Relationships are given here for correcting indicated strains for thermal output and gage factor variation with temperature. The forms these relationships can take depend upon the measuring circumstances - primarily upon the strain indicator gage factor setting and the temperature at which the instrument was balanced for zero strain.

The strain indicator gage factor can be set at any value within its control range, but one of the following three is most likely ^† :

1. Gage factor, , used by Micro-Measurements in determining thermal output data ( = 2.0).
    
2. Room-temperature gage factor as given on the gage package technical data sheet.
    
3. Gage factor of gage at test temperature or at any arbitrary temperature other than room or test temperature.

No single gage factor is uniquely correct for this situation; but, of the foregoing, it will be found that selecting the first alternative generally leads to the simplest form of correction expression. Because of this, the procedure developed here requires that the gage factor of the instrument be set at = = 2.0, the gage factor at which the thermal output data were recorded.

Similarly, the strain indicator can be balanced for zero strain at any one of several strain gage temperatures:

1. Room temperature
    
2. Test temperature
    
3. Arbitrary temperature other than room or test temperature

The second and third of the above choices can be used for meaningful strain measurements only when the test object is known to be completely free of mechanical and thermal stresses at the balancing temperature. Because this requirement is usually difficult or impossible to satisfy, the first alternative is generally preferable, and is thus selected for the following procedure.

As an example, assume that the strain indicator is balanced with the gage at room temperature, and with the gage factor control set at , the value used by Micro-Measurements in recording the thermal output data. Assume also that a strain, , is subsequently indicated at a temperature, , which is different from room temperature. The indicated strain, , is generally in error due both to thermal output and to variation of the gage factor with temperature - and hence the double tilde over the strain symbol.

Consider first the correction for thermal output. Since the gage factor setting of the strain indicator coincides with that used in measuring the thermal output, this correction can be made by direct subtraction of the thermal output (as given on the gage-package technical data sheet) from the indicated strain. That is,

  = indicated strain, uncorrected for either thermal output or gage factor variation with temperature.

  = semi-corrected strain; i.e., corrected for thermal output only.

  = thermal output at temperature (functional notation is used to avoid double and triple subscripts).

Next, correction is made for the gage factor variation with temperature. Because the strain measurement was made at a gage factor setting of , the correction to the gage factor at the test temperature is performed with Eq. (504.9) as follows:

where:

  = strain magnitude corrected for both thermal output and gage factor variation with temperature.

  = gage factor at test temperature.

Combining the two corrections,</>

   Eq.(504.11)

When the prescribed conditions on the gage factor setting and the zero-balance temperature have been met, the strain   from Eq.(504.11) is the actual strain induced by mechanical and/or thermal stresses in the test object at the test temperature. As a numerical example of the application of Eq.(504.11), assume the following:

• Strain gage : WK-06-250BG-350
• Test material : Steel
• ^†† Room-temperature gage factor , : 2.07
• Test temperature : -50° F (-45° C)
• , indicated strain at test temperature
  (with instrument gage factor set at ) -1850 microstrain
• ^†† , thermal output at test temperature : -200 microstrain
• ^†† , deviation at test temperature from room-temperature gage factor : +0.6%

Using Eq.(504.10) to obtain , the gage factor of the gage at test temperature,

Substituting into Eq.(504.11), with = 2.0,

For what might appear to be a more complex case, consider a strain-gage-instrumented centrifugal compressor, operating first at speed , with the temperature of the gage installation at . Under these conditions, the indicated strain is . The compressor speed is then increased to , with a resulting gage installation temperature of and an indicated strain . The engineer wishes to determine the change in stress-induced strain caused by the speed increase from to .

This problem is actually no more difficult than the previous example. Applying Eq.(504.11) to each condition:

The same numerical substitution procedure is followed as before, and the results subtracted to give ( - ), the change in stress-induced strain caused by the speed increase. The subtraction can also be done algebraically to yield a single equation for the strain change:

When computerized data reduction is used, analytical expressions for the functions and can be introduced into the program to permit direct calculation of corrected strains from indicated strains.

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