A resistance wire strain gauge with a gauge factor of 2 is bonded to a steel structural member subjected to a stress of 100 MN / m². The modulus of elasticity of steel is 200 GN / m². The change in the value of gauge resistance due to the applied stress will be

Concept:

The gauge factor is defined as the ratio of per unit change in resistance to per unit change in length. It is a measure of the sensitivity of the gauge.

Mathematically, this is defined as:

\({G_f} = \frac{{{\rm{\Delta }}R/R}}{{{\rm{\Delta }}L/L}}\)

The above can be written as:

\(\frac{{{\rm{\Delta }}R}}{R} = {G_f}\frac{{{\rm{\Delta }}L}}{L} = {G_f}\varepsilon \)

Where ε = strain and is also defined as:

\(\epsilon=\frac{Stress}{Y}\)

Y = modulus of elasticity

Calculation:

Given G_f = 2, Stress = 100 MN/m² and Y = 200 GN/m²

Putting on the respective values, we get:

\(\frac{{{\rm{\Delta }}R}}{R} = {G_f}\varepsilon =G_f\times\frac{Stress}{Y}\)

\(\frac{{{\rm{\Delta }}R}}{R} =2\times \frac{100\times 10^6}{200\times 10^9}\)

∴ The change in the value of gauge resistance due to the applied stress will be:

\(\frac{{{\rm{\Delta }}R}}{R} =2\times 0.5\times 10^{-3}\)

\(\frac{{{\rm{\Delta }}R}}{R} =0.1 \%\)