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DEAKIN UNIVERSITY Faculty of Science and Technology School of Engineering and IT STRESS ANALYSIS SEM 222 Laboratory Manual-Prac 1 Akif Kaynak Ehsan Bafekrpour Khashayar Khoshmanesh Updated 2012...

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DEAKIN UNIVERSITY
Faculty of Science and Technology
School of Engineering and IT
STRESS ANALYSIS
SEM 222
Laboratory Manual-Prac 1
Akif Kaynak
Ehsan Bafekrpour
Khashayar Khoshmanesh
Updated 2012
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SEM222 Laboratory Manual –Prac 1- Page 2
Contents
Experiment 1: Bending under a point load
Experiment 2: Bending under two point loads
Experiment 3: Bending under a distributed load
Experiment 4: Bending under two distributed loads
Experiment 5: Bending of a T-beam
Important notes:
1- Ensure that you apply proper units of distance, force and stress.
2- You should wear enclosed shoes in the lab to meet the safety standards.
3- You should have the prac manuals for the experiments.
SEM222 Laboratory Manual –Prac 1- Page 3
Experiment 1
Bending under a point load
Measurements:
1- Select the steel bar equipped with strain gauges.
2- Measure the dimensions of the bar and record them in table 1.
3- Find the Elastic modulus of the bar from relevant references and record it in table 1.
4- Put the bar on the two supports of the experiment apparatus such that the sensors are located
at the middle of the bar. Set the strain gauge to zero.
5- Apply a point load of 500 g at 10 cm from one end of the bar, as shown below.
bar
supports supports
load
10 cm
Strain gauge
Strain gauge
6- Measure the deflection of the bar at its middle, using manual gauge and record it in table 1.
7- Measure the deflection of the bar at its middle, using strain gauge and record it in table 1.
8- Obtain the scale factor of the strain gauge, as given in table 1.
9- Obtain the actual deflection of the bar, as given in table 1.
Calculations:
10- Calculate the deflection of the bar at the centre using the following equation:
You may use the appendix C of “Mechanics of Materials”, R. C. Hibbeler.
11- Compare the measured and calculated deflections and discuss about the error sources.
12- Calculate the bending moment inertia of the bar and record it in table 1.
13- Calculate the shear forces of the supports using the equations of equilibrium and record them
in table 1.
14- Draw the shear diagram of the bar, using MS-Excel or other software. Manual drawings
are not accepted.
SEM222 Laboratory Manual –Prac 1- Page 4
15- Calculate the bending moment along the beam using the following equation.
16- Draw the moment diagram of the bar, using MS-Excel or other software. Manual drawings
are not accepted.
17- Calculate the maximum bending stress of the bar, as given in table 1.
Table 1- Bending under a point load
Cross section of the bar (mm×mm)
Span of the bar (mm)
Elastic modulus of the bar (Pa)
Moment of inertia of the bar (mm4)
Middle deflection by strain gauge
Middle deflection by manual gauge (mm/100)
strain gauge
manual gauge
Deflection
Deflection
Scale factor ? (mm)
Actual deflection = Middle deflection by strain
gauge×Scale factor (mm)
Shear forces of the supports (N)
Middle deflection by calculation (mm)
measured
calculated measured
Deflection
Deflection Deflection
Relative error
?
?
min
max max
I
Maximum stress ? M C (Pa)
SEM222 Laboratory Manual –Prac 1- Page 5
Experiment 2
Bending under two point loads
Measurements:
1- Select the steel bar equipped with strain gauges.
2- Put the bar on the two supports of the experiment apparatus such that the sensors are located
in the middle of the bar. Set the strain gauge to zero.
3- Apply two point loads of 500 g at 10 cm from each end of the bar, as shown below.
bar
supports supports
load
10 cm
load
10 cm
Strain gauge
Strain gauge
4- Measure the deflection of the bar at its middle, using strain gauge and record it in table 2.
5- Obtain the actual deflection of the bar, as given in table 2.
Calculations:
6- Calculate the shear forces of the supports and record them in table 2.
7- Draw the shear diagram of the bar, using MS-Excel or other software. Manual drawings
are not accepted.
8- Calculate the bending moment along the beam.
9- Draw the moment diagram of the bar, using MS-Excel or other software. Manual drawings
are not accepted.
10- Calculate the deflection at the middle of the bar and record it in table 2. You may use the
appendix C of “Mechanics of Materials”, R. C. Hibbeler. You should apply the
superposition rule to consider the effect of two loads.
