Stress strain measurements ppt

STRESS-STRAIN
MEASUREMENTS
M.BALAJI MTECH,(PHD)
ASSISTANT PROFESSOR
MECHANICAL ENGINEERING

TOPIC COVERED
Stress & strain Measurements:
⚫ Various types- Electrical Strain Gauge.
⚫ Gauge factor
⚫ Method of usage of resistance strain gauge for bending compressive &
Tensile strains
⚫ Usage for Measuring torque.
⚫ Strain gauge Rosettes.

STRESS & STRAIN MEASUREMENTS:VARIOUS TYPES-
ELECTRICAL STRAIN GAUGE.
STRESS : pressure or tension exerted on a material object.
STRAIN :Aforce tending to pull or stretch something to an extreme or damaging degree

What is a Strain Gauge
A strain gauge is a resistor used to measure strain on an object. When an external force is applied on an
object, due to which there is a deformation occurs in the shape of the object. This deformation in the
shape is both compressive or tensile 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.
The strain gauge is sensitive to that small changes occur in the geometry of an object. By measuring the
change in resistance of an object, the amount of induced stress can be calculated.
STRESS & STRAIN MEASUREMENTS: VARIOUS TYPES-
Use of Strain Gauge
In the field of mechanical engineering development.
To measure the stress generated by machinery.
In the field of component testing of aircraft like; linkages, structural damage etc.

STRESS & STRAIN
MEASUREMENTS:
Various types- Electrical Strain Gauge.
The Various types- Electrical Strain Gauge
1. Wire gauge
a) Unbounded
b) Bonded
c) Foil type
2. Semiconductor gauge
•The Electrical strain gauge is a passive, resistive transducer which converts the mechanical
elongation and compression into a resistance change.
•This change in resistance takes place due to variation in length and cross sectional area of the gauge
wire, when an external force acts on it.

STRESS & STRAIN
MEASUREMENTS:
ELECTRICALSTRAIN
GAUGE.
•A strain gauge is a thin, wafer-like device that can be attached to a variety of materials to measure
applied strain.
Working on Wheatstone Bridge
l
R
l
R
K 
K12
The sensitivity of a strain gauge is described in terms of a characteristic called the
gauge factor, defined as unit change in resistance per unit change in length
[OR]
Gauge factor is related to Poisson's ratio μ

Stress & strain Measurements: Electrical Strain Gauge.
R
 K.
R
Resistance =R(Ω)
Changed resistance
=∆R(Ω)
Strain=€;Gage Factor=K

STRESS & STRAIN
MEASUREMENTS:ELECTRICALSTRAIN GAUGE.
UNBONDED STRAIN GAUGE
• An unbounded meter strain gauge is shown in fig
• This gauge consist of a wire stretched between two point in an insulating medium such as air. The wires
may be made of various copper, nickel, crome nickle or nickle iron alloys.
•In fig the element is connected via a rod to diaphragm which is used for sensing the pressure. The wire
are tensioned to avoid buckling when they experience the compressive force.
•The unbounded meter wire gauges used almost exclusively in transducer application employ preloaded
resistance wire connected in Wheatstone bridge as shown in fig.
•At initial preload the strain and resistance of the four arms are nominally equal with the result the output
voltage of the bridge is equal to zero.
Application of pressure produces a small displacement , the displacement increases a tension in two wire
and decreases it in the other two thereby increase the resistance of two wire which are in tension and
decreasing the resistance of the remaining two wire .
•This causes an unbalance of the bridge producing an output voltage which is proportional to the input
displacement and hence to the applied pressure .

STRESS & STRAIN MEASUREMENTS:
UNBONDED STRAIN GAUGE

BONDED STRAIN GAUGE
•The bonded metal wire strain gauge are used for both stress analysis and for construction of
transducer.Aresistance wire strain gauge consist of a grid of fine
• resistance wire. The grid is cemented to carrier which may be a thin sheet of paper Bakelite or Teflon.
•The wire is covered on top with a thin sheet of material so as to prevent it from any mechanical
damage.
•The carrier is bonded with an adhesive material to the specimen which permit a good transfer of
strain from carrier to grid of wires.

METAL FOIL STRAIN GUAGE
silicon and germanium for their construction
± 0.01~0.002
PRECISION

STRAIN GAUGE MEASUREMENT: SPECIAL APPLICATIONS
1.High temperature applications
•tie rods for the steel industry
2.Applications on special material (composite materials, stone, etc.)
•carbon fiber paddle handle
•rear rotor helicopter blade
•marble columns
•specimens stone (marble and tuff)
•Human tooth
5.Installation on pressurized components
•dryer cylinder for paper industry
•manifold prototype
•diesel engine common rail
•centrifugal compressor casing
•moist-heat industrial sterilizers for food industry
• CNG tanks for bus
6.Transducers (load cells, etc.)
7.Installations submerged
•centrifugal compressor casing
•centrifugal pump
8.Thermal characterization of strain gauge installations
•specimen tie rod for steel industry
•steel specimens for thermal characterization
•natural ventilation laboratory oven
3.Miniaturized application
•Metering rod for internal-combustion
engine
• Needle for dental use
4.Installations on rotating components
•couplings (for torque measurements)
•centrifugal compressor impellers
•spindle coupling metal rolling mill

STRAIN GAUGE MEASUREMENT: APPLICATION FIELDS
The strain gage through the SG is a method for points suitable for the measurement of elastic and
plastic strain on any material. The typical resolution is 1 μm/m, while the measurement range is
typically between 5000 and 50000 μm/m (up to 200,000 μm/m with special SG). The method is
suitable for the strain measurements even at low and high temperatures and in hostile environment.
This technique is widely used in many fields, among which:
1. stress experimental analysis
2. residual stress analysis
3. torque and tensional vibration measurements
RELATIONSHIP BETWEEN ELECTRICALRESISTANCE AND STRAIN
K Ro
1 R
 
where:
K gauge factor of the SG( Strain Gauge)
ΔR change in resistance of the installed
SG
R0 initial resistance of the installed SG.
 experimental modal analysis
• stresses dynamic analysis
• pressure vessels

