Strain gauges

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Strain gauges ( DMS ; English strain gauge ) are measuring means for detecting stretching and upsetting deformations. They change their electrical resistance even with slight deformations and are used as strain sensors . They are glued to components with a special adhesive that deform minimally under load. This deformation (expansion) then leads to a change in the resistance of the strain gauge.

They are the core of many types of transducers: force transducers , scales of all sizes, from household scales to crane scales , pressure transducers or torque transducers . Deformation measurements (experimental stress analysis, stress analysis) on many materials can also be carried out using strain gauge measurements. Bridge circuits are mainly used for measurements with strain gauges , including quarter, half and full bridges .

Strain gauges are available in different material designs such as foil, wire and semiconductor strain gauges as well as multiple strain gauges in different arrangements such as strain gauges with transverse strain, full bridge strain gauges and rosette strain gauges.

Strain gauges. The sensor records the stretching (stretching) in the vertical direction


Simmons and Ruge are considered the fathers of the DMS, but they had no contact with each other and worked independently of each other. From today's perspective, however , Edward E. Simmons invented a force transducer based on the strain gauge principle, while Arthur C. Ruge , then employed at the Massachusetts Institute of Technology (MIT), invented the "DMS" sensor type used today as strain gauge in stress analysis. The principle of the DMS was described in 1856 by William Thomson, later Lord Kelvin . Since Simmons had already submitted a patent when Ruge wanted his DMS on the market in 1940, the patent was bought up without further ado to avoid patent disputes (Simmons patent granted: August 1942, Ruge patent granted: June 1944). The first (wire) strain gauges were named SR-4: Simmons, Ruge and 4 others. The year 1938 is considered to be the year of the birth of the DMS , because this year was the year of the publication of Simmons and the main work of Ruge.


Practically constructed strain gauge

Strain gauges are used to record changes in shape ( expansion / compression ) on the surface of components. They enable the experimental determination of mechanical stresses and thus the stress on the material. This is important both in those cases in which these stresses cannot be determined with sufficient accuracy by calculation and for checking the calculated stresses, since assumptions must be made and boundary conditions applied for every calculation. If these do not match reality, the result is incorrect despite the precise calculation. In these cases, the measurement with DMS serves to check the invoice.

Areas of application for strain gauges are the measurement of strain on machines, components, wooden structures, structures, buildings, pressure vessels etc. up to bones or teeth. They are also used in transducers ( sensors ) with which the load on electronic scales ( load cells ), forces ( force transducers ) or torques ( torque transducers ), accelerations and pressures ( pressure transducers ) are measured. Static loads and loads that change over time can be recorded; even vibrations in the high frequency range can be examined for frequency and amplitude.

Sensory tool holder with strain gauges

DMS is used in sensory tool holders to measure the forces that act on a tool. With the help of the built-in sensors, the bending moment, the torsion and the axial force can be measured, which allows conclusions to be drawn about the condition of each individual cutting edge during machining.

Another field of application is the so-called web tension measurement in the production of materials (paper, foil, metal strips and the like) by means of rollers and rollers.

Structure and shapes

Foil strain gauges
Rosette strain gauges

The typical strain gauge is a foil strain gauge, that is, the measuring grid foil made of resistance wire (3–8 µm thick) is laminated to a thin plastic carrier and etched out and provided with electrical connections. Most strain gauges have a second thin plastic film on their top, which is firmly glued to the carrier and mechanically protects the measuring grid. The combination of several strain gauges on a carrier in a suitable geometry is called a rosette strain gauge or strain gauge rosette.

For special applications, e.g. B. in the high temperature range or for very large strain gauges (measurements on concrete), strain gauges made of a thin resistance wire (Ø 18-25 µm) are laid in a meandering shape.

During production, a distinction is made between strain gauges for experimental stress analysis and strain gauges for transducer construction; the strain gauges are optimized differently for each area.

