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UNIVERSITI TUN HUSSEIN ONN MALAYSIA
Faculty of Mechanical and Manufacturing Engineering __________________________________________________________________
COURSE INFORMATION
COURSE TITLE: ENGINEERING LABORATORY III (BDA 27101)
TOPIC 1: TENSILE TEST
1. INTRODUCTION
The tensile experiment is the most common mechanical test that reveals several
important mechanical properties, such as: modulus of elasticity, yield strength,
ultimate tensile strength, ductility, and toughness. The material to be tested is
formed into a shape suitable for gripping in the testing machine, and then pulled at
constant rate until it fractures. The tensile instrument elongates the specimen at a
constant rate and has devices to continuously measure and record the applied load
and elongation of the specimen. During the stretching of the specimen, changes
occur in its physical dimensions and its mechanical properties. The ability to
predict the loads that will cause a part to fail depends upon both material
properties and the part geometry. This experiment involves testing to determine
the relative properties.
2. OBJECTIVES
1. To understand the principles of tensile testing machine.
2. To observe the stress-strain relationship for several standard materials by
performing a tensile test.
3. To obtain approximate values from stress-stain curve such as percentage of
elongation, Yield Strength; Tensile Strength and Modulus of Elasticity, E.
3. LEARNING OUTCOMES
At the end of this experiment, students should be able to:
1. Conduct experiment and identify the dependent and independent variables.
2. Record, tabulate and analyze the raw data.
3. Indicate the important parameters such as yield strength, elastic, plastic
region, maximum load, failure load and explain each parameter.
4. Determine the modulus of elasticity for each specimen.
5. Understand the stress-strain relationship for several standard materials by
performing a tensile test and tensile properties from a stress strain curve.
UNIVERSITI TUN HUSSEIN ONN MALAYSIA
Faculty of Mechanical and Manufacturing Engineering __________________________________________________________________
BDA27101-Edition III/2011
2
4. THEORY
A tensile test, also known as tension test, is probably the most fundamental type of
mechanical test that can be performed on material. Tensile tests are simple,
relatively inexpensive, and fully standardized. By pulling on something, you will
very quickly determine how the material will react to forces being applied in
tension. As the material is being pulled, you will find its strength along with how
much it will elongate.
You can learn a lot about a material from tensile testing. As you continue to pull
on the material until it breaks, a good, complete tensile profile will be obtained. A
curve showing how it reacted to the forces being applied is produced. The point of
failure is typically called its "Ultimate Strength" or UTS on the chart.
For most tensile testing of materials, you will notice that in the initial portion of
the test, the relationship between the applied force, and load, and the elongation
the specimen exhibits is linear. In this linear region, the line obeys the relationship
defined as "Hooke's Law" where the ratio of stress to strain is a constant, or E =
δ/ε. E is the slope of the line in this region where stress (σ) is proportional to
strain (ε) and is called the "Modulus of Elasticity" or "Young's Modulus".
UNIVERSITI TUN HUSSEIN ONN MALAYSIA
Faculty of Mechanical and Manufacturing Engineering __________________________________________________________________
BDA27101-Edition III/2011
3
5. ADDITIONAL THEORY
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UNIVERSITI TUN HUSSEIN ONN MALAYSIA
Faculty of Mechanical and Manufacturing Engineering __________________________________________________________________
BDA27101-Edition III/2011
4
6. APPARATUS
Figure 1: Universal Testing Machine GT-7001-LS10, Tensile Specimen &
Vernier Caliper
7. PROCEDURES
In order to obtain uniform and accurate results, it is important that all tests have to
be conducted under standard conditions. The American Standard for Testing and
Materials (ASTM) has set up standards, which should be followed. The standard
method of mechanical testing is specified by ASTM E-8M for metals. Identify the
material of each specimen used.
1. Record and measure the specimen parameter such as: diameter; and the
gauge length. Fill up Table 1 as d1 and l1.
UNIVERSITI TUN HUSSEIN ONN MALAYSIA
Faculty of Mechanical and Manufacturing Engineering __________________________________________________________________
BDA27101-Edition III/2011
5
2. Mount the specimen in the testing machine, figure 1 and test the specimen
to fracture (the lab technician and/or your lab instructor will help with the
right procedure).
3. Test data will be saved in readable file format and given to your instructor.
Arrange with your instructor to get these test data files.
4. When the specimen is removed from the instrument determine all
parameters that you have measured earlier and Fill up Table 2 as d2 and
l2.
5. Once you have completed the test on all specimens, calculate the
percentage of elongation and area of reduction
6. Draw the stress versus strain curve for each specimen and determine the
ultimate tensile strength, yield strength and the Young’s Modulus for each
specimen.
In all cases, be sure to write your observations for each test. You need to include
these observations in your report. The general stress strain curve for a typical
metal is shown in Figure 2 with all the important properties that can be directly
measured.
