Strain Gage: Theoretical Background
engineering fundamentals Strain Gage: Theoretical Background
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Electric Resistance Strain Gages

The strain gage is one of the most widely used strain measurement sensors. It is a resistive elastic unit whose change in resistance is a function of applied strain.

where R is the resistance, e is the strain, and S is the strain sensitivity factor of the gage material (gage factor in some books).

Among strain gages, an electric resistance wire strain gage has the advantages of lower cost and being an established product. Thus it is the most commonly used type of device. Other types of strain gages are acoustic, capacitive, inductive, mechanical, optical, piezo-resistive, and semi-conductive.

A wire strain gage is made by a resistor, usually in metal foil form, bonded on an elastic backing. Its principle is based on fact that the resistance of a wire increases with increasing strain and decreases with decreasing strain, as first reported by Lord Kelvin in 1856.

Consider a wire strain gage, as illustrated above. The wire is composed of a uniform conductor of electric resistivity r with length l and cross-section area A. Its resistance R is a function of the geometry given by

The resistance change rate is a combination effect of changes in length, cross-section area, and resistivity.

When the strain gage is attached and bonded well to the surface of an object, the two are considered to deform together. The strain of the strain gage wire along the longitudinal direction is the same as the strain on the surface in the same direction.

However, its cross-sectional area will also change due to the Poisson's ratio. Suppose that the wire is cylindrical with initial radius r. The normal strain along the radial direction is

The change rate of cross-section area is twice as the radial strain, when the strain is small.

The resistance change rate becomes

For a given material, the sensitivity of resistance versus strain can be calibrated by the following equation.

When the sensitivity factor S is given, (usually provided by strain gage vendors) the average strain at the point of attachment of the strain gage can be obtained by measuring the change in electric resistance of the strain gage.

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