11- Calculate the maximum bending stress of the bar, as given in table 2.
SEM222 Laboratory Manual –Prac 1- Page 6
Table 2- Bending under two point loads
Cross section of the bar (mm×mm)
Span of the bar (mm)
Elastic modulus of the bar (Pa)
Moment of inertia of the bar (mm4)
Middle deflection by strain gauge
Actual deflection = Middle deflection by strain
gauge×Scale factor (mm)
Shear forces of the supports (N)
Middle deflection by calculation (mm)
measured
calculated measured
Deflection
Deflection Deflection
Relative error
?
?
min
max max
I
Maximum stress ? M C (Pa)
SEM222 Laboratory Manual –Prac 1- Page 7
Experiment 3
Bending under a distributed load
Measurements:
1- Select the steel bar equipped with strain gauges.
2- Apply the specifications of bar recorded in table 1.
3- Insert the bar on the two supports of the experiment apparatus such that the sensors are
located in the middle of the bar. Set the strain gauge to zero.
4- Insert a small block on the bar and then apply a 500 g load on the block to mimic a distributed
load, as shown below.
5- Measure the deflection of the bar at its middle, using strain gauge and record it in table 3.
6- Apply the scale factor calculated in experiment 1 to determine the actual deflection in table 3.
7- Measure the length of the block and record it in table 3.
8- Increase the distributed load by 500 g intervals up to 2000 g.
9- Repeat the steps 6 to 8 and record the results in table 3.
Calculations:
10- Calculate the density of the distributed load, as given in table 3.
11- Calculate the shear forces of the supports at a load of 500 g and record them in table 3.
12- Draw the shear diagram of the bar at a load of 500 g, using MS-Excel or other software.
Manual drawings are not accepted.
13- Calculate the bending moment along the beam.
14- Draw the moment diagram of the bar at a load of 500 g, using MS-Excel or other software.
Manual drawings are not accepted.
SEM222 Laboratory Manual –Prac 1- Page 8
15- Estimating the distributed load as a point load, calculate the deflection at the middle of the bar
and record it in table 3. You may use the appendix C of “Mechanics of Materials”, R. C.
Hibbeler.
16- Compare your actual and estimated deflections and discuss about the sources of difference.
17- Calculate the maximum bending stress of the bar.
18- Students who can apply the appropriate formula to calculate the deflection of the bar at its
middle under a distributed load will receive a 10% bonus on this prac. (optional)
Table 3- Bending under a distributed load
Distributed
load (g)
Load density (N/m)
block lenght
? load
Measured deflection
Actual deflection =
Middle deflection by
strain gauge × scale
factor (mm)
Estimated deflection
(mm)
SEM222 Laboratory Manual –Prac 1- Page 9
Experiment 4
Bending under two distributed loads
Measurements:
1- Select the steel bar equipped with strain gauges.
2- Put the bar on the two supports of the experiment apparatus such that the sensors are located
in the middle of the bar. Set the strain gauge to zero.
3- Put two small blocks on the bar as shown below. Put a 500 g load on each block to mimic two
distributed loads.
bar
supports block
load
supports
10 cm
load
10 cm
Strain gauge
Strain gauge
4- Measure the deflection of the bar at its middle, using strain gauge and record it in table 4.
5- Apply the scale factor calculated in experiment 1 to determine the actual deflection in table 4.
Calculations:
6- Calculate the shear forces of the supports and record them in table 4.
7- Draw the shear diagram of the bar, using MS-Excel or other software. Manual drawings
are not accepted.
8- Draw the moment diagram of the bar, using MS-Excel or other software. Manual drawings
are not accepted.
9- Estimating the distributed load as a point load, calculate the deflection at the middle of the bar
and record it in table 4. You may use the appendix C of “Mechanics of Materials”, R. C.
Hibbeler. You can use the superposition rule to consider the effect of the second load.
10- Compare your actual and estimated deflections and discuss about the sources of difference.
11- Calculate the maximum bending stress of the bar and record it in table 4.
SEM222 Laboratory Manual –Prac 1- Page 10
Table 4- Bending under two distributed loads
Distributed load (g)
Load density = Load / block length (N/m)
Middle deflection by strain gauge
Actual deflection = Middle deflection by strain
gauge×Scale factor (mm)
Shear forces of the supports (N)
Middle deflection by calculation (mm)
measured
calculated measured
Deflection
Deflection Deflection
Relativeerror
?