The measuring grid can in principle consist of metals or semiconductors . Semiconductor strain gauges ( silicon ) use the piezoresistive effect that is pronounced in semiconductors, i.e. the change in specific resistance that occurs when the semiconductor crystal is deformed. The change in resistance due to changes in length and cross-section only plays a subordinate role in semiconductor strain gauges. Due to the pronounced piezoresistive effect, semiconductor strain gauges can have relatively large k-factors and, accordingly, much higher sensitivities than metallic strain gauges. However, their temperature dependence is also very large and this temperature effect is not linear.

For metallic foil strain gauges, constantan or NiCr compounds are usually used as materials . The shape of the measuring grids is varied and oriented towards the different applications. The length of the measuring grid can be set over a range of 0.2… 150 mm. With strain gauges for everyday measuring tasks, the measurement uncertainties are currently between 1% and about 0.1% of the respective full scale value. With increased effort, however, the uncertainties can be reduced to 0.005% of the final value of the measuring range, with the achievement of such uncertainties not only being a question of the transducer technology, but rather the availability of appropriate test equipment from the manufacturer.

The carrier films of the DMS are, inter alia, acrylic resin , epoxy resin or phenol resin or polyamide prepared.

In the case of sensor structures without a carrier film, the strain gauge is sputtered onto a stainless steel measuring body using a thin glass insulating layer . The measuring body can then be integrated into the structure to be examined at a suitable point, for example by means of laser welding. The advantages of this design are insensitivity to creep and moisture (see below).

There are also force gauges that use piezoelectric , optical, inductive or capacitive sensors. In practice, however, they are only used for special applications. For example, capacitive sensors can also be used in the high temperature range above 1000 ° C. Fiber optic strain gages (with fiber Bragg grating ) are very flat and do not require thick connection cables. As a further alternative to the DMS, purely optical processes are also used, which only provide meaningful results in the low temperature range.

Mode of action

Metallic strain gauges are based on the change in resistance due to changes in length and cross-section. If a strain gauge is stretched , its resistance increases. If it is compressed (negative elongation), its resistance decreases.

For the measurement, the strain gauges are glued to the test item with a suitable adhesive . The change in shape of the carrier (expansion / compression) is transferred to the strain gauge. A change in resistance occurs in the strain gauge. The strain gauge has a so-called "K-factor", which indicates the proportionality of the change in resistance to the strain ε .

Change in influencing variables

The resistance of the unloaded strain gauge is:

The individual symbols stand for the following quantities :

The change in resistance under load is generally:

The relative change in resistance is obtained through differentiations and transformations:

The relative change in resistance depends on the longitudinal and transverse expansion.

So it follows:

where the so-called k-factor is:

The individual symbols stand for the following quantities:

  • : relative change in length
  • : relative change in cross-section
  • : Poisson's ratio
  • k : k factor

DMS materials

Materials for metal strain gauges and semiconductor strain gauges
designation composition k factor
Constantan 54% Cu 45% Ni 1% Mn 2.05
Nichrome V 80% Ni 20% Cr 2.2
Chromol C 65% Ni 20% Fe 15% Cr 2.5
Platinum tungsten 92% Pt 8% W 4.0
platinum 100% Pt 6.0
silicon 100% p-type Si: B ( boron in ppm range) + 80 ... + 190
silicon 100% n-type Si: P ( phosphorus in ppm range) −25 ... −100

The change in resistance observed when the strain gauge is mechanically stressed is caused by the geometric deformation of the measuring grid and the change in the specific resistance of the measuring grid material. Different strain gauge materials result in different values ​​for the sensitivity (k-factor) of the strain gauge.

For standard strain gauges, the material constantan is chosen due to the low temperature dependence despite the low k-factor . If a larger temperature range is required or if measurements are to be carried out at temperatures below −150 ° C, NiCr (Karma, Modco) is usually used as the measuring grid material.

For semiconductor strain gauges, silicon is mainly used, either in the form of a thin monocrystalline strip 10 to 20 µm thick or as a vapor-deposited polycrystalline layer. The k-factor can vary greatly depending on the crystal orientation and doping (p- or n-silicon). With n-silicon there are negative k-factors.

