should have returned to its original position when the loading was
removed, but the electrical strain gauge said otherwise. Our group found that there was still a
noticeable amount of strain, albeit small, permanently deforming the beam. This could possibly
indicate that one of the loading forces, most likely the 6000 pound force, had gone beyond the
elastic region of the steel.
Another objective of this lab was to determine the location of the neutral axis. In this experiment,
it was calculated through the use of the simple c = I/S where both the values of I and S were
reference values found online. This neutral axis was found to be .64 inches above the location of
ε ∗ E ∗ I
P ∗ c
inches. It is difficult to validate this value as the lab group was not able to see the experiment in
person and estimate the required distance.
Conclusion:
The objectives of this lab revolved around the theoretical and experimental calculations of many
factors in a beam under the effects of bending, such as the strain, locations of the neutral axis, the
distance between the loads and the end of the beam, and the deflections. All of these values were
found and show the validity of the conceptual theory through the means of numerical
interpretation. It is important to note that the original experiment opted to use a mechanical
gauge to measure strain as well as the electrical one. This experiment, however, only used an
electrical gauge, so it is impossible to determine superiority between the two. Limitations to this
experiment definitely stemmed from the inability to tangibly interact with the experiment as well
as other general cases of human error. And limitations to certain formulas regarding deflection
do not take into account locations that go beyond its intended boundary points. Overall, because
the objectives of the lab were completed, it is safe to assume that it is consequently a
success.There is definitely a better understanding of the concept of pure bending and will
definitely benefit the group’s future endeavors in engineering.
Discussion: The main objectives for this lab report were to compare the theoretical and
experimental strain values, neutral axis location, and deflections. The deflections were
max
Pa
2
− 4 a
2
displayed in a table and compared to the experimental values. The percent differences between
the theoretical and experimental values is displayed, where there was a 5.857% error for 200lb
loading, a 2.076% error for 4000lb loading, a 1.320% error for 6000lb loading, a 2.454% error
for 4000lb unloading, and a 4.354% error for 2000lb unloading. The neutral axis location was
this simple division, the location of the neutral axis is 0.64 for each loading/unloading value. The
experimental neutral axis location was simply found by looking at each strain vs depth graph,
and taking the value where the depth is equal to 0, and those experimental/theoretical values are
compared in a table. Next is the tensile and compressive strain values. The formula
ε t ( bottom )
P ∗ a ∗ c
is used to find the tensile strain values, and the relation
ε
t ( bottom )
=− ε
c ( top )
is then
used to get the compressive strain values. P is the load, a was found to be about 200 inches, c is
the location of the neutral axis, which was found earlier, and E and I are both given. These are
then compared to the experimentally determined electrical strain gauge values, as shown in one
of the above tables. After obtaining all of this information and displaying all of it in the tables
and graphs shown in the analysis section of this lab report, the only thing left to do is to infer a
conclusion from the info.
Answering the discussion questions in the lab manual, there was good agreement
between the theoretical and experimental strain values, and from this lab, it is not accurate to
determine which method has better results, because the lab groups were told to only use the
electrical strain gauge method, not the mechanical one. Hypothetically, mechanical strain gauges
seemed to be more accurate in the past because it was the only method, until electronics became
available and affordable. As such, it is much more difficult today to determine which one is
better without performing the experiment, and comparing the results of the mechanical method
vs the electrical method. The theoretical value of the location of the neutral axis is 0.64 and it
Discussion: This lab was meant to demonstrate the properties to be derived from bending
moment data. Using the collected data groups were to find values for strain deflection and the
location of the neutral axis. These values were then compared to theoretical values derived using
c
max
Pa
2
− 4 a
2
and then compared to values obtained from
loading a sample with 6000lbs, unloading it, and measuring 5 different loads. The discrepancies
for theoretical and experimental values found at 200lbs loading, 4000lbs loading, 6000lbs
loading, 4000lbs unloading and 2000lbs unloading were 5.857%, 2.076%,1.320%,2.454%, and
4.354% respectively. Next strain values were calculated both above the neutral axis in
compression and below the axis in tension. These values were calculated using the theoretical
loading patterns and compared to experimental values measured by an electric strain meter
placed on the sample. These values yielded similarly accurate results with the percent errors for
the 5 loading patterns were all <6%. What can be noted is the symmetry between the 2000lb and
4000lb configurations in both loading and unloading. Though the strains should be identical on
both sides of the maximum load placed on the sample provided the strain remains within the
elastic region. However experimentally there was a skew that occurred during the unloading
configurations that resulted in a constant change in both deflection and in strain. The consistency
of the changes in the measured values in addition to the strain measured in the sample after
loading completed suggested that the load entered the samples plastic region resulting in
permanent deformation. Another point of symmetry in the theoretical data is that
ε
t ( bottom )
=− ε
c ( top )
or for all loading configurations the compression is equal and opposite to
compression about the neutral axis. This formula however treats the sample as weightless though
in reality a sample will react to its own weight in addition to loading configurations. This is
reflected in the experimental values where the tension was never exactly equal and opposite to
the compression.
Conclusion:
This lab attempted to show the various properties involved with bending moments including the
modulus of elasticity and its geometry, specifically the second moment of inertia. It showed how
these values can be used to loosely predict how various materials will perform under different
loading configurations. It is worth noting that while the experimental values and theoretical
values were close, the experiment provides real world insight such as the permanent deformation
that occured during the loading and the discrepancy between the experimental tensile and
compressive forces.
Beer, F. P., Johnston, E. R., DeWolf, J. T., & Mazurek, D. F. (2020). Mechanics of materials
(8th ed.).
Department of Civil and Environmental Engineering. (2020, Spring). Mech 237 Lab Manual.
Newark, New Jersey: New Jersey Institute of Technology. Pages 2-1 to 2-
Engineering ToolBox, (2008). American Standard Beams - S Beam. Retrieved from:
https://www.engineeringtoolbox.com/american-standard-beams-d_1320.html (Accessed April,