?
min
max max
I
Maximum stress ? M C (Pa)
SEM222 Laboratory Manual –Prac 1- Page 11
Experiment 5
Bending of a T-beam
Measurements:
1- Ensure the beam and Load Cell are properly aligned. Turn the thumbwheel on the Load
Cell counter clockwise to apply a positive (down-ward). Set the digital force display to zero.
preload the beam of about 100N and again set the digital display to zero.
2- Take the nine zero strain readings by choosing the number with the selector switch. Fill
in Table 5 with the zero force values.
3- Increase the load to 100N and note all nine of the strain readings. Repeat the procedure
in 100 N increments to 500N. Finally gradually release the load and preload.
SEM222 Laboratory Manual –Prac 1- Page 12
Table 5- Strain at different loads and positions of the section (×10-6)
Gauge
number
Load (N)
XXXXXXXXXX500
1
2
3
4
5
6
7
8
9
Calculations:
4- Normalize the strain reading values by deducting zero strains from non-zero strains. Also
calculate the bending moment at a point between two concentrated loads and fill in Table
6.
SEM222 Laboratory Manual –Prac 1- Page 13
Table 6- Normalized strain at different bending moments and positions of the section
(×10-6)
Gauge
number
Bending moment (Nm)
0
1
2
3
4
5
6
7
8
9
5- Plot a graph of bending moment against normalized strain for all nine various positions
on the same graph.
6- Discuss the relationship between the bending moment and the strain at various positions.
7- 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 reasons why.
8- Calculate the average strains from the pairs of gauges and enter your results in Table 7.
Carefully measure the actual strain gauge position and entre the values into table 7. Take
the top of the beam as the datum.
Table 7- Average of normalized strain at different bending moments and positions of the
section (×10-6)
Gauge
number
Vertical
position
Bending moment (Nm)
0
1
2,3
4,5
6,7
8,9
9- Plot the relative vertical position of the strain gauge pairs against the strain on the same
graph for each value of bending moment. Take the top of the beam as the datum.
10- Find the position of neutral axis from the above plot.
11- Calculate the centroid of the cross section of the beam using the following formula:
SEM222 Laboratory Manual –Prac 1- Page 14
12- Calculate the moment of inertia for the beam using the following formula:
13- Calculate the theoretical stress at various positions of the section for the last loading
(500 N) using the following formula and fill in Table 8:
14- Calculate the experimental stress at various positions of the section for the last loading
(500 N) using the experimentally measured strains listed in Table 7 and the Hook’s Law (
) and complete Table 8 and calculate the errors and discuss about the sources
of difference.
Table 8- Stress at various positions of the section
Vertical position Theoretical stress experimental stress
Error (%)
(Theoretical stress-
Experimental
stress)/Theoretical
stress
Answered Same Day Dec 20, 2021

Solution

Robert answered on Dec 20 2021
130 Votes
Prac one to five Page 1
Aim:
The aim of the experiments is to measure bending moment and deflections of beam on
application of several loads at several locations. The main aim of the experiment is to find
the internal forces of a beam from bending and to find the deflection at middle by applying
two point loads.
Theory:
 Strain gaugeis a system to measure the strain of an object.
 Normal Force,
N: this force that acts perpendicular to the area of the system and occurs on application of
external load.
 Shear Force, V: When the external loads is applied to a body it tends to slide over one
another. The force with which it tends to slide is known as shear force.
 Torque, T: When a couple gets generated on a body due to equal and opposite external
forces it is known as torque.
 Bending Moment,
M: Moment is the bend in the body caused by external loads about an axis within the
plane of the area.
 A beam
Structural element that is horizontal and is capable of withstanding bending moment due to
load.Bending Moment is the bend in the body caused by external loads about an axis
within the plane of the area that occurs in a beam due to seft weight ,span and external
http:
en.wikipedia.org/wiki/Deformation_(mechanics)#Strain
http:
en.wikipedia.org/wiki/List_of_structural_elements
Prac one to five Page 2
load of the beam. Beams can withstand vertical gravitational forces but can also
withstand horizontal force (i.e., loads due to an earthquake or wind). The loads ca
ied
y a beam are transfe
ed to columns, walls, or girders, which then transfer the force to
footings.
 The bending moment
is the total bending that occurs in a beam and the bending moment at any point along the
eam is equal force multiplied the distance.