For the effect in crystalline semiconductors used for a high k-factor, see also piezoresistive effect .

Maximum stretchability

The maximum extensibility of the strain gauge mainly depends on the extensibility of the measuring grid material. Further dependencies exist due to the adhesive (due to its elasticity and bonding strength) and the material of the carrier material. The values ​​of the maximum stretchability at room temperature are typically in the range of a few 1,000 µm / m (semiconductor strain gauges) up to 50,000 µm / m (foil strain gauges). With special strain gauges, however, elongations of more than 100,000 µm / m are possible, although the normal definition of elongation is no longer valid. In the high elongation range, the effective elongation (differential quotient instead of difference quotient) must be used. However, this upper limit is rarely used; the maximum expansion of a strain gauge can usually only be achieved once. Typical elongations (for “normal” materials) are in the range from a few 100 to about 2,000 µm / m. Depending on the quality, the strain gauge in this area (maximum 1,000 µm / m to 2,500 µm / m VDI / VDE 2635) is resistant to continuous alternating loads.

Maximum frequency

The cut-off frequency of the strain gauge has not yet been determined, but measurements in the range from 5 MHz to 8 MHz were carried out, for which the strain gauge still provided error-free results.

DMS resistance

The nominal resistance of a strain gauge is the resistance that is measured between the two connections without loading the strain gauge. Typical values ​​are 120, 350, 700 and 1000 Ω.

The right resistor: The choice of resistor depends on the boundary conditions of the measuring task. 120 ohm strain gauges are relatively insensitive to fluctuations in insulation resistance, e.g. B. by exposure to moisture.

The advantage of higher resistance strain gauges is that they generate less intrinsic heat due to the lower measuring current. They are also less sensitive to ohmic resistances in the connection lines to the measuring amplifier. One disadvantage is that the higher-resistance strain gauges can be more sensitive when receiving interference pulses.

Maximum tension

The maximum voltage (supply voltage) with which a strain gauge can be operated depends on its size and the material to which it was glued. The problem is the power loss resulting from the supply and the strain gauge resistor, which must be dissipated via the strain gauge surface. With "normal" large strain gauges and materials that conduct heat well, 5 to 10 volts are possible, with small strain gauges and poorly heat conducting materials only 0.5 volts may be used.

Disturbance variables


Semiconductor strain gauges are highly temperature-dependent and can therefore only be used in special cases in experimental stress analysis. A large part of the temperature error in the transducer construction is compensated for by the Wheatstone bridge circuit . In addition, the effects in the individual bridge branches differ less from each other due to the construction of all four bridge branches on the same chip than if four semiconductor strain gauges were glued and interconnected. With constantan and NiCr strain gauges, the temperature effect is very low, above 100 ° C the signal changes by less than 1% with constantan.

In practice, however, there is a completely different problem: every material that is to be measured expands when the temperature rises. However, as long as it takes place unhindered, this expansion does not correspond to any load. Therefore, one often does not want to measure this elongation at all. To a certain extent, the so-called "adapted" strain gauge is achieved, that is, the strain gauge is given an additional temperature effect by the manufacturer, which results in a signal opposite to that of the stretching effect caused by the temperature variation of the material on which it sits. Unfortunately, this compensation only works in a certain temperature range and also not completely there - every material has a slightly different thermal expansion, which also depends on the pretreatment (rolled, annealed etc.). Complete compensation can only be achieved by using a strain gauge full bridge or with alternative measures in which the temperature expansion is also measured with a strain gauge on the unloaded component of the same material (so-called temperature compensation strain gauge). The (passive) temperature compensation strain gauges are usually connected to the active strain gauges as a half bridge. This eliminates the temperature-dependent expansion. For very large temperature ranges (150 ° C and more between minimum and maximum temperature), NiCr strain gauges are also cheaper than constantan strain gauges.


