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SIR M VISVESVARAYA INSTITUTE OF TECHNOLOGY
DEPARTMENT OF MECHANICAL ENGINEERING
STRAIN GAUGES
INTEGRATED WITH ARDUINO
TO DISPLY STRAIN IN
GRAPHICAL FORMAT
NAME USN
BS Sri Sumukha 1MV19ME011
Chandan BS 1MV19ME012
Dhanush MP 1MV19ME015
Dinakar MK 1MV19ME017
DETERMINATION OF YOUNGS MODULUS
USING
STRAIN GAUGES
Under The Guidance Of:
MRS .ASHA RANI A
(Assistant professor)
Presented by:
CONTENTS:
1. INTRODUCTION
2. LITERATURE SURVEY
3. WORKING
4. SELECTION CONSIDERATIONS
5. TYPES OF STRAIN GAUGES
6. APPLICATIONS
7. MATERIAL PROPERTIES
What is a Strain Gauge?
• A Strain gauge is a resistor used to measure strain on an object.
Strain Gauges are important geotechnical tools that measure
strain in underground cavities, tunnels, buildings, concrete,
masonry dams, bridges, and embedment in soil/concrete.
etc.
What is a Strain Gauge?
ADD YOUR TITLE HERE
• When an external force is applied on
an object, due to this external force
there is a deformation in the shape of
the object.
• This deformation in the shape is
either compressive or tensile and this
is called strain, and it is measured by
the strain gauge.
• When an object deforms within the limit of elasticity, either it becomes narrower
and longer or it become shorter and broadens. As a result of it, there is a change
in resistance end-to-end.
• As Resistance depends on the Area of cross-section and length, this deformation
alters these properties of the material.
• The strain gauge is sensitive to that small changes that occur in the geometry of
an object. By measuring the change in resistance of an object, the amount of
induced stress can be calculated.
LITERATURE SURVEY
SL
NO
AUTHOR NAME OF THE BOOK PROPERTIES YEAR
1. Askeland,
Donald R ; Phule
, Pradeep P
The Science and
engineering of
materials(5th edition).
Youngs Modulus 2006
2. Beer , Ferdinand
P ; Johnston E
Russell
Mechanics Of Materials Youngs Modulus,
Modulus of
Elasticity
2009
3. Khulna
University Of
Engineering
Analysis of Mechanical
properties of Mild steel
Applying Various Heat
Treatment Department of
Industrial Engineering
and Management.
Properties of Mild
Steel On Various
Heat Treatment
Process.
2014
4. Wikipedia Aluminium Element Properties of
Aluminium
2022
LITERATURE SURVEY
SL
NO
AUTHOR NAME OF THE BOOK PROPERTIES YEAR
5. Sachin Thorat Metrology and
Instrumentation
Introduction To
Strain gauges
Unkown
6. Encardio Rite [Updated] Strain Gauges Principle of Strain
gauges.
2019
7. Circuits Today Strain gauges Types of Strain
gauges
2010
8. IEICOS Strain Indicators Basic understanding
of strain indicator
2011
Working Of Strain Gauges
• strain gauge works on the principle of electrical
conductance and its dependence on the
conductor’s geometry.
• Whenever a conductor is stretched within the
limits of its elasticity, it doesn’t break but, gets
narrower and longer. Similarly, when it is
compressed, it gets shorter and broader,
ultimately changing its resistance.
• We know that
R= L/A
Where,
R = Resistance of the wire
L = Length of the wire
A = Cross-Sectional Area of the wire
• The change in the shape and size of the conductor
also alters its length and the cross-sectional area
which eventually affects its resistance.
• The resistance change is commonly measured using
a Wheatstone bridge.
• Any typical strain gauge will have a long, thin
conductive strip arranged in a zig-zag pattern of
parallel lines.
• The reason behind aligning them in a zig-zag
fashion is that they don’t increase the sensitivity
since the percentage change in resistance for a
given strain for the entire conductive strip is the
same for any single trace.
