# What Is A Strain Gauge?

A strain gauge is an electrical sensor which is used to accurately measure strain in a test piece. Strain gauges are usually based on a metallic foil pattern. The gauge is attached to the test piece with a special adhesive. As the test piece is deformed, so the adhesive deforms equally and thus the strain gauge deforms at the same rate and amount as the test piece. It’s for this reason that the adhesive must be carefully chosen. If the adhesive cracks or becomes detached from the test piece any test results will be useless.

Strain gauges are used not just for metals; they have been connected to the retina of the human eye, insects, plastics, concrete and indeed any material where strain is under investigation. Modern composite materials like carbon fibre when under development are often constructed with strain gauges between the layers of the material.

The strain gauge is effectively a resistor. As the strain increases so the resistance increases.

In a basic sense a strain gauge is simply a long piece of wire. Gauges are mostly made from copper or aluminium (Figure 1). As the wire in the strain gauge is mostly laid from end to end, the strain gauge is only sensitive in that direction.

When an electrical conductor is stretched within the limits of its elasticity it will become thinner and longer. It is important to understand that strain gauges actually deform only a very small amount, the wire is not stretched anywhere near its breaking point. As it becomes thinner and longer it’s electrical characteristics change. This is because resistance is a function of both cable length and cable diameter.

The formula for resistance in a wire is

$Resistance\,in\,Ohms (R) = \frac{{\rho}L}{\alpha}$

where $\rho$ is resistivity in ohm metres, $L$ is length in metres and $\alpha$ in m2.

For example, the resistance of a copper wire which has a resistivity of 1.8 x 10-8 ohm metres, is 1 metre long and has a cross sectional area of 2mm2 would be

$R = \frac{1.8*10^{-8} *1}{0.002^2} = \frac{0.000000018}{0.000004} = 0.0045\Omega$

Resistivity is provided by the manufacturer of the material in question and is a measurement of how strongly the material opposes the flow of current. It is measured in ohm metres.

If in our example the cable was then put under certain strain its length would extended to 2 metres, as it was stretched longer it would get thinner, it’s cross sectional area would decrease. In this example to 0.5 mm2 the resistance now would be

$R = \frac{1.8*10^{-8} *2}{0.0005^2} = \frac{0.000000036}{0.00000025} = 0.144\Omega$

As can clearly be seen the resistance is now different, but the resistances in question are very small. This example shows only the difference when the characteristics of the copper wire have changed. It is not practically possible to stretch and extend a piece of copper wire by these amounts. The example merely shows how resistance changes with respect to length and cross sectional area and demonstrates that strain gauges, by their very nature, exhibit small resistance changes with respect to strain upon them.

These small resistance changes are very difficult to measure. So, in a practical sense, it is difficult to measure a strain gauge, which is just a long wire. Whatever is used to measure the strain gauges resistance will itself have its own resistance. The resistance of the measuring device would almost certainly obscure the resistance change of the strain gauge.

 Figure 2: A Wheatstone bridge Figure 3: With shunt resistor

The solution to this problem is to use a Wheatstone bridge to measure the resistance change. A Wheatstone bridge is a device used to measure an unknown electrical resistance. It works by balancing two halves of a circuit, where one half of the circuit includes the unknown resistance. Figure 2 shows a classical Wheatstone bridge, Rx represents the strain gauge.

Resistors R2, R3 and R4 are known resistances. Normally, $120\Omega$, $350\Omega$ or $1000\Omega$ are used depending on the application. Knowing the supply voltage and the returned signal voltage it’s possible to calculate the resistance of Rx very accurately.

For example if R2, R3 and R4 are $1000\Omega$ and if the measured signal voltage between measurement points A and B was 0 Volts then the resistance of Rx is

$\frac{R3}{R4} = \frac{Rx}{R2}\,or\,Rx=\frac{R3}{R1}*R2$

For our example we get

$Rx = \frac{1000\Omega}{1000\Omega} * 1000\Omega = 1000 \Omega$

This implies a perfectly balanced bridge. In practice, because the strain gauge goes through different strain levels its resistance changes, the measured signal level between measurement points A and B is not zero. This is not a problem when using a system like the Prosig P8000 as it can accurately measure the voltage between measurement points A and B.

It is necessary to know the relationship between resistance and voltage. Only then can the measured voltage be related to a resistance and, hence, a strain value.

Figure 3 shows the addition of another resistor RS, called the shunt resistor. The shunt resistor is a known fixed value, normally $126,000\Omega$.

The Shunt resistor is added for calibration purposes and is a very high precision resistor. By measuring the voltage between measurement points A and B with the shunt resistor across Rx, a voltage with the shunt resistor in place is known. Then by removing the shunt resistor, which is a known $126,000\Omega$ and measuring the voltage between measurement points A and B again, it’s possible to relate the measured voltage change to a known resistance change. Therefore the volt per ohm value is known for this particular bridge and this particular Rx.