The creep of the strain gauge is caused by the spring action of the measuring grid and the holding force of the carrier film and adhesive : With constant elongation, the displayed elongation decreases slightly. Overall, the proportion of adhesive is far greater than the effect between the carrier film and the measuring grid. However, it is relatively low with today's adhesives in the normal areas of application. The range of the maximum temperature of the adhesive is problematic; stronger creep is to be expected here.

In the experimental stress analysis, the creep error is usually not relevant, as it is far below 1% in the normal application areas. In the transducer design, the creep of the strain gauge is even desired: Here the creep behavior of the strain gauge is adapted to the creep of the spring body material in order to compensate for it. The manufacturers therefore offer different creep adjustments.

Cross sensitivity

The cross-sensitivity refers to the fact that at a DMS, which is not claimed in the longitudinal, but in transverse direction, also can measure a change in resistance. In the case of foil strain gauges, however, manufacturers have the option of reducing the cross-sensitivity to values ​​below 0.1%. Therefore, the effect in the experimental stress analysis is mostly insignificant. The effect does not play a role in the construction of the transducer, since the transducer as a whole (with all influences) is calibrated here. Therefore, strain gauges can have high cross-sensitivities for the transducer construction, wire strain gauges also usually have higher cross-sensitivities.

However, the calculation of the error due to cross sensitivity is not that simple: To determine the k-factor, some strain gauges of a production lot are glued to a beam and a known expansion applied according to international standards. However, the signal resulting from the transverse expansion is also included in the k factor. For correction, the difference in the cross number of the test item and the object to be measured must therefore be taken into account.


The DMS itself has no detectable hysteresis . In the transducer structure, however, there is a hysteresis of the transducer material and thus leads to a hysteresis of the transducer.


Most carrier materials are hygroscopic , so the DMS is also sensitive to air humidity and should be protected with suitable materials (cover). Strain gauges for transducer construction often use materials that are not that critical, but the strain gauges are usually embedded or encapsulated here anyway. There are also special strain gauges that are resistant to moisture for at least a while. However, it should be noted that the adhesive must then also be insensitive.

Hydrostatic pressure

The influence of hydrostatic pressure (or vacuum) on the strain gage is minimal. However, the quality of a bond is particularly evident under vacuum or high pressure. If the installation is carried out correctly (gluing), the influence of pressure is very linear and can be set at 8 µm / m per 100 bar.

Nuclear radiation

In the hot area of ​​nuclear reactors, strain gauges can only be used under certain conditions, since here the radiation changes the measuring grid and thus the resistance. In space, however, DMS have been used successfully many times.

electromagnetic fields

Only very strong magnetic fields (superconducting magnets) can generate signals at all. The effect can be suppressed by a suitable choice of the measuring amplifier. Special strain gauges are also available which show even less effects due to a "bifilar" arrangement of the measuring grid.

In practice, it is not the strain gauge, but the connecting cable between the strain gauge and the measuring amplifier that is the critical area: Magnetic fields are usually problematic, electrical fields are usually not important because they can be shielded well.

Measurement method

Circuit technology

The change in resistance is usually recorded by integrating it into an electrical circuit ( Wheatstone bridge circuit ) and fed into an amplifier as a voltage signal. With the Wheatstone bridge, different types of circuit are possible, which lead to different bridge factors depending on the number and orientation of the strain gauges used. In the (force) transducer construction, on the one hand, the transverse contraction of the sensor body is used to (partially) compensate for temperature-related expansion, and on the other hand, the strain gauges are arranged in a special way on the sensor to direct the output signal in the direction of the measured variable of interest to maximize and to compensate in other directions. This is only possible if at least a half bridge or, better still, a full bridge is used and the strain gauges are distributed on the sensor in a special way for each load case ( bending , torsion , compression , shear ). With the Wheatstone bridge, the strain gauges for the half and quarter bridges are supplemented with 2 or 3 fixed resistors each to form the Wheatstone bridge (so-called bridge supplement), whereby all four generally have the same nominal resistance that also applies to the entire bridge, and all strain gauges have the same K-factor. The application of the physical variable leads to a detuning of the measuring bridge, which in the case of voltage-related evaluation leads to a differential voltage due to the constant bridge supply voltage , which is specified in relative terms in .