Figure 2: A schematic stress strain curve for a metallic alloy
8. RESULTS
Measure and fill up Table 1 and Table 2
Table 1: Parameter of specimen before testing
Shaft
Diameter, d1
(mm) Average
Gauge length, l1
(mm) Average
1 2 3 1 2 3
Aluminium
Mild Steel
UNIVERSITI TUN HUSSEIN ONN MALAYSIA
Faculty of Mechanical and Manufacturing Engineering __________________________________________________________________
BDA27101-Edition III/2011
6
Table 2: Parameter of specimen after testing
Shaft
Diameter, d1
(mm) Average
Gauge length, l1
(mm) Average
1 2 3 1 2 3
Aluminium
Mild Steel
9. OBSERVATIONS
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10. CALCULATIONS
Calculate Young’s modulus, percentage reduction of area (RA) and
elongation (EL).
UNIVERSITI TUN HUSSEIN ONN MALAYSIA
Faculty of Mechanical and Manufacturing Engineering __________________________________________________________________
BDA27101-Edition III/2011
7
11. DISCUSSIONS
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1. Explain the advantages of mild steel in comparison with aluminum in
terms of Young’s modulus, yield strength and ultimate tensile strength?
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UNIVERSITI TUN HUSSEIN ONN MALAYSIA
Faculty of Mechanical and Manufacturing Engineering __________________________________________________________________
BDA27101-Edition III/2011
8
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2. List of all possible source of errors include errors in load cell, cross-
sectional dimensions and gauge measurements. How does this error affect
the obtained results?
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UNIVERSITI TUN HUSSEIN ONN MALAYSIA
Faculty of Mechanical and Manufacturing Engineering __________________________________________________________________
BDA27101-Edition III/2011
9
12. CONCLUSION
Write your observations and comments whenever possible in your discussion in
term of achievement, problems facing throughout the experiment and
recommendation for improvement.
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UNIVERSITI TUN HUSSEIN ONN MALAYSIA
Faculty of Mechanical and Manufacturing Engineering __________________________________________________________________
BDA27101-Edition III/2011
10
13. REFERENCES
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UNIVERSITI TUN HUSSEIN ONN MALAYSIA
Faculty of Mechanical and Manufacturing Engineering __________________________________________________________________
BDA27101-Edition III/2011
11
COURSE INFORMATION
COURSE TITLE: ENGINEERING LABORATORY III (BDA 27101)
TOPIC 2: TORSION TEST
1. INTRODUCTION
Torsion tests allow direct measurement of the shear modulus (G) of a material.
This ability makes torsion testing, although not as common, a useful partner for
tensile testing in determining the mechanical properties of a material.
There are two kinds of torsion experiments: torque control and angular speed
control. Torque control experiments apply a uniformly increasing torque to the
specimen and the amount of strain is measured as an angle through which the
specimen has turned. Angular speed control turns the specimen at a specific
angular speed while the torque is measured.
Angular speed control is the type of experiment we will be doing, thus the directly
measured quantity in this experiment will be torque.
Young's modulus (E) is related to the shear modulus and finding E with the
experimentally obtained G reinforces this relationship; they are dependent upon
one another according to the equation:
Where, v is Poisson's ratio.
2. OBJECTIVES
The main objective of this experiment is to determine the elastic and yield
behavior of material when subjected by torque load.
3. LEARNING OUTCOMES
At the end of this experiment, students should be able to:
1. Conduct experiment, record, tabulate and analyze the raw data.
2. Plot the graph of Twisting angle versus Load torque (N.m).
3. Determine the modulus of rigidity for each specimen
4. Compare the value of modulus of rigidity form experiment with the theory
5. Produce good conclusion from the experiment conducted.
UNIVERSITI TUN HUSSEIN ONN MALAYSIA
Faculty of Mechanical and Manufacturing Engineering __________________________________________________________________
BDA27101-Edition III/2011
12
4. THEORY
When a circular shaft is twisted at either end, with no other forces acting upon it,
the bar is said to be in pure torsion. If we let the left-hand end of the shaft remain
fixed, then the right-hand end the bar will rotate through an angle ( ) with respect
to the left end .See Figure 1
Figure 1
Simultaneously, a longitudinal line on the surface of the bar, such as line nn, will
rotate through a small angle with respect to the position nn'. Because of this
rotation, a rectangular element on the surface of the bar, such as the element
shown in the figure between two cross sections distance dx apart, is distorted. This
element is shown again in Figure 2, isolated from the remainder of the bar.
Figure 2
During torsion, the right-hand cross section of the original configuration of the
element (abdc) rotates with respect to the opposite face and points b and d move
to b' and d', respectively. The lengths of the sides of the element do not change
during this rotation, but the angles at the corners are no longer 90°. Thus, the
element is undergoing pure shear and the magnitude of the shear strain is equal
to the decrease in the angle bac.
UNIVERSITI TUN HUSSEIN ONN MALAYSIA
Faculty of Mechanical and Manufacturing Engineering __________________________________________________________________
BDA27101-Edition III/2011
13
This angle is
Note: tan is approximately equal to because under pure torsion the angle (
) is small.
The distance bb' is the length of a small arc of radius r subtended by the angle ,
which is the angle of rotation of one cross section with respect to the other. Thus,
bb' = r . Also, the distance ab is equal to the length of the element, dx.
