Transverse-sensitivity errors in strain-gage measurement

Conclusions

• 1. Equation (5) indicates that the error in an isotropic state of stress does not depend on the properties of the material on which the gage is mounted, but it is a constant for the gage itself. (For example, ifK=+5 percent andν _o=0.285, then the error will be +6.1 percent.)

• 2. Figure 2 indicates that the values of Δ₂ become critical for values ofK _b from 0.0 to −0.5 and the values of Δ₁ become critical for values ofK _b less than −2; i.e., for negative values ofK _b we will find large percentage errors in either one of the principal stresses except ifK _b lies between −0.5 and −2.0. On the other hand, the absolute values of the errors in either one of the principal stresses (i.e., |σ_i-σ₁|) can be of great significance in that range; for example, ifQ ₁=−400×10⁻⁶,Q ₂=+200×10⁻⁶,K=5 percent, ν=0.3 andE=30×10⁶ psi (21×10¹¹ dynes/cm²) thenK _b=−0.5 and Δ₂≅-20 percent

  $$\begin{gathered} \therefore \dot \sigma _2 = \frac{E}{{1 - v^2 }}\left( {Q_2 + vQ_1 } \right) = + 2400{\text{ }}psi \hfill \\ \left( {154 \times 10^5 {N \mathord{\left/ {\vphantom {N {m^2 }}} \right. \kern-\nulldelimiterspace} {m^2 }}} \right) \hfill \\ \end{gathered} $$

  and$\left( {\dot \sigma _2 - \sigma _2 } \right) = - 480{\text{ }}psi$ (−30.6×10⁵ N/m²). The true value of σ₂ would then be +2880 psi (184.3×10⁵ N/m²). In such cases, it is clearly important to take transverse-sensitivity errors into account, specially when theK factor exceeds 2 or 3 percent. For positive values ofK _b the percentage errors, in general, are less. Furthermore, the true values of the stresses are then less than the calculated values, so that in such cases it would be unnecessary to make corrections for the transverse sensitivity.