A presentation on strain gauge: its characteristics equations and types. Along with derivation of gauge factor.

2. • Introduction
Strain
Measurement Techniques
•Types of Strain
•Resistive Strain gauge
•Gauge Factor
•Strain Gauge Sensitivity
•Wheat Stone Bridge
•Types of Strain Gauges
•References

3. STRAIN
A strain is a measure of deformation representing the
displacement between particles in the body relative to a
reference length.
Which is defined as the change in length(Δl) per unit
length(I) Usually in m휀 (휀x10-6)
Strain 휀퐿 = Δ푙
푙

4. Mechanical Force
Strain Gauge
Electrical
Signal
Signal
Conditioning
Calibration
Readout
• Electrical
• Optical
• Mechanical
• Voltage
• Current
• Potential
Divider
• Wheatstone
Bridge
Change
in
Property

5. Based on the Axis of Applied Force
1. Longitudinal (axial) strain -- Force Axis --휺퐿
2. Transverse strain -- Perpendicular Axis -- 휺푇
푷풐풊풔풔풐풏풔 풓풂풕풊풐 흂 =
−휺푻 휺푳
휺푻 < |휺푳|
Longitudinal
Strain
Transverse
Strain

6. Based on the Direction of Applied Force
1.Tensile strain
If the force tends to stretch the gauge
2. Compressive Strain
If the force tends to compress the gauge

7. Strain gauge is bonded to an object ,When subject to strain, its
resistance R changes, the fractional change in resistance Δ푹
푹
being proportional to the mechanical strain Δ푳
푳.
Mechanical strain 휺푳 = Δ풍
풍
Strain Gauge
Electrical strain Δ푹
푹 = 푮. Δ풍
풍
Wheatstone Bridge
Electrical Output 푬풐 ∝ Δ푹
푹
G is the gauge factor (Strain Factor)

8. The resistance R of a conductor of cross section area A, length L, made of material of
resistivity 휌 is 푹 = 흆
푳
푨
Gauge Factor is Defined as 푮 =
Δ푹
푹
Δ푳
푳
=
Δ푹
푹
휺푳
Δ푹 = 푹. 푮. 휺푳
Where Δ푅 푏푒푖푛푔 푐ℎ푎푛푔푒 푖푛 푟푒푠푖푠푡푎푛푐푒 푑푢푒 푡표 푎푥푖푎푙 푆푡푟푎푖푛 휀퐿 푤ℎ푖푐ℎ 푖푠
Δ퐿
퐿
Δ푅
푅
=
Δ휌
휌
+
Δ퐿
퐿
−
Δ퐴
퐴
Δ푅
푅
=
Δ휌
휌
+
Δ퐿
퐿
− 2
Δ퐷
퐷
Δ푅
푅
=
Δ휌
휌
+ 휀퐿 − 2휀푇 Where 휀퐿 =
Area A is geometric dimension of strain gauge,
퐴 =
Δ퐿
퐿
, 휀푇 =
Δ퐷
퐷
Δ푅
푅
휀퐿
=
Δ휌
휌
휀퐿
+
휀퐿
휀퐿
− 2
휀푇
휀퐿
퐺 =
Δ휌
휌
휀퐿
+ 1 + 2흂 ≈ ퟏ + ퟐ흂 Where 휈 = −휀푇
휀퐿
휋
4
퐷2; where D Diameter
Δ퐴
퐴
= 2
Δ퐷
퐷

9. Strain measurement involves a very small quantity (a few 푚휀)
Therefore to measure strain, requires accurate measurement of
a very small change of resistance.
Example:
For a strain of 500 m휺, with Gauge factor= 2, strain gauge has R=120 Ω
Then Δ푹 = 푹. 푮. 휺푳
= 120 X 2 X 500 m휺
Δ푹 = 0.12 Ω (it’s a very small resistance change)
To measure such a small change in resistance, a bridge circuit is needed
to convert this change in resistance to the change in voltage.

