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Bending Stress In A Beam
Mechanical Engineering (University of Johannesburg)
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DEPARTMENT OF MECHANICAL ENGINEERING TECHNOLOGY
Faculty of Engineering and Built Environment
UNIVERSITY OF JOHANNESBURG
Doornfontein Campus
Title: Bending Stress in a Beam
By
ITEMOGENG.B. BABE
(218002346)
A Semester report submitted
in partial fulfilment of the requirements for the module
APPLIED STRENGTH OF MATERIALS 2B
B. ENG TECH (BENG(TECH))
Engineering: Mechanical
Date: 09 October 2020
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Table of Content:
Introduction……………………………………………1
Aim…………………………………………………….2
Assumptions…………………………………………...3
Apparatus………………………………………………4
Procedure………………………………………………5
Results…………………………………………………6
Analysis of results……………………………………...7
Discussion………………………………………………8
Conclusion……………………………………………...9
Recommendations……………………………………..10
References……………………………………………...11
Appendix……………………………………………….12
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1. Introduction:
Strain gauges are the most frequently used devices in stress-strain relation. The electrical strain
gauge operates on the direct relationship between the change in electrical resistance of a wire as it
is stretched and the strain  developed within the material. The ability to precisely measure the
change in electrical resistance gives a direct, precise measure of the strain. As a wire is stretched,
its length increases and its cross-sectional area decreases, which increases the resistance of the
wire. By bonding the strain gauge to a structural member and measuring the change in resistance
as the load is applied, the corresponding strain can be measured. The experimental value of stress
 may be determined from the measured strain  by using Hooke’s Law for uniaxial stress,  =
E. E is the modulus of elasticity of the beam material (Csun, n.d).
2. Aim:
To calculate a bending Stress and compare it to the experimental value
3. Assumptions:
Bending stress is zero at the beam’s neutral axis, which is coincident with the centroid of the
beam’s cross section.
Bending stress increases linearly away from the neutral axis until the maximum values at the
extreme fibers at the top and bottom of the beam.
Material of the beam is homogenous and isotropic.
Beam is straight before loading and remains straight even after load is removed.
Beam is stressed within elastic limit and follows Hooke’s law.
4. Apparatus:
The STR3 Hardware with the frame
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Figure 3
Data acquisition and Laptop computer
5. Procedure:
1. Set up the equipment as illustrated in Figure 3 and connect the laptop, which
has an appropriate data capture software installed.
2. Zero the force gauge and the strain gauges
3. Load the beam with a force of 50 N and record the bending moment together
with strain values from (1 until 9) on the laptop.
4. Repeat the same procedure by loading the beam with 100 N, 150 N, 200 N and
the 250 N and each time recording the bending moment and strain values.
5. Tabulate your results as follows:
6. Results:
Force Bending Gauge Gauge Gauge Gauge Gauge Gauge Gauge Gauge Gauge
Moment 1
2
3
4
5
6
7
8
9
(N)
(Nm)
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50
100
150
200
250
8.7
17.7
26.2
35.2
44.0
326.5
278.0
240.7
202.9
158.9
218.7
179.6
149.9
121.3
88.5
343.5
309.3
285.2
260.3
230.7
208.9
200
191.6
184.5
175.4
113.9
109.5
106.2
103.9
98.9
6.8
8.6
8
8.7
11
0.5
19.4
35.7
51.4
69.1
-163.4
-149.7
-140.3
-129.5
-115.2
Take average value between two strains:
Gauge Vertical
Measured Bending moment (Nm)
number Position (mm) 0
8.7
17.7
26.2
from top
1
0
0
326.5 278
240.7
2,3
8
0
281.1 244.45 217.55
4,5
23
0
161.4 154.75 148.9
6,7
31.7
0
3.65
14
21.85
8,9
38.1
0
-152.6 -135.7
175.35
7. Analysis of results:
Calculations:
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35.2
44
202.9
190.8
144.2
60.1
-117.4
158.9
159.6
137.15
40.05
-96.75
-187.3
-155.5
-131.1
-105.3
-78.3
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Centroid
a1=6.4× 38.1 = 243.84 𝑚𝑚2 =2.4384×10^-4 m^2
a2=6.4×31.7 =202.88 𝑚𝑚2 =2.0288×10^-4 m^2
y1=6.4/2=3.2 mm
y2=6.4+31.7/2=22.25 mm
𝑎1𝑦1+𝑎2𝑦2
y=
𝐴
(243.84)(3.2)+(202.88 )(22.25)
=
243.84+202.88
=11.85mm
𝑦1 =38.1-11.85=26.25 mm
𝑦2,3 =30.1-11.85=18.25 mm
𝑦4,5=15.1-11.85=3.25 mm
𝑦6,7 =11.85-6.4= 5.45 mm
𝑦8,9 =11.85 mm
Segment
1
2
A
243.84
𝑚𝑚2
202.88
𝑚𝑚2
𝑑𝑦
y
3.2
22.25
3.211.85=8.65mm
22.2511.85=10.
