Electrical Resistance Strain Gauge
Lord Kelvin presented to the Royal Philosophical Society the results of an experiment involving the Īelectrical resistance of copper and iron wire when subjected to strainā in 1856. Kelvinās observations are consistent with the relationship of electrical resistance to some of the physical properties of a conductor:
R = rL/A
where R is the electrical resistance, r is the conductivity constant, L is the length of the conductor and A is the cross sectional area. Resistance is directly proportional to the length and inversely proportional to the cross sectional area. The electrical resistance of a metal wire increases as it is stretched as a result of the decreased cross sectional area and an increase in the length of the wire. Conversely, as the wire is compressed and the length decreases, with a corresponding increase in cross sectional area, the electrical resistance of the material decreases.
The relationship between length and cross sectional dimension can be expressed by Poissonās ratio:
n = -(dD/D)/dL/L = eL / ea
where n is Poissonās ratio, D is the cross sectional dimension and L is the length, eL is the lateral strain and ea is the axial strain. It basically states that as the length decreases (compression) for a material, the cross sectional dimension increases and vice versa for an increase (tension) in length for a material.
Lord Kelvinās discovery was not put to any practical use until the 1930ās. Carlson is credited with one of the first recorded instances of a wire resistance strain gauge being applied to measure stress in 1931. The use of a bonded wire gauge to measure strain was conceived at about the same time by Simmons and Ruge in 1938. A wire gauge was mounted and bonded between two thin pieces of paper. The general construction of a bonded wire type strain gauge is shown in Figure 16.
Figure 16 General arrangement of a bonded-wire type strain gauge 
The bonded wire gauge has largely been replaced by the foil gauge which has been in production since the 1950ās. This type of gauge consists of a metal foil grid which is bonded onto an epoxy support. Printed circuit techniques are used in the manufacture of bonded foil strain gauges. Foil configurations can be varied and complicated. (Figure 17)
Figure 17 Different Foil Gauge Configurations
The selection of a strain gauge for a particular application is affected by the following gauge characteristics: grid material and construction, backing material, bonding material, gauge protection and gauge configuration. Gauge design incorporates as many of the following features as possible: high gage factor, high resistivity, temperature insensitivity, high electrical stability, high yield point, high endurance limit, ease of working, low hysteresis, low thermal emf with other materials and durability. A variety of strain gauges are available from commercial sources. Temperature sensitivity is a major concern in the use of strain gauges, and temperature compensation is often incorporated in the circuit.
Strain gauges are normally attached to the member whose strain is being measured through a cement or adhesive. Adhesives and the gauge backing material transmit the force to the grid. Good adhesives possess the following properties: high mechanical strength, high creep resistance, high dielectric strength, good bonding strength, a minimum of temperature restrictions and ease of application. Different types of cements and adhesives are available from the manufacturer with varying life cycles and ease of use.
Most gauge installations require protection from the ambient conditions, which may include mechanical abuse, moisture, oil, dust, etc.. A variety of different coatings and methods are available from the manufacturers of strain gauges to protect the strain gauge assembly.
The basic relationship between strain and the change in gauge resistance can be expressed by:
e = (1 / F) (DR / R)
wheree is the strain, F is the gauge factor and R is the gauge resistance. For a typical gauge F is 2.0 and R is 120 ohm. Strains in the range of 1 microstrain are measurable using commercial systems, which means that a change in gauge resistance of .00024 ohm must be detected for a typical strain gauge. To detect resistance changes of this magnitude a strain gauge bridge circuit (Figure 18) is often used. Other circuit configurations to detect the resistance change in a strain gauge include the voltage dividing potentiometer or ballast circuit and the constant current circuit.
Figure 18 Strain Gauge Bridge Circuit
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Support for the development of this module was provided by the National Science Foundation and The Cooper Union for the Advancement of Science and Art.
Please send questions or comments to Professor Ron Adrezin or Professor Daniel Raichel.