2020-07-23T22:54:29.000-0400

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Strain gauges are used to measure small deflections in objects due to applied loads. Strain measurements are the basis for predicting how long an object will perform without failure due to these loads.

This article explains how strain gauges work, relevant stress and strain background information, and considerations for their proper usage and applications.

1. What Is Stress?

2. What is Strain?

3. Why Measure Stress and Strain?

4. What is a Strain Gauge?

5. Measurement Principles

6. Wheatstone Bridge

7. Practical Example

8. Basic Strain Gauge Configurations

8.1 Quarter Bridge

8.2 Half Bridge

8.3 Full Bridge

9. Directionality

10. Invention of the Strain Gauge

To understand the goal of strain gauge measurements, it is useful to understand the concepts of stress and strain.

Stress is the internal response of a body to an applied force (

Stress is equal to the applied force divided by the cross-sectional area of the object (

Where:

- s is the stress expressed in units of Pa or psi.
- F is the applied force.
- A is the cross-sectional area of the body.

In response to the applied force the body will deform. It will elongate in the direction of the applied force (

The change in length of the body divided by the original length is called the strain (

Where:

- e is the strain.
- Dl is the change in length of the cylinder.
- l is the original length of the cylinder.

Stress is an important quantity in durability analysis. High stresses can cause fatigue damage and product failure. Parts are typically designed to have a certain “design life”. For example, automotive manufactures may offer a 10 year or 100,000 mile powertrain warranty. They will design the powertrain in such a way that it can withstand the stresses caused by operation for at least the lifetime of the warranty.

If the stress on a part is below the target, then the designer can work on improving the design by removing material to improve other attributes (reduce manufacturing costs, reduce weight, improve fuel economy, etc.).

Stress is a difficult quantity to measure. Some sensors directly measure stress (concrete stress sensors, soil stress sensors), but typically stress is measured indirectly by measuring the strain on an object, and then converting it to stress using Hooke’s law (

Where:

- s is the stress.
- E is Young's Modulus (a material property).
- ε is the strain.

Using the resulting stress or strain time histories, the fatigue life of the object of interest can be predicted. See the Knowledge articles “Strain Life Approach” and “What is a SN-Curve” for more information.

Strain is measured using a sensor called a strain gauge. A strain gauge is a uniaxial transducer that is typically made of a thin metallic wire bent into a rectangular grid. Strain gauges work by relating the change in resistance of the gauge to the strain in an object.

Important characteristics of the strain gauge are highlighted in

A strain gauge uses two principles to measure strain. The first is that the resistance of a wire depends on its length and cross-sectional area. If the length or cross-sectional area of the wire changes due to an applied load, then its resistance will change. The resistance of a piece of wire is described by

Where:

- R is the electrical resistance of the wire expressed in Ohms.
- L is the length of the conductor in meters.
- r is the resistivity of the material. Resistivity is an intrinsic material property that varies with temperature.
- A is the cross-sectional area of the wire.

The second is that the change in resistance of the wire can be related to strain by a property known as the gauge factor (

Where:

- GF is the gauge factor of the strain gauge.
- DR/R is the change in resistance of the gauge divided by the nominal resistance.
- e is the measured strain.

The nominal resistance of a strain gauge is typically 120 or 350 ohms, although other resistances exist.

When a strain gauge is placed on a test article it is attached in such a way that the strain experienced by the test article is transferred to the gauge.

When a load is applied to the test article, it will deform. The attached strain gauge will also deform. The thin resistive wire will either elongate (tension) or shorten (compression). Because the length and cross-sectional area of the wire has changed, it’s resistance will also change.

To measure strain, it is required to measure the change in resistance of the strain gauge. In order to measure strain, the change in resistance needs to be converted into a voltage. This is accomplished using a Wheatstone bridge.

A Wheatstone bridge is a voltage divider circuit which can detect small changes in resistance. Two different portrayals of the Wheatstone bridge are shown in

The bridge is a circuit which consists of a supply voltage and four resistors. The voltage across the bridge, labeled Vout, will be measured.

When a voltage is supplied to the bridge, Vout will be zero if R1 = R2 = R3 = R4. This is called a balanced bridge. Now, imagine R1 is replaced with a strain gauge, G1, that initially has the same resistance as R2, R3, and R4 (

If the strain gauge experiences a force it will deform. That deformation will cause a small change in resistance of the gauge. Because the resistance has changed, the bridge is no longer balanced, and a voltage will be measured at Vout. This voltage can be calculated according to

Where:

- R1, R2, R3, and R4 are the resistances of the Resistors 1, 2, 3, and 4
- VOut is the voltage measured across points 1 and 2
- VSupply is the voltage supplied to the Wheatstone bridge.

Where:

- Vout/Vsupply is the ratio of the output voltage to the supply voltage
- GF is the gauge factor of the strain gauge.
- N is the number of gauges in the Wheatstone bridge.
- e is the strain measured by the Wheatstone bridge.

A single strain gauge is placed in a Wheatstone bridge (

Calculate the output voltage of the Wheatstone bridge and the measured strain.