4mm
I=bℎ3 /12
[(38.1)(6.4)^3]/12=832.3072
𝑚𝑚4
[(6.4)(31.7)^3]/12=1.6989×1
0^4𝑚𝑚4
Experimental stress
E=
𝜎
𝜀
𝜕=𝐸 × 𝑒
= (69×10^9) (326.5×10^-6)
=22528500 Pa
Theoretical stress
Moment of inertia about the neutral axis,
I=𝐼1 + 𝐼2
= (832.3072 + 18.2×10^3) +(1.6989×10^4 +21.94 × 103 )
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A×𝑑𝑦 2
243.84×(8.65)^2=18.2×10^
3 𝑚𝑚4
202.88×
(10.4)^2 =
21.94 × 103 𝑚𝑚4
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=58×10^3 𝑚𝑚4
=58×10^-9 𝑚4
𝑀𝑦
𝜕=
𝐼
=
(17.7)(0.01185)
Load
58×10^−9
50
100
150
200
250
=3616293.103 Pa
Bending moment
Experimental
bending Stress
Theoretical
Bending Stress
8.7
17.7
26.2
35.2
44.0
22528500
19182000
16608300
14000100
10964100
1777500
3616293.103
5352931.034
7191724.138
8989655.172
Bending stress ×10^6
Bending stress vs Load
100
80
60
40
20
0
0
50
100
150
200
250
300
Load N
experimental
theoritical
Figure 1: Bending stress against Load graph
8. Discussion:
From the calculations above, it can be observed that the experimental stress is less than the
theoretical stress. As observed in the graph above, it is seen that the graph of theoretical stress is
increasing as the load is being increased and the graph of experimental values decreases as the
load is being increased In the theory it is assumed that the distribution of the load is uniform and
if the values obtains are not the same then it means the load distribution is not uniform.
According to the graph above the experimental bending stress is showing linear relation with the
load means the value of the experimental bending stresses increase with the increase in the value
of applied load and decrease with the decrease in the value of applied load.
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9. Conclusion:
Aim of this task was to calculate a bending Stress and compare it to the experimental value and
the result show that there is a linear relationship between bending stress and applied load. The
strain is directly proportional to the bending moment. As the value of the bending moment
increases, the value of the strain decreases. The bending equation predicts accurately the stress in
the beam. It can be concluded that the experiment was partially successful, however the theoretical
stress was greater than the experimental which could be due to human errors.
10.Recommendations:
For the experiment to be successful and to obtain accurate readings or results, the following should
be considered:
The apparatus should be checked before starting with the experiment. The equipment in the lab
should be either replaced or maintained in order to give accurate readings. More than one recording
of readings should be considered to ensure certainty of each readings. Ensure that the apparatus is
not vibrating that could cause inaccuracy of the results obtained. Take the average of the readings
to perform the calculations.
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11.References:
I.
II.
Csun. (n.d). Available from: https://www.csun.edu/sites/default/files/EXP3.pdf. Accessed
date: 07 October 2020.
Scribd.com. figure 2. Accessed date: 08 October 2020
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12.Appendix:
Figure 2: diagram of a beam
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