GAUGE FACTOR
Gauge factor G:
The sensitivity of the strain gauge is expressed in the terms of a characteristic called the Gauge
factor.
Strain wire Gauge factor G is the ratio between relative change in resistance due to the change in
relative length. R1 R2 R3 R4
G 
L1
R1
L2
R2 
L3
R3
L4
R4
L1 L2 L3 L4
where:
G gauge factor of the SG( Strain Gauge)
ΔR change in resistance of the installed SG
R initial resistance of the installed SG.
ΔL change in length of the installed SG
L change in length of the installed SG

Stress & strain Measurements: Method of usage of resistance strain gauge for
bending compressive & Tensile strains

Stress & strain Measurements: Usage for Measuring torque

BONDED AND UNBOUNDED
STRAIN GAUGES
Working Principle:
The strain gauge working principle is based on the fact that the electrical resistance of
materials varies with deformation. A strain gauge is an example of a passive transducer that
converts the mechanical displacement into electrical quantity.
The resistance of the conductor depends on the length and cross-sectional area.
L = length of the conductor or semiconductor element.
A= Cross sectional area.
ρ = Resistivity.
A
ρL
R 

STRAIN GAUGES
Bonded strain gauge :
Bonded strain gauges are so-called because they are attached to the elastic element surface. The most
commonly used are bonded resistance type strain gauges. They are primarily used for strain analysis.
In bonded resistance wire strain gauges resistance element is cemented to the base which may be a
thin sheet of paper or a thin sheet of bakelite or Teflon. The bonded strain gauge is connected to the
Wheatstone bridge circuit.
WIRE STRAIN GAUGE:
The resistance element is in the form of wire foil or film of
the material.
In a metal bonded strain gauge a fine wire element, about
0.025 mm or less in diameter is looped back and forth on
the base carrier or mounting plate. The base is cemented to
the member subjected to the stress.
The grid fine wire is cemented on a carrier which may be a
thin sheet of paper bakelite or Teflon.

STRAIN GAUGES
METALFOIL:
The strain is detected by using a metal foil. The metal foil is pasted on one side of the plastic The leads
are soldered to the metal foil for connecting the Wheatstone bridge.
The metal and alloys used for the foil or wire are Constantan(Cu-Ni), Nichrome V(Ni-Cr),
Metal Foil strain gauges exhibit a higher
Isoelastic(Fe-Ni-Cr-Mn-Mo), Platinum-Tungsten(Pt-W).
gauge factor than wire foil strain gauges.
ROSETTE STRAIN GAUGES:

STRESS & STRAIN MEASUREMENTS: STRAIN
GAUGE ROSETTES.
A strain gage rosette is, by definition, an arrangement of two or more closely positioned gage grids,
separately oriented to measure the normal strains along different directions in the underlying surface of
the test part. Rosettes are designed to perform a very practical and important function in experimental
stress analysis
To increase the accuracy of a strain rosette, large angles are used. A common rosette of three gages is
where the gages are separated by 45 o, or θa = 0 o, or θb = 45 o, or θc = 90 o. The three equations can
then be simplify to

GAUGE ROSETTES.
A wire strain gage can effectively measure strain in only one direction. To determine the three
independent components of plane strain, three linearly independent strain measures are needed, i.e.,
three strain gages positioned in a rosette-like layout.
Consider a strain rosette attached on the surface with an angle a from the x-axis. The rosette itself
contains three strain gages with the internal angles b and g, as illustrated on the right.
Suppose that the strain measured from these three strain gages are ea, eb, and ec, respectively.
The following coordinate transformation equation is used to convert the longitudinal strain from each
strain gage into strain expressed in the x-y coordinates,
These equations are then used to solve for the three unknowns, ex, ey, and exy.

GAUGE ROSETTES.
The formulas use the strain measure εxy as opposed to the engineering shear strain γxy, . To use γxy,
the above equations should be adjusted accordingly.
The free surface on which the strain rosette is attached is actually in a state of plane stress, while
the formulas used above are for plane strain. However, the normal direction of the free surface is
indeed a principal axis for strain. Therefore, the strain transform in the free surface plane can be
applied.
Case 1: 45º strain rosette aligned with the x-y axes, i.e.,  = 0º,  =  = 45º.

GAUGE ROSETTES.
Case 2: 60º strain rosette, the middle of which is aligned with the y-axis, i.e.,  = 30º,  =  = 60º

REFERENCES
1. EXPERIMENTAL METHODS FOR
ENGINEERS / HOLMAN/MCGRAW HILL.
2. Mechanical Measurements / Sirohi and Radhakrishna / New Age.
3. Instrumentation & Mech. Measurements /A.K. Tayal /Galgotia Publications.
4. Instrumentation and Control systems! S.Bhaskar/Anuradha Agencies.
5. Instrumentation, measurement & analysis IB.C.Nakra & K.K.Choudhary/
TMH.
6. Principles of Industrial Instrumentation and Control Systems Chennakesava R
Alavala/ Cengage Learning.
7. Measurement systems: Application and design, Doeblin Earnest. O.Adaptation
by Manik and Dhanesh/ TMH.
8. Mechanical and Industrial Measurements / R.K. Jain/ Khanna Publishers.
9. Mechanical Measurements / BeckWith, Marangoni,Linehard, PHI / PE.

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