Working Of Strain Gauges
STRAIN GAUGE SELECTION CONSIDERATION:
•Gauges Length
•Number of Gauges in Gauge Pattern
•Arrangement of Gauges in Gauge Pattern
•Grid Resistance
•Strain-Sensitive Alloy
•Carrier Material
•Gauge Width
•Solder Tab Type
•Availability
Types of Strain Gauges
•This classification is based on the type of bridge circuit that is connected to the strain gauge.
There are mainly three types of connections. They are
1. Quarter Bridge Strain Gauge Circuit
As shown in the diagram beside, the imbalance is
detected by the voltmeter in the center of the bridge
circuit. The resistance R2 will be a rheostat and
hence adjustable. The value of this resistance is made
equal to the strain gauge resistance without the
application of any force. The resistances R1 and R3
will have equal values. Thus, according to the
Wheatstone bridge principle the entire circuit will be
balanced and the net force will be zero. Thus the
strain will also be zero. Now provide a compression
or tension on the conductor and the circuit will be
imbalanced. Thus you will get a reading at the
voltmeter.
Types of Strain Gauges
2. Half Bridge Strain Gauge Circuit
As shown in the circuit there are two strain gauges
connected. If one of them does not respond to the
strain produced it becomes a quarter bridge circuit. If
both of them respond in such a way that both the
strain gauges experience opposite forces it becomes a
half bridge strain gauge circuit. By opposite forces,
we mean that a compression on the upper strain
gauge makes a stretch on the lower strain gauge. This
causes both the gauges to make a better response to
strain, thus increasing the response of the bridge to
the applied force. As both the strain gauges act
opposite and proportionally the response to the
changes in temperature will be cancelled thus
reducing the errors due to it.
Types of Strain Gauges
3. Full Bridge Strain Gauge Circuit
In the case of sensitivity, a half bridge strain circuit is
more sensitive than a quarter bridge circuit. The
sensitivity can be increased if all the elements of the
bridge are active. Such a circuit is called full bridge
strain gauge circuit. The circuit is also advantageous
in the fact that it can be used to bond the
complimentary pairs of strain gauges to the testing
specimen. Thus, this is considered to be the best
bridge circuit for strain measurement. The circuit is
also advantageous because of its linearity. That is, the
output voltage is exactly directly proportional to the
applied force. But in the case of a half bridge and
quarter bridge the output voltage is only
approximately proportional to the applied force. Take
a look at the circuit diagram given below.
Applications Of Strain Gauge In Various Fields.
• Aerospace Applications - Strain gauges can monitor the wing
deflection or deformation during flight to ensure it is safe. They
also monitor various on-board units and power supplies.
• Rail applications – strain gauges are used to monitor and measure
the stress the lines are under. The readings they produce can alert
personnel if the railways become under too much stress or strain.
• Measuring stress on circuit boards – some very small strain
gauges can measure stress on electric circuit boards and other
confined spaces.
Advantages Of Using Strain Gauges
• Simple in construction.
• Strain gauges can be calibrated in terms of quantities, such as, force, displacement,
pressure and acceleration.
• Very sensitive.
• They provide good output for indicating and recording purposes.
• Inexpensive and reliable.
Limitations Of Using Strain Gauges
• Strain gauges require the surface on which they are applied on to be of very good finish
and clean. Otherwise the output can be pretty sketchy.
• They are sensitive to overload and get damaged.
• Their performance is affected by humidity, temperature, hysteresis and repeatability and
accuracy drops with prolong use.
• Gauges are suitable to measure static as well as dynamic strain.
• They are not suited for underwater applications. They need to be protected with a water
tight housing.
Materials That Are Being Compared
 Mild Steel:
• Mild steel is a type of carbon steel with a low amount of
carbon – it is also known as “low carbon steel.” Although
ranges vary depending on the source, the amount of carbon
typically found in mild steel is 0.05% to 0.35% by weight,
whereas higher carbon steels are typically described as having
a carbon percentage of 0.6% - 1.5%.