10. OPAM is used to increase the
linearity by reducing the
loading effect on the wheat-stone
Bridge.
푉표푢푡 = (
푅4
푅3 + 푅4
−
푅2
푅1 + 푅2
)푉푖푛
For Balanced Bridge
푖. 푒. 푅1 = 푅2 = 푅3 = 푅4
푉표푢푡 = 0

11. 퐹표푟 푅1 = 푅 + Δ푅 (푇푒푛푠푖푙푒)
푅2 = 푅3 = 푅4 = 푅
푽풐풖풕 =
푽풊풏
ퟒ
.
Δ푹
푹

12. 퐹표푟 푅1 = 푅 + Δ푅 (푇푒푛푠푖푙푒)
푅2 = 푅 − Δ푅 (퐶표푚푝푟푒푠푠푖푣푒)
푅3 = 푅4 = 푅
푽풐풖풕 =
푽풊풏
ퟐ
.
Δ푹
푹
• The arrangement becomes more
sensitive due to two active strain
gauges
• Temperature effects are cancelled
out.

13. 퐹표푟 푅1 = 푅4 = 푅 + Δ푅 (푇푒푛푠푖푙푒)
푅2 = 푅3 = 푅 − Δ푅 (퐶표푚푝푟푒푠푠푖푣푒)
푽풐풖풕 = 푽풊풏.
Δ푹
푹
• This arrangement is used to give
maximum sensitivity combined
with full temperature
compensation

14. Various means like Mechanical, optical or electrical can be used to measure
deformation (strain) of an object.
o Mechanical strain gauges offer certain limitations like low resolutions. Besides
they are bulky and difficult to use.
o Capacitance and Inductance-based strain gages were introduced but these
devices sensitivity to vibration, their mounting requirements, and circuit
complexity restricted their usage.
o A photoelectric gauge can be as short as 1/16 inch but its usage proves to be
extremely costly and delicate.
o Other types of Strain Gauges are:
• Bonded Strain Gauges
• Unbonded Strain Gauges
• Rosettes
• Semiconductor (Piezo-resistive) strain gauges

15.  In this type strain gauge is bonded directly to the surface
of the specimen being tested with a thin layer of adhesive
cement .
 The bonded strain gauge will be either a wire type or a foil
type as shown in the figure below.
 It is connected to a paper or a thick plastic film support.
 The measuring leads are soldered or welded to the gauge
wire.

16.  Unbonded strain gauge is used in places where the
gauge is to be detached and used again and again.
 Unbonded strain gauges consists of frames P and Q
carrying rigidly fixed insulated pins. These two frames
can move relative with respect to each other.
 A fine wire resistance strain gauge
is stretched around the insulated pins.
 When a force is applied on the structure under study
(frames P & Q), frames P moves relative to frame Q,
and due to this strain gauge will change in length and
cross section i.e. resistance changes which is
measured by a Wheatstone Bridge.

17.  It is a combination of strain gauges.
 An element may be subjected to
stress in any direction and hence it
may be difficult to find out the
direction of principal stress.
 Therefore we need a strain gauge
which measures the principal strain
without actually knowing its
direction.
 Rosettes which in combination of
two or three strain gauges are used
for such a purpose.

18.  Employs piezoresistive property, i.e. the
change in value of resistance due to the
change in resistivity
 Semiconductor materials such as silicon or
germanium are used as resistive materials.
 High gauge factor of about ±130.
 Very small in length ranging from 0.7 to 7
mm.

19. Strain: http://en.wikipedia.org/wiki/Strain
Strain Gauge: http://www.omega.com/literature/transactions/volume3/strain.html
Gauge Factor: http://www.scribd.com/doc/53005420/Strain-Gauge
Compression/Tension: http://www.ishida.com/technologies/loadcell/html.html
Gauge Sensitivity:
http://www.efunda.com/designstandards/sensors/strain_gages/strain_gage_sensitivity.cfm
Voltage Equation: http://zone.ni.com/devzone/cda/tut/p/id/3642
Resistivity Equation: http://en.wikipedia.org/wiki/Resistivity
Wheatstone Bridge: http://www.electronics-tutorials.ws/blog/wheatstone-bridge.html
Types of Strain Gauge : http://www.chipkin.com/types-of-strain-gauges/
Bonded Strain gauge:
http://instrumentationandcontrollers.blogspot.in/2010/11/bonded-strain-gauges.html
Unbonded Strain Gauge:
http://instrumentationandcontrollers.blogspot.in/2010/11/unbonded-strain-gauges.html
Semiconductor Strain Gauge:
http://www.kulite.com/docs/products_overview/StrainGageManualDigital.pdf
A.K.Sahwany ,”Electrical And Electronics Measurement”
Alok Baura, “Industrial instrumentation”
C S Rangan, G R Sarma and V S V Mani ,”Instrumentation devices and systems”