ENGINEERING FACULTY
DEPARTMENT OF MECHANICAL ENGINEERING
Laboratory Report 1
Deflection of a Cantilever
Subject: ASM360S
Date Issued: 24th April 2024
Date Due: 2nd May 2024 @ 09h00
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Developed by: Mr. V. Moni
Moderated by: T. Chipanga
TABLE OF CONTENTS
1. Aim of the Experiment
2. Theoretical Background
3. Experimental Apparatus
4. Experimental Procedure
5. Results
6. Discussion of Results
7. Conclusion
Appendix A: Experimental Readings and Calculations
Figure 1 below is SM1004 BEAM APPARATUS
Developed by: Mr. V. Moni
Moderated by: T. Chipanga
1. AIM OF THE LABORATORY EXPERIMENT
1. To prove the relationship between the deflection ( y ) and each of the quantities
length (l ) and load (W ). In this experiment only l and W are varied.
2. To show how to use the cantilever test to find the Young’s Modulus for a beam.
2. THEORETICAL BACKGROUND
Textbooks show that the deflection under the load for a cantilever loaded at the free end
is given by:
Wl3
y= equation (1)
3EI
If EI and l are kept constant then:
y =k1W equation (2)
Where k1is constant.
Also, if EI andW are kept constant:
y = k2l3 equation (3)
Digital
Tie to support Indicator
beam
Cantilever Load
Support Cell-W
Developed by: Mr. V. Moni
Moderated by: T. Chipanga
Figure2: Beam Apparatus arrangement
3. EXPERIMENTAL APPARATUS
3.1 Cantilever support
3.2 One Load Cell (10 N)
3.3 One digital deflection indicator
3.4 Two beams of different material, each of the same thickness (to compare Young’s
Modulus).
3.5 Two beams of different thickness, each of the same material (to compare second
moments of area.
4. EXPERIMENTAL PROCEDURE
1. Choose beams as explained in experiment apparatus section.
2. Fit the cantilever support onto the left side of the frame to have longer working
length (l ).
3. Set up a Load Cell near to the right of the beam apparatus.
4. Fit the beam into cantilever support so that the working length (l ) between the
support and Load Cell is 200 mm, with only a small overhang near to the Load Cell.
5. Use a piece of string to hold up the free end of the beam on the opposite side of the
support (see Figure 2) and unlock the Load Cell.
6. To check the level of the beam, put digital indicator close to cantilever support over
the beam, set digital indicator to zero and slide it across till it aligns with Load Cell.
Adjust the knife-edge of the Load Cell if
necessary until the digital indicator above reads zero. Set the Load Cell to zero.
7. With the digital indicator above the Load Cell, slowly adjust the knifeedge of the Load
Cell to give a reading of 2 N as shown in Table 1.
8. Adjust the knife-edge upwards to give a number of load increments as in the results
table. At each increment, record the load and digital indicator readings.
9. Repeat the experiment with longer values of (l ) as shown in the results table.
10. Repeat the experiment with different beams as explained in apparatus section.
5. RESULTS
1. Plot a chart for each beam. On the chart, plot curves for each length ( l ) of
deflection (y vertical axis) against W (load).
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2. Your charts of yagainst W should prove that y is proportional toW , so that the
equation 2 is correct. The gradient of each line will give
k1for each length.
3. For each beam, choose a load (e.g. 10 N) and plot a chart of deflection (vertical
axis) against l3 .
4. The linearity of your chart of yagainst l3 should prove that equation 3 is correct.
The gradient of the line will givek2 .
5. You can now use the information from the yagainst l3 chart to find the Young’s
Modulus (E ) for the beam.
6. Find the second moment of area ( I ) for your beam and use the equation 1 to
calculate E .
E = Inverse of Gradient x W (where W is the load used for the chart -e.g.