• There are two main reasons for the popular use of steel:
1. It is abundant in the earth’s crust in form of Fe2O3 and
little energy is required to convert it to Fe.
2. It can be made to exhibit great variety of microstructures
and thus a wide range of mechanical properties.
 Aluminium:
• Aluminium (aluminum in American and Canadian
English) is a chemical element with the symbol Al
and atomic number 13. Aluminium has a density
lower than those of other common metals, at
approximately one third that of steel. It has a great
affinity towards oxygen, and forms a protective
layer of oxide on the surface when exposed to air.
Aluminium visually resembles silver, both in its
color and in its great ability to reflect light. It is soft,
non-magnetic and ductile. It has one stable isotope,
27Al; this isotope is very common, making
aluminium the twelfth most common element in the
Universe.
Modulus Of Elasticity:
An elastic modulus is a quantity that measures an object or substance's resistance to being
deformed elastically ,when a stress is applied to it. The elastic modulus of an object is defined as
the slope of its stress–strain curve in the elastic deformation region.
1. Young's modulus (E) describes the tendency of an object to deform along an axis when
opposing forces are applied along that axis; it is defined as the ratio of tensile stress to
tensile strain. It is often referred to simply as the elastic modulus.
2. Modulus of rigidity (G ) describes an object's tendency to shear when acted upon by
opposing forces; it is defined as shear stress over shear strain.
3. The bulk modulus (K) describes the tendency of an object to deform in all directions when
uniformly loaded in all directions; it is defined as volumetric stress over volumetric strain
and is the inverse of compressibility.
Experiment For Youngs Modulus Using Strain Gauges:
Aim: To determine the modulus of elasticity of mild steel using strain gauges.
Apparatus: Cantilever beam with strain gauges, Micro strain indicator, loading device, Weights.
Procedure:
1. A flat rectangular M.S. specimen is held as cantilever beam.
2. The strain gauge is fixed, and the strain indicator is calibrated.
3. A known weight is placed at the specified distance from the fixed end.
4. Strain indicator reading is noted down.
5. The experiment is repeated for different loads and the results are tabulated.
6. The graph of stress v/s strain is plotted and Young ‘s modulus of elasticity is determined by
graph.
Formula:
Modulus of elasticity, (N/m2)
Load cell
1. A load cell converts a force into an electrical signal that can be measured.
2. The electrical signal changes proportionally to the force applied.
3. There are different types of load cells: strain gauges, pneumatic, and hydraulic.
4. Strain gauge load cells are composed of a metal bar with attached strain gauges.
5. A strain gauge is an electrical sensor that measures force or strain on an object.
6. The resistance of the strain gauges varies when an external force is applied to an object.
which results in a deformation of the object’s shape.
Arduino UNO R3:
1. The Arduino UNO is the best board to get started with electronics and
coding.
2. Arduino UNO is a microcontroller board based on the ATmega328P.
3. It has 14 digital input/output pins (of which 6 can be used as PWM
outputs).
4. 6 analog inputs, a 16 MHz ceramic resonator, a USB connection, a power
jack, an ICSP header and a reset button.
5. It contains everything needed to support the microcontroller.
a
HX711 Amplifier:
1. The HX711 amplifier is a breakout board that allows
you to easily read load cells
to measure weight.
1. The HX711 communicates with the microcontroller
using two-wire interface.
2. HX711 IC that allows you to easily read load cells to
measure weight.
Load Cell and HX711 Amplifier with Ardunio:
Installing library:
• Strain Measurement is simplified by use of direct
indicating IEICOS Digital Strain Indicators.
Resistance Strain Gauges are attached to the
member under investigation.
• Strain resulting from stress in the member can be
directly read of from the display in terms of
microstrains.
• Indication can also be obtained in terms of Torque
Load, Pressure or any other Strain producing
physical quantities by calibration with known inputs.
Strain Indicator:
USES:
• VerifyMaterials Properties.
• Demonstrate Stress concentration.
