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Errors Due to Transverse Sensitivity in Strain Gages

Errors Due to Transverse Sensitivity ( continued )

It is imperative to realize that for any strain field except that corresponding to a uniaxial stress field (and even in the latter case, with the gage mounted along any direction except the maximum principal stress axis, or on any material with Poisson's ratio other than 0.285), there is always an error in strain indication if the transverse sensitivity of the strain gage is other than zero. In some instances, this error is small enough to be neglected. In others, it is not. The error due to transverse sensitivity for a strain gage oriented at any angle, in any strain field, on any material, can be expressed as:

     Eq. (509.5)

where:

    = the error as a percentage of the actual strain along the gage axis.
    = the Poisson's ratio of the material on which the manufacturer's gage factor, , was measured (usually 0.285).
  = respectively, the actual strains parallel and perpendicular to the primary sensing axis of the gage.*


*Subscripts (a) and (t) always refer to the axial and transverse directions with respect to the gage (without regard to directions on the test surface), while subscripts (x) and (y) refer to an arbitrary set of orthogonal axes on the test surface, and subscripts (p) and (q) refer to the principal axes.


From the above equation, it is evident that the percentage error due to transverse sensitivity increases with the absolute values of and / , whether these parameters are positive or negative. Equation (509.5) has been plotted in Figure 509.1 for convenience in judging whether the magnitude of the error may be significant for a particular strain field.
 


Fig. 509.1 - Transverse sensitivity errors for various strain ratios.

Figure 509.1 also yields an approximate rule-of-thumb for quickly estimating the error due to transverse sensitivity - that is:    (percent)

As Equation (509.5) shows, this approximation holds quite well as long as the absolute value / is not close to . For an example, assume the task of measuring Poisson (transverse) strain in a uniaxial stress field. In this case, the Poisson strain is represented by , the strain along the gage axis, and the longitudinal strain in the test member by , since the latter is transverse to the gage axis (as shown here).







If the test specimen is an aluminum alloy, with = 0.32, then / = -1/ = -3.1. Assuming that the transverse sensitivity of the strain gage is -3% (i.e., = -0.03*), the rule of thumb gives an approximate error of +9.3%. The actual error, calculated from Equation (509.5), is +8.5%.


* For substitution into any equation in this publication, must always be expressed decimally. Thus, the value of (in percent) from the gage package data sheet must be divided by 100 for conversion to its decimal equivalent.



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