## STRAIN GAGES Fundamentals: Piezoresistive Effect

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On: 08 Jun, 2017

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Strain gages are based on the variation of resistance of a conductor or se...

Strain gages are based on the variation of resistance of a conductor or semiconductor when subjected to a mechanical stress.

For a wire having length *1, *cross section *A, *and resistivity p. the electric resistance is

*R **= p ** *When it is stressed longitudinally, each of the three quantities that affect r

*R*change and therefore

*R*undergoes a change given by

= + -

*The change in length that results when a force*

*F*is applied to a wire, within the elastic limit (Figure 2.4), is given by Hooke’s law,

= = Ee = E

where

*E*is a constant for each material, called

*Young’s modulus, o*is the mechanical stress, and r is the strain (unit deformation). r has no dimens ions, but to improve clarity, it is usually given in “microstrains” (1 micro- strain

**—**1 r —

**106**rn/rn).

Consider a wire that in addition to a length

*I*has a transverse dimension

**t.**As a result of longitudinal stress not only does

*1*change but

**t**does too. The relationship between both changes is given by Poisson’s law

*v = -*

where v is the Poisson ratio. It usually ranges from 0 to

*0.5;*it is, for example, 0.17 for cast iron, 0.303 for steel, and 0.33 for aluminum and copper. Note that for the volume to remain constant, it should be

*v*=

*0.5.*

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