• Calibrate Strain Gauges.
• Create and Construct Transducers.
Literature survey report
• Askeland, Donald R.; Phulé, Pradeep P. (2006). The science and engineering of materials
(5th ed.). Cengage Learning. P. 198. ISBN 978-0-534-55396-8.
• Beer, Ferdinand P.; Johnston, E. Russell; Dewolf, John; Mazurek, David (2009). Mechanics
of Materials. McGraw Hill. P. 56. ISBN 978-0-07-015389-9.
• Alawode, A.J., (2002), Effects of Cold Work and Stress Relief Annealing Cycle on
the Mechanical Properties and Residual Stresses of Cold-Drawn Mild Steel Rod, M.
Eng Thesis, Mechanical Engineering Department, University of Ilorin, Nigeria
• Keil, Stephan (2017). Technology and Practical Use of Strain Gages With Particular
Consideration of Stress Analysis Using Strain Gages. John Wiley & Sons, Ltd. ISBN 978-
3-433-60666-7
• M. Varanis, A.L. Silva, P.H.A. Brunetto and R.F. Gregolin, Revista Brasileira de Ensino de
Física 38,1301(2016), F.L. Francesco, G. Navarra and M. Oliva, Meccanica 52,3221
(2017).M. Varanis, A.L. Silva and A.G. Mereles, Revista Brasileira de Ensino de Física 40,
e1304 (2017)
REFERENCES:
1. Askeland, Donald R ; Phule , Pradeep P ; The Science and engineering of materials (2006).
2. Beer , Ferdinand P , Johnston E Russell ; Mechanics Of Materials (2009).
3. Khulna university of Engineering ; Analysis of Mechanical properties of Mild steel Applying Various Heat
Treatment Department of Industrial Engineering and Management (2014).
4.Sachin Thorat ; Metrology and instrumentation.
5. Encardio Rite ; Strain gauges (2019).
6. Circuits Today:https://www.circuitstoday.com/strain-gauge (2010).
7. IEICOS: https://www.ieicos.com/strain_gauges_strain_indicators.html (2011).

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1658821432126_Strain Gauges PPT-2.pptx

  • 1. SIR M VISVESVARAYA INSTITUTE OF TECHNOLOGY DEPARTMENT OF MECHANICAL ENGINEERING STRAIN GAUGES INTEGRATED WITH ARDUINO TO DISPLY STRAIN IN GRAPHICAL FORMAT
  • 2. NAME USN BS Sri Sumukha 1MV19ME011 Chandan BS 1MV19ME012 Dhanush MP 1MV19ME015 Dinakar MK 1MV19ME017 DETERMINATION OF YOUNGS MODULUS USING STRAIN GAUGES Under The Guidance Of: MRS .ASHA RANI A (Assistant professor) Presented by:
  • 3. CONTENTS: 1. INTRODUCTION 2. LITERATURE SURVEY 3. WORKING 4. SELECTION CONSIDERATIONS 5. TYPES OF STRAIN GAUGES 6. APPLICATIONS 7. MATERIAL PROPERTIES
  • 4. What is a Strain Gauge? • A Strain gauge is a resistor used to measure strain on an object. Strain Gauges are important geotechnical tools that measure strain in underground cavities, tunnels, buildings, concrete, masonry dams, bridges, and embedment in soil/concrete. etc.
  • 5. What is a Strain Gauge? ADD YOUR TITLE HERE • When an external force is applied on an object, due to this external force there is a deformation in the shape of the object. • This deformation in the shape is either compressive or tensile and this is called strain, and it is measured by the strain gauge.
  • 6. • When an object deforms within the limit of elasticity, either it becomes narrower and longer or it become shorter and broadens. As a result of it, there is a change in resistance end-to-end. • As Resistance depends on the Area of cross-section and length, this deformation alters these properties of the material. • The strain gauge is sensitive to that small changes that occur in the geometry of an object. By measuring the change in resistance of an object, the amount of induced stress can be calculated.