Substituting these expressions into the preceding equation, we have
Under pure torsion, the rate of change /dx of the angle of twist are constant
along the length of the bar. This constant is equal to the angle of twist per unit
length. Thus, = / L, where L is the length of the shaft. Then, we have
Now, observe that for linear elastic material, the magnitude of the shear stress,
(shown in Figure 1) is.
From here we can establish the relationship between the applied torque T and the
angle of twist which it produces. The resultant of the shear stresses shown in
Figure 3, below, must be statically equivalent to the total torque T. The shear
force acting on an element of area dA (shown shaded in the figure) is dA, and the
moment of this force is also equal to dAG 2 . The total torque T is the summation
over the entire cross-sectional area of these elemental moments;
Thus, where J is equal to the polar moment of inertia of the circular cross section
GrG
UNIVERSITI TUN HUSSEIN ONN MALAYSIA
Faculty of Mechanical and Manufacturing Engineering __________________________________________________________________
BDA27101-Edition III/2011
14
Thus, we have
(Note that GJ is called the torsional rigidity of the shaft.) Finally, since the total
angle of twist is equal to L, we have that
This is the result we want. The experiment you are about to perform will yield
data on the torque T and the angle from which we can calculate G, the shear
modulus, given the dimensions of the shaft. Important to note that for a solid
circular shaft of uniform radius:
5. ADDITIONAL THEORY
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Figure 3
UNIVERSITI TUN HUSSEIN ONN MALAYSIA
Faculty of Mechanical and Manufacturing Engineering __________________________________________________________________
BDA27101-Edition III/2011
15
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6. APPARATUS
Figure: Torsion Testing Machine, Torsion Specimen & Vernier Caliper.
UNIVERSITI TUN HUSSEIN ONN MALAYSIA
Faculty of Mechanical and Manufacturing Engineering __________________________________________________________________
BDA27101-Edition III/2011
16
7. PROCEDURES
1. Record and measure the Specimen length and diameter at three different
locations and calculate the average length and diameter. Also measure
pully length. Fill up Table 1.
2. Mount the Specimen in the testing machine and test the Specimen (the lab
technician and/or your lab instructor will help with the right
procedure).Make sure pulley is in Horizontal position.
3. Attach the angle indicator and zero the readings.
4. Measure the angle of twist when load (W) is added from 0 to 200N and
when load is removed from 200N to 0N for both specimens. Fill up Table
2 and Table 3.
8. RESULTS
Table 1: Diameter of specimen
Shaft Diameter, D (mm)
Average Length, L (mm)
Average 1 2 3 1 2 3
Brass
Mild Steel
Pulley Length
Table 2: Torsion test result for Brass Shaft
Load, W (N) 0 50 100 150 200
Angle of
twist during
additional of
load
Angle of
twist during
removal of
load
UNIVERSITI TUN HUSSEIN ONN MALAYSIA
Faculty of Mechanical and Manufacturing Engineering __________________________________________________________________
BDA27101-Edition III/2011
17
Table 3: Torsion test result for Mild Steel Shaft
Load, W (N) 0 50 100 150 200
Angle of
twist during
additional of
load
Angle of
twist during
removal of
load
9. OBSERVATIONS
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10. CALCULATIONS
Calculate torsion constant and shear modulus for the brass and mild steel
specimens. Determine the shear stress and strain for both specimens.
UNIVERSITI TUN HUSSEIN ONN MALAYSIA
Faculty of Mechanical and Manufacturing Engineering __________________________________________________________________
BDA27101-Edition III/2011
18
11. DISCUSSIONS
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1. If the cross section of shaft is not cylinder, explain how to perform the
torsion analysis.
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UNIVERSITI TUN HUSSEIN ONN MALAYSIA
Faculty of Mechanical and Manufacturing Engineering __________________________________________________________________
BDA27101-Edition III/2011
19
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2. Briefly explain some of the important factors in designing a high-quality
shaft.
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UNIVERSITI TUN HUSSEIN ONN MALAYSIA
Faculty of Mechanical and Manufacturing Engineering __________________________________________________________________
BDA27101-Edition III/2011
20
12. CONCLUSIONS
Write your observations and comments whenever possible in your discussion in
term of achievement, problems facing throughout the experiment and
recommendation for improvement.
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UNIVERSITI TUN HUSSEIN ONN MALAYSIA
Faculty of Mechanical and Manufacturing Engineering __________________________________________________________________
BDA27101-Edition III/2011
21
13. REFERENCES
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UNIVERSITI TUN HUSSEIN ONN MALAYSIA
Faculty of Mechanical and Manufacturing Engineering __________________________________________________________________
BDA27101-Edition III/2011
22
COURSE INFORMATION
COURSE TITLE: ENGINEERING LABORATORY III (BDA 27101)
TOPIC 3: SHEAR FORCE OF A BEAM
1. INTRODUCTION
This guides describes how to set up and perform Shear Force in a Beam
experiments. It clearly demonstrates the principles involved and gives practical
support to your studies.