V_out can be found by rearranging

Rearranging and solving yields:

Because the measured strain is small and dimensionless, a common way of reporting the value is to multiply it by 10e6 and display the units as mm/m or me:

100 mm/m or 100 me

This example highlights several important aspects of strain gauges:

- The output voltage measured from the Wheatstone bridge is very small, usually microvolts. Due to these low levels, gauge measurements can be susceptible to electro-static interference. See the Knowledge article “Simcenter Testlab and Long Strain Cables” for more information.

- The output from the Wheatstone bridge can be increased by either increasing the supply voltage or configuring the bridge with more active strain gauges. High supply voltages can cause excessive heating on the gauge and introduce errors due to thermal strain. To choose an appropriate supply voltage consult this community article "Strain Gauges: Selecting an Excitation Voltage".

- Strain sensors are ratiometric. Most sensors output a voltage that is proportional to an engineering quantity (e.g. mV/g for an accelerometer). A strain gauge outputs a voltage ratio (Vout/Vsupply) that is proportional to strain (mV/V/e).

In order to measure with a strain gauge there must be a complete Wheatstone bridge. If only a single strain gauge is used, as shown below in

There are three basic strain gauge configurations, all based on the Wheatstone Bridge Circuit. They are the quarter-bridge, half bridge, and whole bridge.

The number and orientation of strain gauges in the Wheatstone bridge will determine the sensitivity of the bridge, the types of strain that can be measured (bending, axial, torsion), and ability to compensate for temperature and electromagnetic interference.

A quarter bridge is depicted below. It has one (1) active strain gauge and three (3) high precision resistors (

However, the quarter bridge has a lower sensitivity than the other configurations and it cannot compensate for errors due to thermal effects on the gauge. A quarter bridge can only measure the superimposed strain on an object. It cannot separate bending and axial strains.

A half bridge has two (2) active strain gauges and two (2) high precision resistors (

Depending on the orientation of the gauges, a half bridge can compensate for thermal strains and measure bending and axial strain.

A full bridge has four (4) active strain gauges (

When properly configured a full bridge can be instrumented to measure bending or axial stresses and can be used to measure the torque on a shaft. Full bridges form the basis of more complex sensors like load cells or pressure transducers.

Strain gauges measure the strain along their active direction. It is very important to consider the orientation of the gauge when instrumenting a test object. An example is shown below in

The cylinder is subjected to a compressive force which will cause a compressive strain in the vertical direction. The gauge on the left-hand side will correctly measure the strain caused by the compressive load because the active length of the gauge is in the same direction as the strain.

The gauge on the right will not measure the correct compressive strain. It will measure the poisson strain due to the applied load and some strain due to the transverse sensitivity of the gauge. It will not measure the total compressive strain due to the applied force. Because of the importance of strain gauge orientation, strain gauge rosettes are commonly used to measure strain fields where the direction of the applied load is unknown.

**10. Invention of the Strain Gauge**

Modern bonded wire resistant strain gauge (*Figure 13*) was invented by Edward E. Simmons of the California Institute of Technology (Caltech) and Arthur C. Ruge from the Massachusetts Institute of Technology (MIT) independently in 1938.

*Figure 13: Bonded wire resistant stain gauges in rosette formation.*

MIT released the rights to Ruge's invention, saying that, while “interesting,” the strain gauge didn’t show much potential.

Questions? Email nicholas.divincenzo@siemens.com

The gauge on the right will not measure the correct compressive strain. It will measure the poisson strain due to the applied load and some strain due to the transverse sensitivity of the gauge. It will not measure the total compressive strain due to the applied force. Because of the importance of strain gauge orientation, strain gauge rosettes are commonly used to measure strain fields where the direction of the applied load is unknown.

Modern bonded wire resistant strain gauge (

MIT released the rights to Ruge's invention, saying that, while “interesting,” the strain gauge didn’t show much potential.

Questions? Email nicholas.divincenzo@siemens.com

**Related Durability Links**

- Index of Testing Knowledge Articles
- History of Fatigue
- Stress and Strain
- Calculating Damage with Miner's Rule
- What is a SN-Curve?
- Strain Life Approach
- Neuber's Rule
- Rainflow Counting
- Mean Stress Corrections and Stress Ratios
- Difference between 'Range-Mean' and 'From-To' Counting
- Power Spectral Density
- Fatigue Damage Spectrum
- Shock Response Spectrum (SRS)
- How to Calculate a Shock Response Spectrum with Testlab?
- Some Thoughts on Accelerated Durability Testing
- Goodman-Haigh Diagram for Infinite Life
- Measuring Strain Gauges in Simcenter Testlab
- Rosette Strain Gauges
- Digital Image Correlation for Static Measurements
- Calculating Damage in Simcenter Tecware Process Builder
- Simcenter Testlab Neo: Strain Life Method
- Strain Gauges: Selecting an Excitation Voltage
- Simcenter Testlab SCADAS and Long Strain Cables
- Durability On-Demand Webinars