  • 7. LITERATURE SURVEY SL NO AUTHOR NAME OF THE BOOK PROPERTIES YEAR 1. Askeland, Donald R ; Phule , Pradeep P The Science and engineering of materials(5th edition). Youngs Modulus 2006 2. Beer , Ferdinand P ; Johnston E Russell Mechanics Of Materials Youngs Modulus, Modulus of Elasticity 2009 3. Khulna University Of Engineering Analysis of Mechanical properties of Mild steel Applying Various Heat Treatment Department of Industrial Engineering and Management. Properties of Mild Steel On Various Heat Treatment Process. 2014 4. Wikipedia Aluminium Element Properties of Aluminium 2022
  • 8. LITERATURE SURVEY SL NO AUTHOR NAME OF THE BOOK PROPERTIES YEAR 5. Sachin Thorat Metrology and Instrumentation Introduction To Strain gauges Unkown 6. Encardio Rite [Updated] Strain Gauges Principle of Strain gauges. 2019 7. Circuits Today Strain gauges Types of Strain gauges 2010 8. IEICOS Strain Indicators Basic understanding of strain indicator 2011
  • 9. Working Of Strain Gauges • strain gauge works on the principle of electrical conductance and its dependence on the conductor’s geometry. • Whenever a conductor is stretched within the limits of its elasticity, it doesn’t break but, gets narrower and longer. Similarly, when it is compressed, it gets shorter and broader, ultimately changing its resistance. • We know that R= L/A Where, R = Resistance of the wire L = Length of the wire A = Cross-Sectional Area of the wire
  • 10. • The change in the shape and size of the conductor also alters its length and the cross-sectional area which eventually affects its resistance. • The resistance change is commonly measured using a Wheatstone bridge. • Any typical strain gauge will have a long, thin conductive strip arranged in a zig-zag pattern of parallel lines. • The reason behind aligning them in a zig-zag fashion is that they don’t increase the sensitivity since the percentage change in resistance for a given strain for the entire conductive strip is the same for any single trace. Working Of Strain Gauges
  • 11. STRAIN GAUGE SELECTION CONSIDERATION: •Gauges Length •Number of Gauges in Gauge Pattern •Arrangement of Gauges in Gauge Pattern •Grid Resistance •Strain-Sensitive Alloy •Carrier Material •Gauge Width •Solder Tab Type •Availability
  • 12. Types of Strain Gauges •This classification is based on the type of bridge circuit that is connected to the strain gauge. There are mainly three types of connections. They are 1. Quarter Bridge Strain Gauge Circuit As shown in the diagram beside, the imbalance is detected by the voltmeter in the center of the bridge circuit. The resistance R2 will be a rheostat and hence adjustable. The value of this resistance is made equal to the strain gauge resistance without the application of any force. The resistances R1 and R3 will have equal values. Thus, according to the Wheatstone bridge principle the entire circuit will be balanced and the net force will be zero. Thus the strain will also be zero. Now provide a compression or tension on the conductor and the circuit will be imbalanced. Thus you will get a reading at the voltmeter.
  • 13. Types of Strain Gauges 2. Half Bridge Strain Gauge Circuit As shown in the circuit there are two strain gauges connected. If one of them does not respond to the strain produced it becomes a quarter bridge circuit. If both of them respond in such a way that both the strain gauges experience opposite forces it becomes a half bridge strain gauge circuit. By opposite forces, we mean that a compression on the upper strain gauge makes a stretch on the lower strain gauge. This causes both the gauges to make a better response to strain, thus increasing the response of the bridge to the applied force. As both the strain gauges act opposite and proportionally the response to the changes in temperature will be cancelled thus reducing the errors due to it.
