1. STRAIN GAUGE

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

3. INTRODUCTION
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(∆l) per unit length(I)Usually in m𝜀 (𝜀x10-6)
Strain 𝜀 𝐿 = ∆𝑙 𝑙

4. DEFINITION
A strain gauge is an example of passive transducer that converts a mechanical displacement into a change of resistance.
A strain gauge is a thin, wafer-like device that can be attached to a variety of materials to measure applied strain.

5. STRUCTURE
The majority of strain gauges are foil types, available in a wide choice of shapes and sizes to suit a variety of applications. They consist of a pattern of resistive foil which is mounted on a backing material.
They operate on the principle that as the foil is subjected to stress, the resistance of the foil changes in a defined way.

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

7. Types of Strain 1. Longitudinal (axial) strain -- Force Axis -- 𝜺 𝐿
Based on the Axis of Applied Force
1. Longitudinal (axial) strain -- Force Axis -- 𝜺 𝐿
2. Transverse strain -- Perpendicular Axis -- 𝜺 𝑇
Longitudinal Strain
𝑷𝒐𝒊𝒔𝒔𝒐𝒏𝒔 𝒓𝒂𝒕𝒊𝒐 𝝂 = −𝜺 𝑻 𝜺 𝑳
𝜺 𝑻 <| 𝜺 𝑳 |
Transverse Strain

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

9. Resistive Strain Gauge
Strain gauge is bonded to an object ,When subject to strain, its resistance R changes, the fractional change in resistance ∆𝑹 𝑹 being proportional to the mechanical strain ∆𝑳 𝑳 .
Mechanical strain 𝜺 𝑳 = ∆𝒍 𝒍
Electrical strain ∆𝑹 𝑹 =𝑮. ∆𝒍 𝒍
Electrical Output 𝑬 𝒐 ∝ ∆𝑹 𝑹
G is the gauge factor (Strain Factor)
Strain Gauge
Wheatstone Bridge

10. Gauge Factor
The resistance R of a conductor of cross section area A, length L, made of material of resistivity 𝜌 is 𝑹=𝝆 𝑳 𝑨
Gauge Factor is Defined as 𝑮= ∆𝑹 𝑹 ∆𝑳 𝑳 = ∆𝑹 𝑹 𝜺 𝑳
∆𝑹=𝑹.𝑮. 𝜺 𝑳
Where ∆𝑅 𝑏𝑒𝑖𝑛𝑔 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑟𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑑𝑢𝑒 𝑡𝑜 𝑎𝑥𝑖𝑎𝑙 𝑆𝑡𝑟𝑎𝑖𝑛 𝜀 𝐿 𝑤ℎ𝑖𝑐ℎ 𝑖𝑠 ∆𝐿 𝐿
∆𝑅 𝑅 = ∆𝜌 𝜌 + ∆𝐿 𝐿 − ∆𝐴 𝐴
∆𝑅 𝑅 = ∆𝜌 𝜌 + ∆𝐿 𝐿 −2 ∆𝐷 𝐷
∆𝑅 𝑅 = ∆𝜌 𝜌 + 𝜀 𝐿 −2 𝜀 𝑇 Where 𝜀 𝐿 = ∆𝐿 𝐿 , 𝜀 𝑇 = ∆𝐷 𝐷
∆𝑅 𝑅 𝜀 𝐿 = ∆𝜌 𝜌 𝜀 𝐿 + 𝜀 𝐿 𝜀 𝐿 −2 𝜀 𝑇 𝜀 𝐿
𝐺= ∆𝜌 𝜌 𝜀 𝐿 +1+2𝝂≈𝟏+𝟐𝝂
Area A is geometric dimension of strain gauge, 𝐴= 𝜋 4 𝐷 2 ; where D Diameter
∆𝐴 𝐴 =2 ∆𝐷 𝐷
Where𝜈= −𝜀 𝑇 𝜀 𝐿

11. Strain Gauge Sensitivity
Strain measurement involves a very small quantity (a few 𝑚𝜀)
Therefore to measure strain, requires accurate measurement of
a very small change of resistance.
Example:
For a strain of 500 m𝜺, with Gauge factor= 2, strain gauge has R=120 Ω
Then ∆𝑹=𝑹.𝑮. 𝜺 𝑳
= 120 X 2 X 500 m𝜺
∆𝑹 = 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.

12. Wheatstone Bridge
OPAM is used to increase the linearity by reducing the loading effect on the wheat-stone Bridge.
𝑉 𝑜𝑢𝑡 =( 𝑅 4 𝑅 3 + 𝑅 4 − 𝑅 2 𝑅 1 + 𝑅 2 ) 𝑉 𝑖𝑛
For Balanced Bridge
𝑖.𝑒. 𝑅 1 = 𝑅 2 = 𝑅 3 = 𝑅 4
𝑉 𝑜𝑢𝑡 =0

13. Quarter Bridge 𝐹𝑜𝑟 𝑅 1 =𝑅+∆𝑅 (𝑇𝑒𝑛𝑠𝑖𝑙𝑒) 𝑅 2 = 𝑅 3 = 𝑅 4 =𝑅
𝐹𝑜𝑟 𝑅 1 =𝑅+∆𝑅 (𝑇𝑒𝑛𝑠𝑖𝑙𝑒)
𝑅 2 = 𝑅 3 = 𝑅 4 =𝑅
𝑽 𝒐𝒖𝒕 = 𝑽 𝒊𝒏 𝟒 . ∆𝑹 𝑹

14. Half Bridge
The arrangement becomes more sensitive due to two active strain gauges
Temperature effects are cancelled out.
𝐹𝑜𝑟 𝑅 1 =𝑅+∆𝑅 (𝑇𝑒𝑛𝑠𝑖𝑙𝑒)
𝑅 2 =𝑅−∆𝑅 (𝐶𝑜𝑚𝑝𝑟𝑒𝑠𝑠𝑖𝑣𝑒)
𝑅 3 = 𝑅 4 =𝑅
𝑽 𝒐𝒖𝒕 = 𝑽 𝒊𝒏 𝟐 . ∆𝑹 𝑹

15. Full Bridge
This arrangement is used to give maximum sensitivity combined with full temperature compensation
𝐹𝑜𝑟 𝑅 1 = 𝑅 4 =𝑅+∆𝑅 (𝑇𝑒𝑛𝑠𝑖𝑙𝑒)
𝑅 2 = 𝑅 3 =𝑅−∆𝑅 (𝐶𝑜𝑚𝑝𝑟𝑒𝑠𝑠𝑖𝑣𝑒)
𝑽 𝒐𝒖𝒕 = 𝑽 𝒊𝒏 . ∆𝑹 𝑹

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

17. Bonded Strain Gauge
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.                                                                                                                                            

18. Unbonded Strain Gauge
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.

19. Rosettes 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.

20. Semiconductor Strain Gauge
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.