 The moment of inertia
of an object about a given axis is the difficulty by which it is to change its angular motion
about that axis. Therefore moment of inertia is the square of the distance of the mass from
the axis multiplied by mass. The farther out the object's mass is, the more rotational inertia
the object has, and the more force is required to change its rotation rate.
 Stress in a beams
Three types of stresses occur. These are compressive ,tensile and shear stresses.Due to
external gravity load the length of the beam gets reduced. The arc formed on top results in
compression,the bottom chord of the beam is in tension.The original length in the middle
portion which forms arc is neither in compression or tension and gives the position of
neutral axis
 The Force is the component, perpendicular to the surface of contact. The ground
eaction force is known as normal force and may coincide with it. For example if we
consider a person standing still on the ground, the ground reaction force is equal to the
normal force. Another example is if an object hits a surface with some velocity, the normal
force provided for a rapid deceleration will depend on the flexibility of the surface.
http:
en.wikipedia.org/wiki/Vertical_direction
http:
en.wikipedia.org/wiki/Gravitational
http:
en.wikipedia.org/wiki/Force
http:
en.wikipedia.org/wiki/Horizontal_plane
http:
en.wikipedia.org/wiki/Earthquake
http:
en.wikipedia.org/wiki/Column
http:
en.wikipedia.org/wiki/Wall
http:
en.wikipedia.org/wiki/Girde
http:
en.wikipedia.org/wiki/Ground_reaction_force
http:
en.wikipedia.org/wiki/Ground_reaction_force
Prac one to five Page 3
 Shear force
The force in the beam acting perpendicular to its longitudinal (x) axis is known as shear
force. For design purposes, the beam's ability to resist shear force is more important than
its ability to resist an axial force. Axial force is the force in the beam acting parallel to the
longitudinal axis.
Method:
 Experiment 1: Bending under a point load:
A strain sensor attached steel bar is selected. The dimension of the beam is noted
down.Elastic modulus,bending moment inertia of the beam is calculated and recorded.The
ar is placed on the support in such a way that the sensor is in the middle and the strain
gauges are at zero reading position.Then a load of 500 gm is applied at a distance of 10 cm
from one support.The net load is sum of the load applied and the self weight of the
eam.The deflection of the beam is first measured by strain gauge and then by manual
gauge.Then the values are compared to gauge the scale factor of strain gauge.
 Experiment 2: Bending under two point loads:
ar
supports supports
load
10 cm
Strain gauge
Strain gauge
Prac one to five Page 4
Firstly, the steel bar equipped with strain gauges was selected. Then, the bar was put on the
two supports of the experiment apparatus such that the sensors are located in the middle
of the bar. Then, the strain gauge was set to zero.Then two point load of 500 gm is applied
at a distance of 10 cm from each support. The deflection of the beam is first measured by
strain gauge and then by manual gauge. Then the values are compared to gauge the scale
factor of strain gauge.Actual deflection is then obtained.
ar
supports supports
load
10 cm
load
10 cm
Strain gauge
Strain gauge

 Experiment 3: Bending under a distributed load:
A strain sensor attached steel bar is selected. The dimension of the beam is noted down.
Elastic modulus, bending moment inertia of the beam is calculated and recorded. The bar is
placed on the support in such a way that the sensor is in the middle and the strain gauges
are at zero reading position. Then a block bar is inserted of 500 gm is applied. The deflection
of the beam is first measured by strain gauge and then by manual gauge. Then the values
are compared to gauge the scale factor of strain gauge Then, the scale factor applied which
calculated in experiment 1 to determine the actual deflection. Length of the beam is
measured and recorded. Then the UDL is increased from 500g to 2000g with regular
succession and values are repeated and noted.
Prac one to five Page 5
a
supports
lock
load
supports
10 cm
Strain gauge
Strain gauge

.
 Experiment 4: Bending under two distributed loads:
A strain sensor attached steel bar is selected. The dimension of the beam is noted down.
Elastic modulus, bending moment inertia of the beam is calculated and recorded. The bar is
placed on the support in such a way that the sensor is in the middle and the strain gauges
are at zero reading position. Then two block bar is inserted of 500 gm is applied which acts
as a UDL. The deflection of the beam at the middle is first measured by strain gauge Then,
the scale factor applied which calculated in experiment 1 to determine the actual deflection.
Prac one to five Page 6
a
supports block
load
supports
10...
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