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# lsli10.4up - 10-1 10-1 10-2 10-2 Strain Force and Pressure...

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10-1 10-1 Strain, Force, and Pressure Force is that which results in acceleration (when forces don’t cancel). Strain is the change in shape of an object ... usually due to some force. (Force is usually called stress in this context.) Pressure is force per unit area. 10-1 EE 4770 Lecture Transparency. Formatted 13:26, 23 December 1997 from lsli10. 10-1 10-2 10-2 Strain Consider an object in two situations: with and without a force ap- plied. Let a force be applied along a dimension. Let L 1 be the length of the object along the dimension when no force is applied. Let L 2 be the length when the force is applied. Then the object’s strain is deﬁned to be L 2 - L 1 L 1 . The symbol ± is usually used to denote strain. In most situations, strains of interest will be very small, | ± | < 0 . 0001. 10-2 EE 4770 Lecture Transparency. Formatted 13:26, 23 December 1997 from lsli10. 10-2 10-3 10-3 Strain Transducers Called strain gauges. Symbol: no common symbol. Construction Flexible card with strip of some conductor arranged in special pattern. Card is mounted (glued) onto the object being measured. Conductor is usually a metal or semiconductor. Pattern is chosen so that strain (to be measured) occurs along direction of current ﬂow. Current is passed through conductor. 10-3 EE 4770 Lecture Transparency. Formatted 13:26, 23 December 1997 from lsli10. 10-3 10-4 10-4 Principle of Operation For Both Types Conductor maintains an almost constant volume with strain. That is, conductor is not compressible. Recall that the resistance of a conductor is R = ρ L A , where L is its length, A is its area, and ρ is its resistivity. Suppose force causes length of the conductor to decrease. Since volume does not change much, area must increase. Thus, resistance decreases. Model Function H t1 ( x )= R 0 (1 + G f x ), where G f is a constant called the gauge factor. For metal strain gauges, G f =2. (An integer!) For semiconductor strain gauges G f is much higher. 10-4 EE 4770 Lecture Transparency. Formatted 13:26, 23 December 1997 from lsli10. 10-4

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10-5 10-5 Complementary Pairs In some cases the strain ... in two places on the object will be of equal magnitude—but opposite sign. For example, a cantilever beam: Force Strain Gauges The upper part of beam is stretched (positive strain) and the lower part of beam is compressed (negative strain). The two strain gauges therefore form complementary pairs. 10-5 EE 4770 Lecture Transparency. Formatted 13:26, 23 December 1997 from lsli10. 10-5 10-6 10-6 Derivation of Gauge Factor for Ideal Metal Ideal metal’s properties: Non-compressible. (Does not change volume.) Resistivity is constant. Consider an Ideal Metal Block Regardless of strain: volume is S and resistivity is ρ . When unstrained: call length L 1 , area A 1 , and resistance R 1 . By standard resistivity formula, R 1 = ρ L 1 A 1 .
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lsli10.4up - 10-1 10-1 10-2 10-2 Strain Force and Pressure...

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