Strain Measurements with Strain Gages: How-To Guide

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Strain and Strain Gage Overview

Strain is the amount of deformation of a body due to an applied force. More specifically, strain (e) is defined as the fractional change in length, as shown in Figure 1 below. While there are several methods of measuring strain, the most common is with a strain gage, a device whose electrical resistance varies in proportion to the amount of strain in the device. The most widely used gage is the bonded metallic strain gage.

View a 60-second video on how to take a Strain Gage Measurement

 

Figure 1. Definition of Strain

The metallic strain gage consists of a very fine wire or, more commonly, metallic foil arranged in a grid pattern. The grid pattern maximizes the amount of metallic wire or foil subject to strain in the parallel direction (Figure 2). The grid is bonded to a thin backing, called the carrier, which is attached directly to the test specimen. Therefore, the strain experienced by the test specimen is transferred directly to the strain gage, which responds with a linear change in electrical resistance. Strain gages are available commercially with nominal resistance values from 30 to 3000 Ω, with 120, 350, and 1000 Ω being the most common values.

Figure 2. Bonded Metallic Strain Gauge

In practice, the strain measurements rarely involve quantities larger than a few millistrain (e x 10^-3). Therefore, to measure the strain requires accurate measurement of very small changes in resistance. To measure such small changes in resistance, strain gages are almost always used in a bridge configuration with a voltage excitation source. The general Wheatstone bridge, illustrated below, consists of four resistive arms with an excitation voltage, V_EX, that is applied across the bridge.

Figure 3.  Full-Bridge Circuit

The output voltage of the bridge, V_O, will be equal to:

From this equation, it is apparent that when R₁/R₂ = R₄/R₃, the voltage output V_O will be zero. Under these conditions, the bridge is said to be balanced. Any change in resistance in any arm of the bridge will result in a nonzero output voltage.

Therefore, if we replace R₄ in Figure 3 with an active strain gage, any changes in the strain gage resistance will unbalance the bridge and produce a nonzero output voltage. If the nominal resistance of the strain gage is designated as R_G, then the strain-induced change in resistance, DR, can be expressed as DR = R_G*GF*e. Assuming that R₁ = R₂ and R₃ = R_G, the bridge equation above can be rewritten to express V_O/V_EX as a function of strain (see Figure 4). Note the presence of the 1/(1+GF*e/2) term that indicates the nonlinearity of the quarter-bridge output with respect to strain.

Figure 4. Quarter-Bridge Circuit

Ideally, we would like the resistance of the strain gage to change only in response to applied strain. However, strain gage material, as well as the specimen material to which the gage is applied, will also respond to changes in temperature. Strain gage manufacturers attempt to minimize sensitivity to temperature by processing the gage material to compensate for the thermal expansion of the specimen material for which the gage is intended. While compensated gages reduce the thermal sensitivity, they do not totally remove it.

By using two strain gages in the bridge, the effect of temperature can be further minimized. For example, Figure 5 illustrates a strain gage configuration where one gage is active ( R_G+ DR), and a second gage is placed transverse to the applied strain. Therefore, the strain has little effect on the second gage, called the dummy gage. However, any changes in temperature will affect both gages in the same way. Because the temperature changes are identical in the two gages, the ratio of their resistance does not change, the voltage V_O does not change, and the effects of the temperature change are minimized.

Figure 5. Use of a Dummy Gage to Eliminate Temperature Effects

The sensitivity of the bridge to strain can be doubled by making both gages active in a half-bridge configuration. For example, Figure 6 illustrates a bending beam application with one bridge mounted in tension ( R_G+ DR) and the other mounted in compression ( R_G+ DR). This half-bridge configuration, whose circuit diagram is also illustrated in Figure 6, yields an output voltage that is linear and approximately doubles the output of the quarter-bridge circuit.

Figure 6. Half-Bridge Circuit

Finally, you can further increase the sensitivity of the circuit by making all four of the arms of the bridge active strain gages in a full-bridge configuration. The full-bridge circuit is shown in Figure 7.

Figure 7. Full-Bridge Circuit

Thus, a single arm is an active strain gage in a quarter-bridge circuit; two arms are active strain gages in a half-bridge circuit while all four arms are active strain gages in a full-bridge circuit.

Strain gages do not have polarity, although depending upon which one of the above three categories a strain gage, there will be different number of connections that you will have to make to the measurement hardware as explained in the section below.

How to Make a Strain Gage Measurement

Most strain gage measuring solutions will provide an option to measure quarter-, half- and full-bridge configurations.

Let’s take an example of a NI CompactDAQ system with a NI 9237 4-channel simultaneous bridge module (Figure 8).

Figure 8: NI CompactDAQ and NI 9237 bridge module

Figure 9 below shows connection diagram for wiring a strain gage in quarter-bridge configuration to this module. Connect one end of a quarter bridge gage to CH+ terminal on the module and other end to the QTR terminal. Notice that the EX- terminal on the module is left unwired because for quarter-bridge configuration, R3 is internal to the measurement hardware (Figure 9)

 

Figure 9: Wiring in quarter-bridge configuration

For measuring a half-bridge configuration, connect two wires from the two active elements to EX+ and EX- terminals on the module. Lastly, connect a wire between the common point of the two active elements to the QTR terminal on the measurement module.

Figure 10: Wiring in half-bridge configuration

For measuring in a full-bridge configuration, connect the common point between R1 and R4 to EX+ and common point between R2 and R3 to EX-. Also, connect the common point between R3 and R4 to CH+ and common point between R1 and R2 to CH-.

 
Figure 11: Wiring in full-bridge configuration

 Getting to see your measurement:

Now that you have your sensor connected to the measurement device, you can bring that data into computer and visualize using NI LabVIEW graphical programming software.

Figure 12 shows an example of displaying measured strain data on a chart indicator inside the LabVIEW programming environment.

Figure 12: Strain Data Measurements with LabVIEW

 

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