Single Gage in a Uniform Biaxial Strain Field

When a strain gage is bonded to a test surface at a small angular error with respect to the intended axis of strain measurement, the indicated strain will also be in error due to the gage misalignment. In general, for a single gage in a uniform biaxial strain field, the magnitude of the misalignment error depends upon three factors (ignoring transverse sensitivity):

1. The ratio of the algebraic maximum to the algebraic minimum principal strain, / .
    
2. The angle between the maximum principal strain axis and the intended axis of strain measurement.
    
3. The angular mounting error, , between the gage axis after bonding and the intended axis of strain measurement.

These quantities are defined in the following figures for the particular but common case of the uniaxial stress field. The first is a polar diagram of strain at the point in question, and the second gives the concentric Mohr's circles for stress and strain for the same point. In the polar diagram, the distance to the boundary of the diagram along any radial line is proportional to the normal strain along the same line. The small lobes along the Y axis in the diagram represent the negative Poisson strain for this case. It can be seen qualitatively that when is 0 or 90 degrees, a small angular misalignment of the gage will produce a very small error in the strain indication, since the polar strain diagram is relatively flat and passing through zero-slope at these points.

Polar strain distribution corresponding to uniaxial stress, illustrating the error in indicated strain when a gage is misaligned by + from the intended angle, .

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