Error Magnitudes and Corrections

The Bridge Arrangement Table gives, for the class of instruments described in the previous section , the output voltage as a function of the applied strain for a variety of cases representing different strain states and different arrangements of gages on the structural member and within the Wheatstone bridge. While the magnitudes of the nonlinearities are difficult to judge from the table, it can be seen from the column of bridge and strain arrangements that only when the resistance changes are such that the currents in the bridge arms remain constant - that is, when and - is the output a linear function of the strain. The table also includes, for each case, the ratio of the actual strain to the uncorrected strain, permitting correction of indicated strains with these formulas in the nonlinear cases.

Quarter Bridges

The first case in the accompanying Bridge Arrangement Table is applicable whenever a single active strain gage is used in a quarter-bridge arrangement (as shown below); and occurs very commonly in the practice of strain measurement for experimental stress analysis purposes.

Because of its basic importance, this case will later be used in several numerical examples to demonstrate the procedure for making nonlinearity corrections. The character of the nonlinearity associated with the quarter-bridge arrangement can be illustrated by writing the bridge output equation in the following form:

Eq. (507.1)

where:

= dimensionless bridge output, mV/V
= output voltage, mV
= bridge supply voltage, V
= gage factor of strain gage
= actual strain, microstrain

In Eq. (507.1), the term in parentheses represents the nonlinearity. It is evident from the form of the nonlinearity term that its magnitude will be less than unity for tensile strains and greater than unity for compressive strains. And the errors in strain indication due to the nonlinearity will correspond. In other words, indicated tensile strains will be too small and indicated compressive strains too large. For subsequent convenience, the incremental nonlinearity error, or correction, ( ), is defined as the amount which must be added algebraically to the indicated strain to obtain the actual strain. That is,

Eq. (507.2)

where:

= actual strain causing a resistance change in one arm of the Wheatstone bridge, microstrain
= indicated strain (corresponding to ) as read from a strain indicator with the specifications given in the Bridge Arrangement Table, microstrain
= incremental error in indicated strain, microstrain

For the single active gage in a quarter-bridge arrangement, it can be shown that the incremental error (in microstrain) is represented by the following expression:

Eq. (507.3)

The correction [which, from Eq. (507.3), always has a positive sign, irrespective of the sign of the indicated strain] is to be added algebraically, to the indicated strain. That is, the magnitude of an indicated tensile strain is always increased by adding the correction, while that of a compressive strain is always reduced.

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