EN 122 Engineering Mechanics
Experiment One (1): Analysis of Deflection of a cantilever
Laboratory Report on Deflection of a Cantilever
Name
ID Number
: Boas Kama
: 22302769
Course Code
: BEEL - 01
Subject Code
: EN 122 – Mechanics
Lab Number
: Laboratory Report #02
Lecture
: Dr. Steven K. Ales
Date of Experiment: 21/08/23
Laboratory Report (02) | Engineering Mechanics |
Submission Date: 15/08/2023
|University of Technology| 2023
Laboratory Report
Experiment 1: ANALYSIS OF DEFLECTION OF CANTILEVERS
Abstract
Deflection in a cantilever is the deviation of the free end of the beam from its
original position. The deflection can be measured by comparing the free end
with the tangent line thought the fixed end of the beam. The deflection depends
on the load, the length, the cross-section, and the materials of the beam. The
maximum deflection occurs when the load is located at the free end of the
beam.
Introduction
In this modern civilized world, the engineers are the back bone of the
development with the aid of technologies. Engineering’s varies under different
categories brings to life the processed materials by way of designing and
building designed plans by in collaborating them together to achieved an
optimal output as lively essence of infrastructure demanded by societies. On
that juncture, the infrastructures development project is economical so
structural engineers need to know the pros and cons of it. The Deflection of
cantilevers is a vital standard procedure where it helps engineers who deals
and engineered structures must follow and equipped with. As structures are
design and build to withstand loads and pressures exerted on it, it needs
proper approached with skilled personal to deals with. Therefore, the lab set up
of Deflection of beams and cantilever equipment is a standard for engineers to
run lab tests. It is a rigid structural element that is supported at one end and
free at another end. A cantilever beam bend downwards when it is subject to
vertical loads. It can be subjected to point load, uniform load, or varying load.
Irrespective of types of load it bends downwards. This bending creates tension
in the upper fiber and compression in the lower fibers. In this experimental set
up, the three different types of beam used are Brass, Steel and Aluminum.
When load exerted to the free end of the cantilever frame set up, the beam
undergoes deformation due to the bending movements along its length This
deflection is a critical consideration in structural engineering.
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Objectives
Certainly, here are the main objectives of the Deflection of Cantilever.
The primary objective of deflection of cantilevers is to calculate the internal
forces (tension and compression) that develop in the beam when loaded by
careful analysis of beams used in structures. This helps engineers understand
how the beams bear the load and assists in selecting appropriate materials
with its required loads.
Overall, the objectives of deflection of cantilevers typically revolve around
understanding how forces or applied pressures are transmitted through beams,
ensuring structural integrity using this foundational knowledge to create safe
and efficient engineering designs by understanding beams behaviors and to
verifies the theoretical prediction of loading effects for proper documentation
and reporting for engineering design consideration as in terms of structural
analysis. To give students hands on experience with the exposer of laboratory
set up.
Equipment’s or Materials
✓ STR4 Beam Deflection Test Rig Equipment
✓ Specimen (Brass, Steel, Aluminum)
➢ Specimen Data
• Length – 200 mm
• Weigh – 19 mm
• Depth - 3 mm
✓ Weights (10 g)
✓ Digital deflection registering Meter
✓ Hook Wire/ Hanger4 (10 g)
✓ Note books
✓ Pencil / Pens
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Experimental Procedures/ Method
1. Check and inspect the Beam Deflection Test Rig with all the loads (mass)
with the hanger are in place and also beam specimen (Brass, Steel,
Aluminum) are made available in the lab.
2. Insert Brass beam bar into the clipper and adjust it till it reaches 200 mm in
length.
3. Attached the digital deflection registering meter and loses its node or
pointer onto the beam bar and see it must be zero, if not adjust using the
origin button till its reading reaches zero.
4. Apply a load of 100 g on the hanger and hang it on the specimen beam
bar and record the reading. Put the result in table form and register the
reading accordingly to the specimen.
5. Use 200g, 300g, 400g and 500g of load which is required then record the
reading accordingly.
6. Repeat the same procedures with the other two beam bars (Steel and
Aluminum).
Pictured below is Beam Deflection Cantilever Test Equipment in the lab.
Mechanical Engineering Lab – Unitech PNG
Figure A. Beam Deflection Cantilever Test Fig.
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Figure B. The Schematic diagram of the Beam
Deflection Test Fig.
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Figure C. Loads used in the experiment.
Weights in hanger.
Figure B. Shows the hanger, beam bars & loads
all assemble.
Figure D. The three-specimen used in the experiment. Brass, Steel and Aluminum and a steel ruler for
taking measurement.
Laboratory Report (02) | Engineering Mechanics |
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Results
Table 1. Results are tabled here.
No #
1
2
3
4
5
Specimen
Brass
Steel
Aluminium
Mass (Kg) Def (mm) Mass (Kg) Def (mm) Mass (Kg) Def (mm)
100
0.6
100
0.29
100
1.61
200
1.15
200
0.55
200
2.49
300
1.68
300
0.51
300
3.29
400
2.21
400
1.07
400
4.02
500
2.78
500
1.33
500
4.78
The results of the three specimens are recorded and tabulated accordingly.
Graph 1. The Graphical representation of the data tabulated above.
GRAPH OF DEFLECTION OF CANTILEVERS
6
DEF (MM)
5
4
3
2
1
0
0
100
200
300
400
500
600
MASS (KG)
Brass Def (mm)
Steel Def (mm)
Aluminium Def (mm)
Table 1.1. The conversion from Mass to Newton.