Figure 1 shows the Shear Force in a Beam experiment. It consists of a beam
which is ‘cut’. To stop the beam collapsing a mechanism, (which allows
movement in the shear direction only) bridges the cut on to a load cell thus
reacting (and measuring) the shear force. A digital display shows the force from
the load cell.
A diagram on the left-hand support of the beam shows the beam geometry and
hanger positions. Hanger supports are 20mm apart, and have a central groove
which positions the hangers.
Figure 1: Shear Force In A Beam Experiments.
UNIVERSITI TUN HUSSEIN ONN MALAYSIA
Faculty of Mechanical and Manufacturing Engineering __________________________________________________________________
BDA27101-Edition III/2011
23
2. OBJECTIVES
The objectives of this experiment are as follows:
3. LEARNING OUTCOMES
At the end of this experiment, students should be able to:
1. Conduct experiment and identify the dependent and independent variables.
2. Record, tabulate and analyze the raw data.
3. To draw shear diagram.
4. Compare the theoretical and experimental result
5. Produce good conclusion from the experiment conducted.
4. THEORY
Beams are defined as structural members supporting loads at various points along
the member. Transverse loadings of beams are classified as concentrated loads or
distributed loads. One of the main concerns that should be put into consideration
when designing beams for strength is how the material and the cross section of a
beam of a given selected span should be selected if the beam is not to fail under a
given loading.
Applied loads result in internal forces consisting of a shear force (from the shear
stress distribution) and a bending moment (from the normal stress distribution).
For prismatic beam, that is straight beam with a uniform cross section; their
design depends primarily upon the determination of the largest value of the
bending moment and shear force created in the beam by a given loading. The
determination of these values and of the critical sections of the beam in which
they occur is greatly facilitated by drawing a shear force diagram and bending
moment diagram. The variation of the shear force V (N) and the bending moment
M (Nm) along the beam may be investigated from these diagrams. The values of
V and M at various points may be obtained either by drawing free body diagram
of successive portions of the beam or from relationship that involves the applied
load, shear force and bending moment.
Determination of the maximum normal stress (σmax) and maximum shearing
stress (τ max) requires identification of maximum internal shear force and bending
moment. Shear force and bending moment at a point are determined by passing a
section through the beam and applying an equilibrium analysis on the beam
portions on either side of the section as shown in Figure 2 and 3. Sign
conventions for shear forces V and V’ and bending couples M and M’
1. To comprehend the action of shear in a beam.
2. To measure the shearing force at a normal section of a loaded beam and to
check its agreement with theory.
UNIVERSITI TUN HUSSEIN ONN MALAYSIA
Faculty of Mechanical and Manufacturing Engineering __________________________________________________________________
BDA27101-Edition III/2011
24
Figure 2: Beam section at point C (at distance x from left end A)
Figure 3: Internal forces (positive shear and positive bending moment)
5. ADDITIONAL THEORY
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UNIVERSITI TUN HUSSEIN ONN MALAYSIA
Faculty of Mechanical and Manufacturing Engineering __________________________________________________________________
BDA27101-Edition III/2011
25
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6. APPARATUS
Figure 4: Shearing force of a beam experiment in the structures frame.
UNIVERSITI TUN HUSSEIN ONN MALAYSIA
Faculty of Mechanical and Manufacturing Engineering __________________________________________________________________
BDA27101-Edition III/2011
26
Before setting up and using the equipment, always:
Visually inspect all parts, including electrical leads, for damage or wear.
Check electrical connections are correct and secure.
Check all components are secured correctly and fastenings are sufficiently
tight.
Position the Test Frame safely. Make sure it is mounted on a solid, level
surface, is steady, and easily accessible.
Note: Never apply excessive loads to any part of the equipments. If the meter
is only 0.1 N, lightly tap the frame (there may be a little ‘stiction’ and this
should overcome it).
7. PROCEDURES
6.1 Experiments 1: Shear Force Variation with an Increasing Point Load
Figure 5: Force Diagram.
The equation we will use in this experiment is:
Shear force at cut, =
Where a is the distance to the load (not the cut)
Distance a = 260mm
You may find the following table useful in converting the masses used in the
experiment to loads.
Table 1: Grams to Newton’s Conversion Table
Mass (Grams) Load (Newton)
100 0.98
200 1.96
300 2.94
400 3.92
500 4.90
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BDA27101-Edition III/2011
27
Step 1 to 4 of the following instructions may already have been completed for
you.
1. Place an assembled Test Frame (refer to the separate instructions supplied
with the Test Frame if necessary) on a workbench. Make sure the
‘window’ of the Test Frame is easily accessible.
2. There are four securing nuts in the top member of the frame. Slide them to
approximately the positions shown in figure 5.
3. With the right-hand end of the experiment resting on the bottom member
of the Test Frame, fit the left- hand support to the top member of the
frame. Push the support on to the frame to ensure that the internal bars are
sitting on the frame squarely. Tighten the support in position by screwing
two of the thumbscrews provided into the securing nuts (on the front of the
support only).
