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.

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Jeremy Church
12 years ago

The picture of the gage at the top can be misleading by showing only 2 lead wires. One of the bigger sources of error due to temperature is the lead wires. This can be compensated for with a 3-wire lead configuration. In a quarter bridge setup there should be two lead wires from one side of gage and one from the other. These leads should all run together to experience whatever temperature delta is present. The resistance change is then canceled by the bridge circuit. It is stated that 3-wire should be used under the quarter bridge but does not state how it should be laid out. A simple jumper at the connector would do the job but not properly compensate for the temperature and introduce error.

12 years ago

I having a hard time to download and actual browse the pdf file. It took me forever so I finally quit

mok
12 years ago

A strain gauge has two fixed resistors R3 and R4 of 150? each and a variable resistor R2 which is 110? at zero strain and 110.75? with the strain (R1=Rg). The gauge factor is 2.54. How to determine the strain, where the strain gauge is attached? Can you help me on this problem? Thank you sir…

12 years ago

Hello Mok,

It really sounds like your trying to do it all in one giant step. Perhaps you should break the problem down into smaller chunks.

A strain gauge is like a resistor, a strain gauge bridge is made of 4 resistive elements.

All the resistors in the bridge should be of the same value, 120 Ohms is often used in industry. The resistors must be the same value to balance the bridge. There are other techniques to balance a bridge, but for clarity in this case we’ll assume the bridge must be balanced by the four resistors having the same resistance.

When you have setup your bridge you should attach the active strain gauge (assuming you have only one active element in your bridge) to the area where you are interested in knowing the strain. I am afraid we cannot offer advice about where to attach your gauge.

You should then be able to read back a value of zero volts from your bridge, then when your material under test has some forced applied, which produces a strain in the area your gauge is attached, you’ll see the voltage from the bridge change to something other than zero. This voltage change is proportional to the strain in that gauge.

You simply then use the bridge and gauge factor, supply voltage, output voltage and non-deformed and deformed gauge resistance values to calculate the strain.

Alex
11 years ago

What could cause large spikes (+ and -, some to infinity) in strain gauge readings? I am using strain gauges to measure the force required to cycle through exercise bikes at different levels of resistance. The resulting graphs reveal trends of required force but there are so many spikes and variations it is not accurate enough. The gauges are electrically grounded. They are subjected to vibration during the testing.

Nick
11 years ago

Hello!

I would like to ask you a question. Is it possible to measure vibrations with the strain gauges? I do not want to use an accelerometer because they are too big for my application (I wanted something like the surface bonded strain gauges).

ayesha
11 years ago

hi
i am doing mechanical engg.in final year now.we are trying to fabricate a dynamometer to measure torque using electrical strain gauges.but we are facing the problem of slip rings.that we cannot afford them.could you please suggest any idea how to use strain gauges on a rotating shaft to measure torque with any altrnative to slip rings or any other techinique.thanx

9 years ago

If you are still interested in wireless measurement it is worth having a look at this website :

http://www.datatel-telemetry.de/en/

Editor
11 years ago

Hello Ayesha
I am not a strain gauge expert, but I will pass your question to some of our tech guys and see what they say.

Stephen Barnes
9 years ago

Thanks for putting this together! I noticed a small detail in the beginning. Resistivity has units of resistance * length. Normally it’s listed as ohm*meters (or micro-ohm*centimeters). The formula you listed says ohms per meter which is incorrect.

Jon Wilson
9 years ago

Excellent article explaining how strain gages work in bridge circuits.
Many strain gages, used in transducers, are silicon chips doped to optimize their strain constants. They have much greater sensitivity than metal gages, but also are more difficult to match and to temperature compensate. Most recent transducers use four strain gages plus various compensation resistors in the bridge circuit.

pankaj
9 years ago

hello.
i am doing electronics engg. i am working on real time experiment of weight measurement using strain gauge using labview software and data acquitation cards. please let me know how strain gauge works in this experiment.

9 years ago

Dear James,

Sorry to be pedantic, but the second equation for resistance of a piece of copper wire appears to be incorrect. The wire is stretched to 2m and its diameter decreases to 0.5mm^2, which equates to 0.0005m^2, not 0.005m^2. So the resistance is 0.144 Ohms, not 0.00144 Ohms.

Yours sincerely,

Bruce Hefford

Teer
8 years ago

Hello,

I am working with strain gauge measurement on the electrical steel lamination, any effect with strain if while I am measuring the lamination vibrate ?

Thanks.

selva
8 years ago

Sir am studying final year electronics engineering.I am in interest of doing project with strain gauge.My doubt is “how to measure an input value and output value of the strain gauge and also how to use in lab view “.I need a full explanation about this.pls help me…..

MECHRI
8 years ago

Hellow Mr. James Wren

Please, I would like to know eatch kind of strain will be mesured by the strain gauges :
ENG. Strain or the True strain.

Beginner

Regards

Arash
8 years ago

For electrical steel laminates (specially grain oriented laminates), it’s a bit tricky to polish the surface to mount strain gages. These samples are very thin, and by sanding you can significantly change the thickness of the laminates right at the spot where you are mounting the gage. How do you prepare the surface of electical steel laminates for good bonding of strain gages?

karthik
8 years ago

Hello.
what kind of wires can we use to connect the lead wires of strain gauge. we use 2 mm gauge length strain gauge ?? And how can we decide the sampling rate so the we don’t pic the noise ??

7 years ago

now, I have a question, I should design a sensor who can mesure 2 forces fx, fy and moment, but I have some vibration around these forces and moment,(you konw,there is a cantilever beam and all of the forces and moment effect on that) does strain gage sense the vibration, how can I do that? do you have any idea? because I serached alot about these problem..but… I used a strain gage in direction of longitude and one in latitude for mesuring fx, fy,M, I will be glad if some one helps me?

mukund
7 years ago

Sir,
I want to know about the role of gauge factor in strain calculation.we are using 3 element strain gauge and quarter bridge configuration at data logger side.

Natacha
7 years ago

That’s an awesome explanation thanks. I’ve seen some great models of strain gauges to get a more precise idea here: http://www.directindustry.com/industrial-manufacturer/strain-gauge-73369.html

Daniel Jones
7 years ago

Hi,

Great blog, I have been doing some research and it looks like a fundamental parameter of the strain gauge is the sensitivity to strain, which is the gauge factor. I believe the gauge factor is defined as the ratio of change in resistance to the change in length (strain). The gauge factor for metallic strain gages is typically around 2, or so it seems.

Can you comment on this please?

6 years ago

Hi,
I have some questions, does strain gauge have minimum strain range? in which the strain gauge cannot give any response with gauge strain smaller than that minimum. And what’s the difference in accuracy between a 2-element gauge(plane and cross) and two single gauge.

I guess some small vibration of sample may not deform the gauge, so is there any data or specifications of strain gauge which relate to that?

Nikhil Gupta
5 years ago

Hi,
Please tell me the option in DATS which is used to remove spike in strain gauge signal.

Thanks,
Nikhil.

Deepak
4 years ago

Hi,
Could you explain if pressure and vibration affect strain gauge?

5 months ago

The post is well explained about how strain gauges work in bridge circuits. Keep sharing such helpful information.

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