Discussion
A resistance wire strain gauge with a gauge factor of 2 is bounded to a steel structural member subjected to a stress of 100 MN/m2. The modulus of elasticity is 200 GN/m2. Percentage change in the value of gauge resistance due to the applied stress is __________.
Answer: C
The resistance changes by 0.1%.
First find the strain from Hooke's law, then multiply by the gauge factor, \(\frac{\Delta R}{R} = G\varepsilon\).
\[ \begin{aligned} \varepsilon &= \frac{\sigma}{E} = \frac{100 \times 10^{6}}{200 \times 10^{9}} = 5 \times 10^{-4} \\ \frac{\Delta R}{R} &= 2 \times 5 \times 10^{-4} = 10^{-3} \end{aligned} \]
A fractional change of \(10^{-3}\) is 0.1%. 0.01% and 1% come from slipping a factor of ten in the prefixes M and G, and 10% would mean an impossible strain for steel.
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