4. Lift the right-hand support into a position and locate the two remaining
thumbscrews into the securing nuts. Push the support on to the frame to
ensure the internal bars are sitting on the frame squarely. Position the
support horizontally so the rolling pivot is in the middle of its travel.
Tighten the thumbscrews.
5. Make sure the Digital Force Display is ‘on’. Connect the mini DIN lead
from ‘Force Input 1’ on the Digital Force display to the socket marked
‘Force Output’ on the left- hand support of the experiment. Ensure the lead
does not touch the beam.
6. Carefully zero the force meter using the dial on the left-hand beam of the
experiments. Gently apply a small load with a finger to the centre of the
beam and release. Zero the meter again if necessary. Repeat to ensure the
meter returns to zero.
7. This experiment examines how shear force varies with an increasing point
load. Figure 5 shows the force diagram for the beam.
8. Check the Digital Force Display meter reads zero with no load. Place a
hanger with a 100 g mass to the left of the ‘cut’ (40mm away).Record the
Digital Force Display reading in table as in Table 2. Repeat using masses
of 200g, 300g and 500g. Convert the mass into a load (in N).
9. Remember, Shear force at the cut = Displayed force.
10. Calculate the theoretical shear force at the cut and complete the Table 2.
6.2 Experiment 2: Shear Force Variation for Various Loading Conditions
This experiment examines how shear forces varies at the cut position of the beam
for various loading conditions. Figure 6, Figure 7 and Figure 8 show the force
diagrams.
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BDA27101-Edition III/2011
28
Figure 6: Force Diagram.
Figure 7: Force Diagram.
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29
Figure 8: Force Diagram.
We will use the statement: “The Shear Force at the ‘cut’ is equal to the
algebraic sum of the forces acting to the left or right of the cut”
1. Check the Digital Force Display meter reads zero with no load.
2. Carefully load the beam with the hangers in the positions shown in Figure 6,
using the loads indicated in Table 1.
3. Record the Digital Force Display reading as in Table 3. Remember, Shear
force at the cut (N) = Displayed Force.
4. Calculate the support reactions (RA and RB) and calculate the theoretical shear
force at the cut.
5. Repeat the procedure with the beam loaded as in Figure 7 and Figure 8.
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8. RESULTS
7.1 Fill up Table 2 for part 1 experiment and Table 3 for Part 2 experiment.
Experiments 1
Table 2: Results for Experiment 1
Mass (g) Load (N) Experimental
Shear Force (N)
Theoretical
Shear Force (N)
0
100
200
300
400
500
Experiment 2
Table 3: Results for Experiment 2.
Figure W1
(N)
W2
(N)
Experimental
Shear Force
(N)
RA
(N)
RB
(N)
Theoretical
Shear Force
(N)
6 3.92 0
7 1.96 3.92
8 4.91 3.92
9. OBSERVATIONS
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UNIVERSITI TUN HUSSEIN ONN MALAYSIA
Faculty of Mechanical and Manufacturing Engineering __________________________________________________________________
BDA27101-Edition III/2011
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10. CALCULATIONS
Plot a graph for shear force vs. load for both experimental and theoretical
results in experiment 1. Calculate support reactions (RA and RB) and
theoretical shear force at the cut.
UNIVERSITI TUN HUSSEIN ONN MALAYSIA
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BDA27101-Edition III/2011
32
11. DISCUSSIONS
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1. Comment on the shape of the graph. What does it tell us about how shear
force varies due to an increased load? Does the equation we used
accurately predict the behavior of the beam?
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UNIVERSITI TUN HUSSEIN ONN MALAYSIA
Faculty of Mechanical and Manufacturing Engineering __________________________________________________________________
BDA27101-Edition III/2011
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2. Comment on how the results of the results of the experiments compare
with those calculated using the theoretical.
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UNIVERSITI TUN HUSSEIN ONN MALAYSIA
Faculty of Mechanical and Manufacturing Engineering __________________________________________________________________
BDA27101-Edition III/2011
34
12. CONCLUSION.
Write your observations and comments whenever possible in your discussion in
term of achievement, problems facing throughout the experiment and
recommendation for improvement.
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UNIVERSITI TUN HUSSEIN ONN MALAYSIA
Faculty of Mechanical and Manufacturing Engineering __________________________________________________________________
BDA27101-Edition III/2011
35
13. REFERENCES
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UNIVERSITI TUN HUSSEIN ONN MALAYSIA
Faculty of Mechanical and Manufacturing Engineering __________________________________________________________________
BDA27101-Edition III/2011
36
COURSE INFORMATION
COURSE TITLE: ENGINEERING LABORATORY III (BDA 2711)
TOPIC 4: BENDING STRESS IN A BEAM
1. INTRODUCTION
The Bending Stress in a Beam experiment introduces students to stress and strain,
bending moment, section properties and the bending equation. It allows students
to investigate the stresses and strains within a structure in relation to bending
loads. The experiments are quick, clear, and accurate and clearly demonstrate the
principles involved and gives practical support to subject studied.
2. OBJECTIVES.
The main objective of this experiment is to study the stress distribution (bending
force and strains) across the section of a beam.