  • 14. Types of Strain Gauges 3. Full Bridge Strain Gauge Circuit In the case of sensitivity, a half bridge strain circuit is more sensitive than a quarter bridge circuit. The sensitivity can be increased if all the elements of the bridge are active. Such a circuit is called full bridge strain gauge circuit. The circuit is also advantageous in the fact that it can be used to bond the complimentary pairs of strain gauges to the testing specimen. Thus, this is considered to be the best bridge circuit for strain measurement. The circuit is also advantageous because of its linearity. That is, the output voltage is exactly directly proportional to the applied force. But in the case of a half bridge and quarter bridge the output voltage is only approximately proportional to the applied force. Take a look at the circuit diagram given below.
  • 15. Applications Of Strain Gauge In Various Fields. • Aerospace Applications - Strain gauges can monitor the wing deflection or deformation during flight to ensure it is safe. They also monitor various on-board units and power supplies. • Rail applications – strain gauges are used to monitor and measure the stress the lines are under. The readings they produce can alert personnel if the railways become under too much stress or strain. • Measuring stress on circuit boards – some very small strain gauges can measure stress on electric circuit boards and other confined spaces.
  • 16. Advantages Of Using Strain Gauges • Simple in construction. • Strain gauges can be calibrated in terms of quantities, such as, force, displacement, pressure and acceleration. • Very sensitive. • They provide good output for indicating and recording purposes. • Inexpensive and reliable.
  • 17. Limitations Of Using Strain Gauges • Strain gauges require the surface on which they are applied on to be of very good finish and clean. Otherwise the output can be pretty sketchy. • They are sensitive to overload and get damaged. • Their performance is affected by humidity, temperature, hysteresis and repeatability and accuracy drops with prolong use. • Gauges are suitable to measure static as well as dynamic strain. • They are not suited for underwater applications. They need to be protected with a water tight housing.
  • 18. Materials That Are Being Compared  Mild Steel: • Mild steel is a type of carbon steel with a low amount of carbon – it is also known as “low carbon steel.” Although ranges vary depending on the source, the amount of carbon typically found in mild steel is 0.05% to 0.35% by weight, whereas higher carbon steels are typically described as having a carbon percentage of 0.6% - 1.5%. • There are two main reasons for the popular use of steel: 1. It is abundant in the earth’s crust in form of Fe2O3 and little energy is required to convert it to Fe. 2. It can be made to exhibit great variety of microstructures and thus a wide range of mechanical properties.
  • 19.  Aluminium: • Aluminium (aluminum in American and Canadian English) is a chemical element with the symbol Al and atomic number 13. Aluminium has a density lower than those of other common metals, at approximately one third that of steel. It has a great affinity towards oxygen, and forms a protective layer of oxide on the surface when exposed to air. Aluminium visually resembles silver, both in its color and in its great ability to reflect light. It is soft, non-magnetic and ductile. It has one stable isotope, 27Al; this isotope is very common, making aluminium the twelfth most common element in the Universe.
  • 20. Modulus Of Elasticity: An elastic modulus is a quantity that measures an object or substance's resistance to being deformed elastically ,when a stress is applied to it. The elastic modulus of an object is defined as the slope of its stress–strain curve in the elastic deformation region. 1. Young's modulus (E) describes the tendency of an object to deform along an axis when opposing forces are applied along that axis; it is defined as the ratio of tensile stress to tensile strain. It is often referred to simply as the elastic modulus. 2. Modulus of rigidity (G ) describes an object's tendency to shear when acted upon by opposing forces; it is defined as shear stress over shear strain. 3. The bulk modulus (K) describes the tendency of an object to deform in all directions when uniformly loaded in all directions; it is defined as volumetric stress over volumetric strain and is the inverse of compressibility.
