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Electric-Resistance Strain Gauge

Strain express the specific deformation, often expressed as a percentage, caused in a material by the action of a stress i.e., a force per unit area e.g.,lb./in 2 kg/cm2. In an elastic material such as steel there is direct proportionality between stress and strain. Because of this definite relationship it is possible to determine the magnitude of the stresses in a structure if the strains are known. The latter can be measured by devices termed strain gauges, which are extensively used in science and engineering for purposes of research and testing. There are different types of strain gauge. One very widely used type is the bonded electric-resistance strain gauge, first developed some thirty years ago. In its simplest form it consists of a length of fine wire in a zigzag or grid pattern cemented between two thin sheets of paper (Figs.1 and 2).

The gauge is bonded to the part being tested, and the wire grid participates in the deformations thereof, either in compression (shortening) or tension (elongation) so that the length and cross-sectional area of the wire undergo changes, which cause changes in the electrical resistance of the wire which are proportional to the changes in length (elongation causes an increase, shortening causes a decrease in resistance). These changes in resistance, though usually very small, can be measured by means of suitable electrical circuits and instruments.

The relationship between the unit change in resistance and strain is expressed by the formula: DR/R = k. Dl/l, where k is the so-called gauge factor, DR is the change in resistance caused by the strain, R is the original resistance of the gauge, and Dl/l is the strain under the gauge; l is the original gauge length and Dl is the change in length. The gauge factor (k) and the original resistance (R) are predetermined values for any particular strain gauge and are supplied by the manufacturer. Such gauges are very sensitive; strains as low as 0.001% corresponding to one millionth of an inch over a gauge length of one inch can be detected.

A single strain gauge measures strains in one direction only. To measure strains in more than one direction at any particular point, two or more gauges can be affixed there for example, three gauges in a rosette arrangement which measure strains in three directions at 120 degrees in relation to one another (Fig.3). Strain gauges can be used for a variety of technical and scientific purposes involving the measurement of small amounts of deformation or displacement.

Thus a specially, shaped strain gauge affixed to a diaphragm enables the deformations of the diaphragm, and therefore the magnitude of the pressure acting on it, to be measured in (Figs 4 and 5) shows an acceleration pickup for the measurement of accelerations varying with time. When the device is subjected to acceleration in the direction of the arrow, the part A with the bonded on strain gauge undergoes a deflection in the opposite direction which is directly proportional to the acceleration.

The small variations in the electrical resistance of a strain gauge are measured by means of an arrangement called a measuring bridge which embodies the principle of the Wheatstone bridge (Fig.6) which comprises two resistance branches connected in parallel, each branch consisting of two resistances in series. The supply voltage is applied at the two diagonal points I and II.

The measuring instrument galvanometer connected between the other two diagonal points III and IV will give a zero voltage reading only when the same voltage drop occurs between I and III as between I and IV for example, when R1 = R4 and R2= R3, and also when R1 = R2 and R3 = R4. In general, the bridge will be in equilibrium i.e., the measuring instrument will give a zero reading, when the mathematical relationship R1:R2 = R4:R3 is satisfied. If three of the resistances are of known value, e.g., R2, R3 and R4, then the (unknown) fourth resistance R1 can be determined by balancing the bridge by varying the resistance R2 and calculating it from R1 = R1 R4 / R3.

For measurements performed with strain gauges, all four resistances of the bridge may be replaced by strain gauges, all of equal resistance (Fig.7) ; alternatively, only two equal strain gauges may be connected into the bridge circuit, while the other two resistance are incorporated in the measuring-bridge apparatus itself (Fig.8). When bridge is balanced, i.e., the measuring instrument has been brought to a zero reading, a variation in the magnitude of one or more of the resistances will cause the needle of the instrument to deflect from the zero position. The arrangement shown in Fig.7 may, for example, be applied in measuring the strains occurring at the top and at the underside of a beam loaded in bending (Fig.9).

When there is no load on the beam, the bridge is in equilibrium. When load is applied, the two gauges R1 and R3 undergo an equal tensile strain (elongation), while the two gauges R2 and R4 undergo an equal compressive strain (shortening). The purpose of the arrangement in Fig.10 is to measure the strain at the top of the beam subjected to a combination of flexural and tensile loading. Only the strain gauges R1 and R3 are affixed to the beam; the gauges R3 and R4 are dummies in that they do not participate in the strain of the beam, but provide temperature compensation i.e., they are installed in the vicinity of the other two, so that any changes in the temperature of the surroundings whereby the resistances are altered affect all the gauges equally.

Similar compensation can be provided in the arrangement shown in Fig.8 and applied to the strain measurement on a beam as shown in Fig.11. With strain gauges of equal resistance the measuring arrangement in Fig.10 is twice as sensitive as that in Fig 11, because in the former case the change in resistance of both R1 and R3 causes twice the deflection of the measuring instrument as does the change in Resistance of R1 alone in the latter case. Fig.12 shows strain gauges for measuring the strains in a shaft subjected to a torque (twisting moment). The largest strains occur in directions at 45° to the center line of the shaft.