3. LEARNING OUTCOMES
At the end of this experiment, students should be able to understand the
relationship between stresses and strains within a structure in relation to bending
loads and the relationship between bending moment and the strain at the various
positions.
4. THEORY
Figure 1: Beam set-up and schematic
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37
As well as the information given on the unit you will need the following formulae
(The bending equation):
Where,
And
Where,
5. ADDITIONAL THEORY
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UNIVERSITI TUN HUSSEIN ONN MALAYSIA
Faculty of Mechanical and Manufacturing Engineering __________________________________________________________________
BDA27101-Edition III/2011
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6. APPARATUS
Figure 2 shows the Bending Stress in a Beam experiment, while Figure 3 shows
the Bending Stress in a Beam experiment in the structures frame. It consists of an
inverted Aluminum T-beam, with strain gauges fixed on the section. The panel
assembly and Load Cell apply load to the top of the beam at two positions each
side of the strain gauges. Strain gauges are sensors that experience a change in
electrical resistance when stretched or compressed. T-beam has strain gauges
bonded to it. These stretch and compress the same amount as the beam, thus it
measure strain in the beam. The Digital Strain Display converts the change in
electrical resistance of the strain gauges to show it as displacement (strain). It
shows all the strains sensed by the strain gauges, reading in micro strain (με).
UNIVERSITI TUN HUSSEIN ONN MALAYSIA
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39
Figure 2: Bending stress in a beam experiment
Figure 3: Bending stress in a beam experiment in the structures frame
Thumbwheel
Set zero control
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BDA27101-Edition III/2011
40
Figure 4: Bending stress in a beam experiment from the structure software
7. PROCEDURES
1. Ensure the beam and load cell is properly aligned. (Request instructor to
align.)
2. Turn the `Thumbwheel’ (refer to Figure 3) in the structures frame on the
Load Cell to apply a positive (downward) preload to the beam for 100 ±
5N.
3. After preload, turn `set zero control’ knob back to zero load reading.
4. Click `Zero Strain Gauges’ to zero strain signals on the software.
5. Take the readings and fill up Table 1 with force values.
6. Increase the load to 100 N and by clicks the `record data table’ button
and fill up Table 1 with all the strain value. Repeat the procedure 6 in
100N increments up to 500 N. (DO NOT EXCEED LOAD LIMIT)
7 Finally, gradually release the load and preload.
8 Correct the strain reading values by eliminating zero error (be careful with
your signs!) and convert the load to a bending moment then fill up Table
2.
9 From your results, plot a graph of strain against bending moment for all
nine gauges (on the same graph).
10 Calculate the average strains from the pairs of gauges and enter your
results in Table 3 (disregard the zero values). Carefully measure the actual
strain gauge positions and enter the values into Table 3. Plot the strain
against the relative vertical position of the strain gauge pairs on the same
Load reading
Zero strain gauge
Record data table
Strain gauges
values
Bending moment
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graph for each value of bending moment. Take the top of the beam as the
datum.
11 Calculate the second moment of area and position of the neutral axis for
the section (use a Vernier to measure the exact size of the section) and add
the position of the neutral axis to the plot.
*Never apply excessive loads to any part of the equipment.
8. RESULTS
Table 1: Results for Experiment 1 (uncorrected)
Gauge
Number
Load (N)
0 100 200 300 400 500
1
2
3
4
5
6
7
8
9
Table 2: Results for Experiment 1 (corrected)
Gauge
Number
Bending Moment (Nm)
0 17.5 35 52.5 70 87.5
1 0
2 0
3 0
4 0
5 0
6 0
7 0
8 0
9 0
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Table 3: Averaged strain readings for Experiment 1
Gauge
Number
Vertical
Position
(mm)
Bending Moment (Nm)
0 17.5 35 52.5 70 87.5
1 0
2,3 6.4
4,5 23
6,7 31.7
8,9 38.1
9. OBSERVATIONS
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10. CALCULATIONS
Plot a graph for strain vs. bending moment and strain vs. position.
Calculate bending moment. Determine experimental and theoretical
maximum stress.
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BDA27101-Edition III/2011
43
11. DISCUSSIONS
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1. What is the relationship between the bending moment and the strain at the
various positions?
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Faculty of Mechanical and Manufacturing Engineering __________________________________________________________________
BDA27101-Edition III/2011
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2. What do you notice about the strain gauge readings on opposite sides of
the section? Should they be identical? If the readings are not identical, give
two reasons why.
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12. CONCLUSION.
Write your observations and comments whenever possible in your discussion in
term of achievement, problems facing throughout the experiment and
recommendation for improvement.
