Problem 2.6. Data reduction for the "stress gauge"
A "fish-bone" strain gauge has the configuration shown in
fig. 2.4. The various sub-gauges, inclined at angles +α and
−α with respect to the gauge direction, measure strains along
those two directions, denoted $\epsilon_\alpha$ and $\epsilon_{-\alpha}$, respectively. The
sub-gauges are electrically connected in such a way that a single measurement is made, $e = \epsilon_\alpha + \epsilon_{-\alpha}$. The fish-bone gauge,
also known as a "stress gauge," is intended to measure the
stress, σ, along the direction of the gauge, independently of
any other stress components acting at that location. (1) Find
the value of angle α for which the gauge measurement, e, becomes independent of the other
stress components. (2) Find the relationship between the measurement and the stress, σ, in the
gauge direction.
Fig. 2.4. Configuration of
the "fish-bone" gauge.