Mass (grams)
100
200
300
400
500
Load (Newton)
0.98
1.96
2.94
3.92
4.91
Table 2. Here attached therein is the conversion from mass
to newton.
Formula used to convert Mass (kg) to Load (Newton).
[Given Mass ÷ 1000] x [9.81] acceleration due to gravity
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Calculations.
Formula used to Calculate Second Moment of Area
I = b3xh/12
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Table 1.2 below is for Brass Specimen Deflections
Materials / Specimens
E = 100 Nm-2
I = 42.75x10-12 m
Brass Specimen
B = 3 mm
H = 19 mm
Mass
(g)
0
100
200
300
400
500
Theoretical Deflection
(mm)
0 mm
0. 61 mm
1.2 mm
1.8 mm
2.5 mm
3.1 mm
Actual Deflection
(mm)
0 mm
0.6 mm
1.12 mm
1.68 mm
2.21 mm
2.78 mm
Graph A. The graph below shows the Actual and Theoretical Deflection of the
Brass.
Brass Deflection Gaph
3.5
Deflection
3
2.5
2
1.5
1
0.5
0
0
100
200
300
400
500
Actual Deflection (mm)
0
0.6
1.12
1.68
2.21
2.78
Theoretical Deflection (mm)
0
0.61
1.2
1.8
2.5
3.1
Mass (g)
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Table 1.3. Table below shows Steel Specimen Deflections
Materials / Specimens
E = 210 Nm-2
I = 42.75x10-12 m
Mass
(g)
0
100
200
300
400
500
Actual Def
(mm)
0
0.29
0.58
0.9
1.1
1.5
Steel Specimen
B = 3 mm
H = 19 mm
Theoretical Def
(mm)
0
0.29
0.55
0.51
1.07
1.33
Graph B. The graph below shows the Actual and Theoretical Deflection of the
Steel specimen.
Steel Deflection Graph
1.6
1.4
Deflection (mm)
1.2
1
0.8
0.6
0.4
0.2
0
0
100
200
300
400
500
Mass (g)
Actual Def (mm)
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Theoretical Def (mm)
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Table 1.4. Table below shows Aluminum Specimen Deflections
Materials / Specimens
E = 70 Nm-2
I = 42.75x10-12 m
Aluminum Specimen
B = 3 mm
H = 19 mm
Mass (g) Actual Def (mm) Theoretical Def (mm)
0
0
0
100
1.61
0.87
200
2.49
1.75
300
3.29
2.62
400
4.02
3.5
500
4.78
4.38
Graph C. The graph below shows the Actual and Theoretical Deflection of the
Aluminum specimen.
Aluminium Deflection Graph
6
Deflection (mm)
5
4
3
2
1
0
0
100
200
300
400
500
Mass (g)
Actual Def (mm)
Theoretical Def (mm)
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Discussion
To analyze the deflection of cantilever beams made of Brass, Steel, and
Aluminum, we will consider a simple case where a uniform load is applied to
the free end of each beam. The deflection of each beam can be calculated using
the formula given above in the calculation section.
Brass Cantilever: Given Brass's moderate modulus of elasticity and yield
strength, it may exhibit moderate deflection under a given load. However, its
ductility allows it to deform without undergoing catastrophic failure, making it
suitable for applications where some deformation is acceptable.
Steel Cantilever: Steel's high modulus of elasticity and yield strength suggest
that it will have minimal deflection compared to Brass and Aluminum under
the same load. Steel's stiffness and strength make it ideal for applications
requiring minimal deflection and high load-bearing capacity.
Aluminum Cantilever: Aluminum's low modulus of elasticity implies that it
will undergo more significant deflection than Brass and Steel under the same
load. However, its lightweight nature can make it preferable for applications
where weight is a critical factor, even if some deflection is acceptable.
Therefore, this experiment helps engineers to understand the concept with
specific parameters according to design and specification before the approvals
of the implementation of the projects.
The Mythology and procedures of the experiments implicates the loads
suspended onto the structure under different loads and condition to which the
structure must go true for it to be durable and to give confidents to implement
the design structures.
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Conclusion
Cantilever beams are common structural elements used in various engineering
applications, such as bridges, buildings, and machine components.
Understanding the deflection behavior of different materials is crucial for
designing and optimizing such structures.
The deflection behavior of cantilever beams made of Brass, Steel, and
Aluminum depends on the material properties and the applied load. Steel, with
its high modulus of elasticity and yield strength, is the stiffest and exhibits the
least deflection. Brass, while less stiff than steel, offers good ductility.
Aluminum, with its low modulus of elasticity, will exhibit the most significant
deflection but is lightweight. Engineers must consider these material
characteristics when selecting materials for cantilever beam applications to
ensure that the chosen material can meet the structural and performance
requirements of the specific project
Referencing
1. Google Search engine. http://www.Google.com
2. Dr. Steven K. Ales, PhD Mechanical Engineering Department.
“Deflection of Cantilever’’ [Lab Instruction Guide & Notes]. (2023) PNG
Unitech
3. http;//www.engineersdaily.com>3...
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Appendix
The units used and the physical quantities of measurements used to measure
parameters in this lab report is all tabulated below. The International System of
Units (SI).
Name
Meters
Kilogram
Newton
Pascal
Square Meter
Quantity
Length
Mass
Force
Pressure
Area
Symbols
m
kg
N
Pa
m2
The gravitational force acted on a body under normal condition is called
gravity. The acceleration due to gravity (g) is; g = 9.81 m/s2
Laboratory Report (02) | Engineering Mechanics |
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