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UNIVERSITI TUN HUSSEIN ONN MALAYSIA
Faculty of Mechanical and Manufacturing Engineering __________________________________________________________________
BDA27101-Edition III/2011
46
13. REFERENCES
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UNIVERSITI TUN HUSSEIN ONN MALAYSIA
Faculty of Mechanical and Manufacturing Engineering __________________________________________________________________
BDA27101-Edition III/2011
47
COURSE INFORMATION
COURSE TITLE: ENGINEERING LABORATORY III (BDA 27101)
TOPIC 5: THIN CYLINDER
1. INTRODUCTION
The analysis of the stress distribution in a thin walled cylinder is of considerable
importance in pressure vessels and gun barrels. Strain gauges mounted on various
radius and at different alignments throughout the cylinder wall provide the
measurement of the strains. Thus stress distribution throughout the wall of a
cylinder subjected to an internal pressure could be analyzed.
2. OBJECTIVES.
The objectives of this experiment are as follows:
1. To enable comprehensive analysis of stresses and strains in a thin cylinder
under internal pressure.
2. To allow investigations with the cylinder in both open-ends and closed-
ends conditions
3. LEARNING OUTCOMES
At the end of this experiment, students should be able to get an appreciation of:
1. A biaxial stress system
2. The use of strain gauges
3. Young’s Modulus
4. Poisson’s ratio
4. THEORY
Consider a thin cylinder of plate thickness t, mean diameter d and length l,
subjected to internal pressure p. Now consider that the cylinder is sectioned by the
x-plane of symmetry and by the two z-planes (of distance z apart) as shown in
Figure 1.
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Consider the equilibrium of forces in the x-direction acting on the sectioned
cylinder shown in Figure 2. It is assumed that the circumferential stress is
constant through the thickness of the cylinder.
Force due to internal pressure p acting on area dz = pdz
Force due to circumferential/Hoop stress ( H ) acting on area 2tz = H. 2tz
Equating: , Therefore:- or
Figure 1
Figure 2
t
prH
t
pdH
2pdztzH 2
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Now consider the equilibrium of forces in the z-direction acting on the part
cylinder shown in Figure 3.
Force due to internal pressure p acting on area d2/4 = p. d
2/4
Force due to longitudinal stress ( L ) acting on area dt =L. dt
Equating: , Therefore:- or
In the “open” ends condition, there is no obstruction to the end of cylinder.
Therefore,
But . Therefore:-
Hoop Strain,
Longitudinal Strain,
While, in the “closed” ends condition, the force applied onto element are due to
and .
Therefore:-
Hoop Strain,
Longitudinal Strain,
Figure 3
t
prH
t
pdL
4
4
2dpdtL
0L
HHE
1
HLE
1
HL
t
prL
2
HLLE
1
LHHE
1
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5. ADDITIONAL THEORY
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6. APPARATUS
Figure 4: The SM1007 Thin Cylinder apparatus.
In the “open” ends condition the hand wheel is fully screwed in. This pushes the
two pistons away from the cylinder end caps so that there is no contact between
them. Therefore, the axial force is transmitted from the pressurized oil into the
frame rather than the cylinder. See Figure 5.
Figure 5: Open Ends Condition
In the “closed” ends condition the hand wheel is wound out. This allows the
pistons to move outward against the cylinder end caps so that there is no contact
with the frame. Therefore the axial force is transmitted from the pressurized oil
into the cylinder itself. See Figure 6.
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Figure 6: Closed Ends Condition
Technical Information
Length 358.8 mm
Wall Thickness 3 mm
Inner diameter, D1 80 mm
Guage factors 2.105
Cylinder material Aluminium alloy 6063
Young’s Modulus 69 GN/m2
Poisson’s ratio 0.33
Maximum allowable test pressure 3.5 MN/m2
Strain gauges Electrical Resistance Type
Figure 7: Orientation of strain gauges
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53
7. PROCEDURES
7.1 Experiment 1 – Thin Cylinder with Open Ends
In this experiment we will pressurize the cylinder in the open ends condition and
readings from all six strain gauges are taken, we will then analyze the results in
various ways to establish some important relationships. Examine the cylinder and
the diagram on the front panel to understand the notation and placement of the
strain gauges in relation to the axis of the cylinder. The experimental method
utilizes the SM1007 software to display and take readings
1. CONNECT TO SM1007 from the same menu. The virtual meters on
the screen should now display values of pressure and strain. (If it’s already
running, leave it as it is).
2. Close the pump release valve and zero the readings by selecting ZERO
ALL GAUGES from the EXPERIMENTS menu option. All the virtual
strain meters should now read 0±0.3με, and the pressure meter should read
0±0.01MPa.
3. Take the first set of readings (at zero) into the data table by selecting
RECORD GAUGE READINGS from the EXPERIMENTS menu
option. Display the data table by selecting DATA TABLE in the
RESULTS menu.
4. Pump the handle slowly until a pressure of around 0.5 MPa and record the
readings into the data table again by selecting RECORD GAUGE
READINGS from the EXPERIMENT menu option. Wait a few
seconds between pumps for the gauges to stabilize.
5. Carefully increase the pressure in 0.5 MPa increment, record the readings
into the data table until you have reached a value of 3 MPa (Do not exceed
a maximum cylinder pressure of 3.5 MPa). Record all data in Table 1.
7.2 Experiment 2 – Thin Cylinder with Closed Ends
We will now test the cylinder by taking the same readings as in experiment 1 but
with the cylinder in the closed ends condition to show the effect of the biaxial
stress system.