Since the strain-related change in resistance is small compared to the nominal resistance , the following applies to a strain gauge Wheatstone bridge:

From the above equation

follows with a full bridge:

With the half bridge , with the quarter bridge and for a strain gauge bridge circuit that is favorably wired according to the criteria mentioned, and with the full bridge it is also negative, and thus follows:

Bridge type B. Number of strain gauges
Full bridge 4th 4th
Full br. with transverse contraction 4th
Half bridge 2 2
Half-br. with transverse contraction 2
Quarter bridge 1 1

B stands for the so-called bridge factor , for the Poisson's ratio of the material on which the strain gauges are installed.

Quarter-bridge or half-bridge circuits are mostly used in experimental stress analysis, while only full bridges are used in transducer construction. In the case of the quarter bridge circuit (individual strain gauges), there are various connections analogous to the Pt100 (temperature measurement by means of resistance): with two wires (disadvantage: great influence of the supply line), with three wires (voltage drop in the supply lines can be calculated) or with four lines ( four-wire - or Kelvin connection; errors due to voltage drops on the supply lines do not apply here. In the case of the three-wire circuit, amplifiers are available which, up to a certain cable length, can compensate for the voltage losses in the supply lines based on the voltage drop in one of the lines; this is called a regulated three-wire circuit.

The output signal at the nominal load of a transducer (four active strain gauges) is typically 2 millivolts per volt of supply voltage.

Electronics for signal evaluation

Since the change in resistance of strain gauges is relatively small, it must be evaluated using suitable methods. An excitation signal is given to the DMS or the DMS bridge, which is of different types depending on the method. The system response of the DMS is then amplified or, as in the TDC process, evaluated directly. There are at least four measurement methods for strain gauges:

  1. Carrier frequency differential amplifier
  2. DC voltage differential amplifier
  3. Constant current
  4. Temporal evaluation via TDC

The carrier frequency amplifiers the excitation signal or the supply voltage is a constant AC voltage ( carrier frequency ) of 200 Hz to 50 kHz, the carrier frequency is referred to, when DC amplifier, a constant DC voltage , wherein the constant current evaluation, a constant current source and the temporal evaluation, a square pulse .

The first two process a differential voltage that represents the output signal due to the connection of the strain gauges to the full bridge . This has the particular advantage of good common-mode rejection , e.g. B. from interference radiation on the sensor cable. Common to all methods is a low-pass behavior , whereby the cut-off frequency should be adapted to the application in order to attenuate interference frequencies above the highest useful signal frequency .

In the carrier frequency method, the amplitude-modulated AC voltage difference signal, which is amplitude-modulated by the strain gauge bridge deflection, is amplified and demodulated, this demodulator acting like a narrow-band bandpass that only allows the excitation frequency f to pass. This is then filtered out by a low-pass filter, so that a DC voltage is present at the output that is proportional to the strain gauge deflection and has a useful signal bandwidth of up to the limit frequency of this low-pass filter.

In the time-to-digital conversion process (TDC), one or more strain gauges are supplemented with a capacitor to form an RC element and the time characteristics of the impulse response are digitized directly by time measurement. The other three methods do not originally include digitization , but nowadays it is widely used in the form of voltage digitization using an analog-digital converter .

