lsli10 - 10-1 10-1 Strain Force and Pressure Force is that...

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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
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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
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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
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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
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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 .
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