  • 21. Experiment For Youngs Modulus Using Strain Gauges: Aim: To determine the modulus of elasticity of mild steel using strain gauges. Apparatus: Cantilever beam with strain gauges, Micro strain indicator, loading device, Weights. Procedure: 1. A flat rectangular M.S. specimen is held as cantilever beam. 2. The strain gauge is fixed, and the strain indicator is calibrated. 3. A known weight is placed at the specified distance from the fixed end. 4. Strain indicator reading is noted down. 5. The experiment is repeated for different loads and the results are tabulated. 6. The graph of stress v/s strain is plotted and Young ‘s modulus of elasticity is determined by graph. Formula: Modulus of elasticity, (N/m2)
  • 22. Load cell 1. A load cell converts a force into an electrical signal that can be measured. 2. The electrical signal changes proportionally to the force applied. 3. There are different types of load cells: strain gauges, pneumatic, and hydraulic. 4. Strain gauge load cells are composed of a metal bar with attached strain gauges. 5. A strain gauge is an electrical sensor that measures force or strain on an object. 6. The resistance of the strain gauges varies when an external force is applied to an object. which results in a deformation of the object’s shape.
  • 23. Arduino UNO R3: 1. The Arduino UNO is the best board to get started with electronics and coding. 2. Arduino UNO is a microcontroller board based on the ATmega328P. 3. It has 14 digital input/output pins (of which 6 can be used as PWM outputs). 4. 6 analog inputs, a 16 MHz ceramic resonator, a USB connection, a power jack, an ICSP header and a reset button. 5. It contains everything needed to support the microcontroller.
  • 24. a HX711 Amplifier: 1. The HX711 amplifier is a breakout board that allows you to easily read load cells to measure weight. 1. The HX711 communicates with the microcontroller using two-wire interface. 2. HX711 IC that allows you to easily read load cells to measure weight.
  • 25. Load Cell and HX711 Amplifier with Ardunio:
  • 27. • Strain Measurement is simplified by use of direct indicating IEICOS Digital Strain Indicators. Resistance Strain Gauges are attached to the member under investigation. • Strain resulting from stress in the member can be directly read of from the display in terms of microstrains. • Indication can also be obtained in terms of Torque Load, Pressure or any other Strain producing physical quantities by calibration with known inputs. Strain Indicator:
  • 28. USES: • VerifyMaterials Properties. • Demonstrate Stress concentration. • Calibrate Strain Gauges. • Create and Construct Transducers.
  • 29. Literature survey report • Askeland, Donald R.; Phulé, Pradeep P. (2006). The science and engineering of materials (5th ed.). Cengage Learning. P. 198. ISBN 978-0-534-55396-8. • Beer, Ferdinand P.; Johnston, E. Russell; Dewolf, John; Mazurek, David (2009). Mechanics of Materials. McGraw Hill. P. 56. ISBN 978-0-07-015389-9. • Alawode, A.J., (2002), Effects of Cold Work and Stress Relief Annealing Cycle on the Mechanical Properties and Residual Stresses of Cold-Drawn Mild Steel Rod, M. Eng Thesis, Mechanical Engineering Department, University of Ilorin, Nigeria • Keil, Stephan (2017). Technology and Practical Use of Strain Gages With Particular Consideration of Stress Analysis Using Strain Gages. John Wiley & Sons, Ltd. ISBN 978- 3-433-60666-7 • M. Varanis, A.L. Silva, P.H.A. Brunetto and R.F. Gregolin, Revista Brasileira de Ensino de Física 38,1301(2016), F.L. Francesco, G. Navarra and M. Oliva, Meccanica 52,3221 (2017).M. Varanis, A.L. Silva and A.G. Mereles, Revista Brasileira de Ensino de Física 40, e1304 (2017)
  • 30. REFERENCES: 1. Askeland, Donald R ; Phule , Pradeep P ; The Science and engineering of materials (2006). 2. Beer , Ferdinand P , Johnston E Russell ; Mechanics Of Materials (2009). 3. Khulna university of Engineering ; Analysis of Mechanical properties of Mild steel Applying Various Heat Treatment Department of Industrial Engineering and Management (2014). 4.Sachin Thorat ; Metrology and instrumentation. 5. Encardio Rite ; Strain gauges (2019). 6. Circuits Today:https://www.circuitstoday.com/strain-gauge (2010). 7. IEICOS: https://www.ieicos.com/strain_gauges_strain_indicators.html (2011).