# Theory of Strain Gauges

The strain in an element is a ratio of change in length in the direction of applied load to the original length of an element. The strain changes the resistance R of the element.

Therefore, we can say,

ΔR/R α ε;

ΔR/R = G ε …eq1

where G is the constant of proportionality and is called as gauge factor. In general, the value of G is considered in between 2 to 4 and the resistances are taken of the order of 100 Ω.

Resistance strain gauge follows the principle of change in resistance as per the equation 1.

It comprises of a pattern of resistive foil arranged as shown in Figure. These foils are made of Constantan alloy (copper-nickel 55-45% alloy) and are bonded to a backing material plastic (ployimide), epoxy or glass fiber reinforced epoxy.

The strain gauges are secured to the workpiece by using epoxy or Cyanoacrylate cement Eastman 910 SL. As the workpiece undergoes change in its shape due to external loading, the resistance of strain gauge element changes.

This change in resistance can be detected by a using a Wheatstone’s resistance bridge as shown in below Figure . In the balanced bridge we can have a relation,

R2/ R1 = Rx / R3

where Rx is resistance of strain gauge element, R2 is balancing/adjustable resistor, R1 and R3 are known constant value resistors. The measured deformation or displacement by the stain gauge is calibrated against change in resistance of adjustable resistor R2 which makes the voltage across nodes A and B equal to zero.

## Applications of strain gauges

Strain gauges are widely used in experimental stress analysis and diagnosis on machines and failure analysis. They are basically used for multi-axial stress fatigue testing, proof testing, residual stress and vibration measurement, torque measurement, bending and deflection measurement, compression and tension measurement and strain measurement.

Strain gauges are primarily used as sensors for machine tools and safety in automotives. In particular, they are employed for force measurement in machine tools, hydraulic or pneumatic press and as impact sensors in aerospace vehicles.