In order to go one step further and calculate the strain from the resistance, the gauge factor must be known. This is a calibrated number provided by the manufacturer of the strain gauge. With this information the sensitivity of the whole sensor can be calculated. That is, the volt per strain is known.

Inside the P8000 the resistors used to complete the bridge are very high precision. This allows the Prosig P8000 to calculate the resistance, and therefore, strain with a high degree of accuracy.

Strain gauge readings can be affected by variations in the temperature of the strain gauge or test piece. The wire in the strain gauge will expand or contract as an effect of thermal expansion, which will be detected as a change in strain levels by the measuring system as it will manifest itself as a resistance change. In order to address this most strain gauges are made from constantan or karma alloys. These are designed so that temperature effects on the resistance of the strain gauge cancel out the resistance change of the strain gauge due to the thermal expansion of the test piece. Because different materials have different thermal properties they therefore have differing amounts of thermal expansion.

So, where temperature change during the test is an issue, temperature compensating strain gauges can be used. However this requires correctly matching the strain gauge alloy with the thermal expansion properties of the test piece and the temperature variation during the test. In certain circumstances temperature compensating strain gauges are either not practical nor cost effective. Another more commonly used option is to make use of the Wheatstone bridge for temperature compensation.

When using a Wheatstone bridge constructed of four strain gauges, it is possible to attach the four gauges in a fashion to remove the changes in resistance caused by temperature variation. This requires attaching the strain gauge Rx in the direction of interest and then attaching the remaining strain gauges, R2, R3 and R4, perpendicular to this. The piece under test however must only exhibit strain in the direction across Rx and not in the perpendicular direction.

It’s important to understand that the R2, R3 and R4 strain gauges should not be under strain, hence their direction. This means the whole bridge is subject to the same temperature variations and therefore stays balanced from a thermal expansion point of view. As the resistance changes due to temperature, all the resistances in all four gauges change by the same amount. So the voltage at measurement point A and B stays constant due to temperature fluctuations. Only the strain in the desired direction, across Rx, in the test piece affects the measured voltage readings.

The Prosig P8000 system has multi-pin inputs, these allow for the connection of strain gauges in all the various different bridge configurations.

 Figure 4: Quarter bridge Figure 5: Half bridge Figure 6: Full bridge

The configurations that strain gauges can be used in are,

Quarter Bridge is the most common strain gauge configuration. As can be seen in Figure 4 it is actually a three wire configuration. The rest of the bridge as shown in Figure 2 is completed inside the Prosig P8000 system. Quarter Bridge uses three wires to allow for accurate measurement of the actual voltage across S1.

Half Bridge is not an often used strain gauge configuration. As can be seen in Figure 5 it is actually a five wire configuration. The rest of the bridge as shown in Figure 2 is completed inside the Prosig P8000 system. The main advantage of the Half Bridge configuration is that both the strain gauges S1 and S2 can be attached to the test piece, but perpendicular to each other. Which as previously discussed allows for temperature compensation.

Full bridge is used for situations where the fullest degree of accuracy is required. The Full Bridge configuration is a six wire system, as shown in Diagram-5. The Full Bridge configuration is the most accurate in terms of temperature variation because it can have two active gauges, S1 and S4. The gauges can be configured with S1 and S4 in the direction of interest on the test piece and S2 and S3 perpendicular to this. Further the voltage sense lines have no effective current flow and therefore have no voltage drop, therefore the voltage measured by the Prosig P8000 system is the actual voltage that is exciting the bridge. The reason for this requirement is that strain gauges are often on long wires and all wires have their own resistance. The Prosig P8000 system could be exciting the gauge with 5 Volts for example, but the voltage at the active part of the bridge might be 4.95 Volts because of the resistance of the wires carrying the supply voltage. This small change once measured using the sense lines it can be allowed for automatically in the strain calculations inside the data acquisition system.

### Strain gauge measurements with direction

 Figure 7: Strain gauge rosette

Strain Gauges can be configured in a particular pattern that allows for the calculation of the overall strain component, this is often referred to as a strain gauge rosette. As shown in Figure 7, three strain gauges are placed either very close together or in some cases on top of each other. These can be used to measure a complex strain, the strain is complex because it has both amplitude and a direction. Using the Prosig DATS software it is possible to calculate the principle component of the strain, the amplitude over time and to calculate the direction as an angle from the reference X axis over time.

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#### James Wren

Former Sales & Marketing Manager at Prosig
James Wren was Sales & Marketing Manager for Prosig Ltd until 2019. James graduated from Portsmouth University in 2001, with a Masters degree in Electronic Engineering. He is a Chartered Engineer and a registered Eur Ing. He has been involved with motorsport from a very early age with a special interest in data acquisition. James is a founder member of the Dalmeny Racing team.