All methods have different advantages and disadvantages. The third method offers the possibility of using long line lengths for the individual bridge circuits without the signal being corrupted. With both carrier frequency and DC voltage, however, cable losses are now compensated for by electronic circuits that are easy to implement, so that this historical advantage of constant current supply no longer applies. This procedure no longer plays a major role in practice today. The main difference between the carrier frequency and the DC voltage is the achievable signal bandwidth of the amplifiers available on the market: DC voltage up to about 100 kHz, with carrier frequencies usually only a few 100 Hz to about 3 kHz. Another difference lies in their susceptibility to failure, which, however, also depends on the respective environment and use. The carrier frequency method is also insensitive to interference DC voltages such as B. thermal voltages , and - if the interference frequencies are outside the carrier frequency plus / minus bandwidth - also against push-pull interference . Furthermore, carrier frequency amplifiers generally have an excellent signal-to-noise ratio , especially those with a relatively low carrier frequency (0.2 to 3 kHz). However, several carrier frequency amplifiers have to be synchronized with one another so as not to interfere with one another.

With the TDC method, a very good signal-to-noise ratio can be achieved in combination with a large useful signal bandwidth, whereas these two requirements have opposing (antagonistic) effects in the other methods, i.e. H. cannot be maximized at the same time. The disadvantage of the TDC method is a significantly greater sensitivity to the disturbance variables of the sensor line, u. a. their line capacity.

DC amplifiers can be used without any problems in the laboratory or under optimal conditions. Carrier frequency measuring amplifiers are sometimes more advantageous under industrial conditions, where measurements often have to be carried out under strong interference fields. Ultimately, however, this depends on the frequencies involved in interfering radiation and amplifiers; a general judgment is no longer possible today, since not only 50 Hz occurs as the interference frequency (this could only be completely suppressed by a carrier frequency amplifier if the useful frequency is 50 Hz on the strain gauge or includes). Even modern direct voltage differential amplifiers can - at least with a low signal bandwidth - have a very good signal-to-noise ratio in combination with good immunity to interference , especially if the output voltage is digitized and this data stream is then digitally filtered in a suitable manner .

Some typical fields of application

Mechanical elongation indicator

With the introduction of foil balloons made of temporary, limited stretchable foil, which can be inflated into balls , these so-called Orbz balloons were delivered by Anagram with an inflation gauge called an expansion indicator . This single-use indicator is self-adhesive in two places and is stuck to the part of the balloon where the greatest stretch is to be expected. A glue point anchors a scale formed by 4 colored fields (white / green / yellow / red). When the balloon is filled, its foil expands linearly by about 20-25%, while one finger of the indicator, connected to the other adhesive point about 4 cm away, is dragged across the scale. When the line on the finger is drawn from the starting line in the white to the middle of the green, the correct degree of stretching of the balloon is displayed. Later this expansion indicator will be dispensed with and the correct filling will be omitted from the disappearance of the transverse folds at the weld seams.

Web links

Commons : Strain Gauges  - Collection of Images, Videos, and Audio Files

Standards and guidelines

  • VDI / VDE / GESA 2635 sheet 1: Experimental structural analysis; Strain gauges with a metallic measuring grid - parameters and test conditions
  • VDI / VDE / GESA 2635 sheet 2: Experimental structural analysis; Recommendation for performing strain measurements at high temperatures


  • K. Hoffmann: An introduction to the technique of measuring with strain gauges . 1987
  • S. Keil: Stress determination with strain gauges 1st edition. 1995
  • P. Giesecke: Strain gauge technology . 1994
  • K. Fink, S. Rohrbach: Handbook of tension and strain measurement. 1st edition. 1958
  • E. Baumann: Electrical force measurement technology.
  • Keil, Stefan: Technology and Practical Use of Strain Gages - With Particular Consideration of Stress Analysis Using Strain Gages , September 2017, ISBN 978-3-433-03138-4

Individual evidence

  1. DR.-ING. W. KOEHLER: USE OF A SENSORY TOOL HOLDER FOR PROCESS DESIGN. In: pro-micron. pro-micron, accessed on November 15, 2019 (German).
  2. Orbz & Ultra Shapes Demo HD 720p Anagram Balloons,, September 19, 2013, accessed March 25, 2019. Video (6:10) - 3:06 Orbz Ballon, 5: 20–5: 40 stretching indicated by inflation gauge .