###### 30th December 2015 | By: pambospalas

## Strain Gauges [PART 1 – Strain Definition]

This series of posts will cover the fundamental principles of strain gauges, and provide a brief introduction of how they work and how they can be used. Measuring strain is a very basic necessity for a wide range of engineering applications, and whilst there are many methods for doing so, the strain gauge is one of the most common.

Strain can be defined as a normalized measure of the fractional deformation that a body undergoes relative to a reference length, due to an applied force. This is seen more clearly below in Figure 1, along with the equation for strain.

It should be noted that strain can be positive, in the case of tension, or negative when the body is in compression. In fact, in almost all cases, there is a combination of both – this can be seen in the bending of a beam in Figure 2.

Figure 2 – Tensile and Compressive strains in a beam.

Even in the case of uniaxial tension, shown in Figure 1, some compressive Poisson Strain is evident in the transverse direction, whereby the beam will contract. The amount of strain is defined by the Poisson Ratio, which is a material property and defined as the negative ratio of transverse to axial strain – for mild steel this is about 0.3, meaning that for every unit of axial tension the beam will contract in the perpendicular direction by 0.3 units.

Values of strain are usually expressed in parts per million, or microstrains (e x 10^-6), as in practice they are very small. So if a beam with length 1m undergoes axial forces and is extended to 1.000005m, then the strain is: (1.000005 – 1)/1 = 0.000005 or 5 microstrains. It should also be noted that strain is dimensionless.

The next section will focus on the strain gauge itself and how it works.

## Peter

## 3rd February 2015 @ 16:49

Fascinating article, one of the best ones here.

Could you please elaborate on how the Poisson Ratio is related to the axial strain?

Also, how do you predict or anticipate the direction of contraction, on paper?

## Pambos Palas

## 7th February 2015 @ 12:02

Thank you Peter!

The Poisson Ratio is the (negative) ratio of axial strain to transverse strain – so if you know the strain in one direction, let’s say 1mm expansion along the x-axis, you will know that for a material with a Poisson Ratio of 0.25 you will have a contraction of 0.25 mm in the y and z axes. This is true for isotropic materials, where the properties are similar in all orientations.

As for the direction of expansion/contraction, this is quite straightforward for simple shapes, as it is in the perpendicular directions to the force or principle strain.