10 N)
3x I
NB: The gradient is k2 i.e. for y varies proportional to l3 or equation 3
Table 1: Beam 1 results
material Mild steel
E value: 102.218 GPa Width:19mm
I value: 434.8229mm^4 Depth:6.5mm
l (mm) 200 300 400
W (N) y (mm)
2 -0.12 -0.32 -0.66
4 -0.25 -0.63 -1.53
6 -0.37 -1.11 -2.44
8 -0.7 -1.54 -3.05
10 -0.81 -1.83 -3.69
Developed by: Mr. V. Moni
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For length of 200mm
Load (N) Actual deflection Theoretical Percentage error
(mm) Deflection(mm) (%)
0 0 0 0
2 -0.12 0.12 0%
4 -0.25 0.24 4%
6 -0.37 0.36 2.7%
8 -0.7 0.48 31.42%
10 -0.81 0.6 25.92%
For length of 300mm
Load (N) Actual deflection Theoretical Percentage error
(mm) deflection (mm) (%)
0 0 0 0
2 -0.32 0.41 -28.125%
4 -0.63 0.81 -28.5715%
6 -1.11 1.23 -10.81%
8 -1.54 1.62 -5.19%
10 -1.83 2.03 -10.93%
For length of 400mm
Load (N) Actual deflection Theoretical Percentage error
(mm) deflection (mm) (%)
0 0 0 0
2 -0.66 0.96 -45.45%
4 -1.53 1.92 -25.49%
6 -2.44 2.88 -18.03%
8 -3.05 3.84 -25.90%
10 -3.69 4.8 -30.085
Developed by: Mr. V. Moni
Moderated by: T. Chipanga
Table 2: Beam 2 results
material Brass
E value: 55.76GPa Width:19mm
I value: 434.8229 mm 4 Depth:6.5mm
l (mm) 200 300 400
W(N) y (mm)
2 -0.22 -0.56 -1.39
4 -0.41 -1.24 -2.89
6 -0.68 -1.85 -4.01
8 -0.95 -2.44 -5.11
10 -1.11 -2.95 -6.36
For 200mm length
Load (N) Actual deflection Theoretical Percentage error
(mm) deflection (mm)
0 0 0 0
2 -0.22 0.22 0%
4 -0.41 0.44 -7.32%
6 -0.68 0.66 2.94%
8 -0.95 0.88 7.368%
10 -1.11 1.09 1.80%
For 300mmlength
Load(N) Actual deflection Theoretical Percentage error
(mm) deflection (mm) (%)
0 0 0 0
2 -0.56 0.74 -32.143%
4 -1.24 1.48 -19.35%
6 -1.85 2.22 -20%
8 -2.44 2.97 -21.72%
10 -2.95 3.71 -25.76%
For 400mmlength
Developed by: Mr. V. Moni
Moderated by: T. Chipanga
Load(N) Actual deflection Theoretical Percentage error
(mm) deflection (mm) (%0
0 0 0 0
2 -1.39 1.76 -26.62%
4 -2.89 3.52 -21.79%
6 -4.01 5.28 -31.67%
8 -5.11 7.04 -37.77%
10 -6.36 8.79 -38.21%
Table 3: Beam 3 results
material Mild steel
E value: 168 GPa Width:4.5mm
I value: 144.281mm^4 Depth:19mm
l (mm) 200 300 400
W (N) y (mm)
2 -0.22 -0.47 -2.02
4 -0.49 -1.08 -3.38
6 -0.71 -1.78 -4.81
8 -0.91 -2.33 -7.12
10 -1.10 -2.98 -8.97
For 200mm length
Load (N) Actual deflection Theoretical Percentage error
(mm) deflection (mm)
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Moderated by: T. Chipanga
0 0 0 0
2 -0.22 0.22 0%
4 -0.49 0.44 10.2%
6 -0.71 0.66 7.04%
8 -0.91 0.88 3.29%
10 -1.10 1.10 0%
For 300mmlength
Load(N) Actual deflection Theoretical Percentage error
(mm) deflection (mm) (%0
0 0 0 0
2 -0.47 0.74 -57.45%
4 -1.08 1.48 -37.04%
6 -1.78 2.23 -25.28%
8 -2.33 2.97 -33.18%
10 -2.98 3.71 -24.49%
For 400mmlength
Load(N) Actual deflection Theoretical Percentage error
(mm) deflection (mm) (%0
0 0 0 0
2 -2.02 1.76 12.87%
4 -3.38 3.52 4.14%
6 -4.81 5.28 -9.77%
8 -7.12 7.04 1.12%
10 -8.97 8.8 1.89%
6. DISCUSSION OF RESULTS
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Developed by: Mr. V. Moni
Moderated by: T. Chipanga
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7. CONCLUSION
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Notes:
1. This document is a laboratory guide and should assist you to execute the
experiment successfully.
2. If results analysed do not make sense the experiment must be repeated.
3. The structure of writing experiments should be adhered to otherwise what is
provided here is just a guide. The graphs drawn must be accompanied by
explanations and all critical calculations performed with clear headlines must be
in the main document.
4. The conclusion should be clearly linked to the experimental findings.
Developed by: Mr. V. Moni
Moderated by: T. Chipanga