1. Open the pump release valve and carefully unscrew the hand wheel
enough to set up the closed ends condition. To check that the frame is not
transmitting any load, close the pump release valve and pump the handle
and observe the pressure gauge, you may need to pump a number of times
as the oil pushes the pistons outward.
2. Once a pressure of around 3MPa has been achieved, gently push and pull
the cylinder along its axis, the cylinder should move in the frame
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54
indicating that the frame is not transmitting any load. If it doesn’t move,
wind the hand wheel out some and try again.
3. Release the pressure from cylinder by opening the pump release valve.
4. In the SM1007 software choose CLOSED ENDS CONDITION from the
EXPERIMENTS menu option. Then connect the SM1007 unit by selecting
CONNECT TO SM1007 from the same menu. The virtual meters on the
screen should now display values of pressure and strain.
5. Repeat steps 3 to 5 in Experiment 1.
8. RESULTS
Table 1: Thin Cylinder with Open Ends Experiment 1
Pressure Gauge
1 2 3 4 5 6
0.5
1.0
1.5
2.0
2.5
3.0
Table 2: Thin Cylinder with Closed Ends Experiment 2
Pressure Gauge
1 2 3 4 5 6
3.0
9. OBSERVATIONS
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UNIVERSITI TUN HUSSEIN ONN MALAYSIA
Faculty of Mechanical and Manufacturing Engineering __________________________________________________________________
BDA27101-Edition III/2011
55
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10. CALCULATIONS
Calculate hoop strain and longitudinal strain for open ends and closed ends
conditions.
UNIVERSITI TUN HUSSEIN ONN MALAYSIA
Faculty of Mechanical and Manufacturing Engineering __________________________________________________________________
BDA27101-Edition III/2011
56
11. DISCUSSIONS
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1. Explain the difference between the “Open End” and “Closed End”
conditions?
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UNIVERSITI TUN HUSSEIN ONN MALAYSIA
Faculty of Mechanical and Manufacturing Engineering __________________________________________________________________
BDA27101-Edition III/2011
57
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2. Which case experiences “uniaxial state of stress” and which case
experiences “biaxial state of stress”?
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UNIVERSITI TUN HUSSEIN ONN MALAYSIA
Faculty of Mechanical and Manufacturing Engineering __________________________________________________________________
BDA27101-Edition III/2011
58
12. CONCLUSION.
Write your observations and comments whenever possible in your discussion in
term of achievement, problems facing throughout the experiment and
recommendation for improvement.
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UNIVERSITI TUN HUSSEIN ONN MALAYSIA
Faculty of Mechanical and Manufacturing Engineering __________________________________________________________________
BDA27101-Edition III/2011
59
13. REFERENCES
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UNIVERSITI TUN HUSSEIN ONN MALAYSIA
Faculty of Mechanical and Manufacturing Engineering __________________________________________________________________
REFERENCES
REFERENCES
SOLID MECHANICS I:
Gere, J.M. and Goodno, B.J., 2009. “Mechanics of Materials”, 7th
Edition,
Cengage Learning.
Beer, F.P., Johnston, E. R. and Deworlf, J.T., 2009. “Mechanics of Materials”, 5th
Edition, Mc Graw Hill.
Hibbeler, R.C., 2008. “Mechanics of Materials”, 7th
Edition, Pearson Prentice
Hall.
Ugural, A.C., 2008. “Mechanics of Materials”, John Wiley & Sons Inc.
Riley, W.F., Sturges, L.D., and Morris, D.H., 2007. “Mechanics of Materials”, 6th
Edition, John Wiley & Sons Inc.
UNIVERSITI TUN HUSSEIN ONN MALAYSIA
Faculty of Mechanical and Manufacturing Engineering __________________________________________________________________
APPENDICES
DEPARTMENT OF ENGINEERING MECHANICS
SOLID MECHANICS I LABORATORY
LAPORAN MAKMAL/LABORATORY REPORT
Kod M/Pelajaran/
Subject Code
ENGINEERING
LABORATORY III BDA 27101
Kod & Tajuk Ujikaji/
Code & Title of Experiment
Kod Kursus/
Course Code
Seksyen /Section
Kumpulan/Group No. K.P / I.C No.
Nama Pelajar/Name of
Student
No. Matrik
Lecturer/Instructor/Tutor’s
Name
1.
2.
Nama Ahli Kumpulan/
Group Members
No.
Matrik Penilaian / Assesment
1.
Teori / Theory 10 %
2.
Keputusan /
Results 15 %
3. Pemerhatian
/Observation 20 %
4. Pengiraan /
Calculation 10 %
5. Perbincangan /
Discussions 25 %
Tarikh Ujikaji /
Date of Experiment
Kesimpulan /
Conclusion 15 %
Tarikh Hantar /
Date of Submission
Rujukan /
References 5 %
JUMLAH /
TOTAL 100%
COP DITERIMA/APPROVED STAMP
ULASAN PEMERIKSA/COMMENTS
Recommended