Transverse-sensitivity errors in strain-gage measurement

Abstract

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 andνo=0.285, then the error will be +6.1 percent.) 2. Figure 2 indicates that the values of Δ2 become critical for values ofKb from 0.0 to −0.5 and the values of Δ1 become critical for values ofKb less than −2; i.e., for negative values ofKb we will find large percentage errors in either one of the principal stresses except ifKb 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., |σi-σ1|) can be of great significance in that range; for example, ifQ1=−400×10−6,Q2=+200×10−6,K=5 percent, ν=0.3 andE=30×106 psi (21×1011 dynes/cm2) thenKb=−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 ofKb 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.