Numerical Examples

Example (1) As a first example, assume that a Wheatstone bridge with a single active gage (quarter-bridge) was initially balanced resistively, after which the gaged test member was loaded until the strain indicator registered 15 000 microstrain in tension. Calculation yields the correction as 230 microstrain at a gage factor of 2.0. The actual strain is thus 15 230 microstrain.

Example (2) It was assumed in the previous example that the Wheatstone bridge was initially in a state of resistive balance. In the practice of experimental stress analysis with strain gages, this may not always be the case. For instance, during the bonding of a strain gage the resistance of the gage may be altered significantly from the manufactured value by poor installation technique. It may also happen that the gage is strained to the plastic range by assembly or preload stresses before subsequent strain measurements are to be made. The initial resistive unbalance, unless it is known to be insignificant, should be measured and properly accounted for in making nonlinearity corrections. When great enough to warrant consideration, the initial unbalance (expressed in strain units) must be added algebraically to any subsequent observed strains so that the nonlinearity correction is based on the total (or net) unbalance of the Wheatstone bridge at any stage in the strain measurement process.

For this example, assume that by interchanging the connections to the active and dummy arms of the Wheatstone bridge, the strain indicator indicates an initial unbalance of -4500 microstrain in an installed strain gage. This is an indicated unbalance, and includes a small nonlinearity error which will be corrected for, in this case, to illustrate the procedure. By calculation, the correction is 20 microstrain, and thus the actual resistive unbalance is -4480 microstrain. After taking this reading (but not resistively balancing the Wheatstone bridge arms), the gaged test object is loaded until the indicated applied strain is -8000 microstrain. The total indicated unbalance in the Wheatstone bridge is then -12 500 microstrain, for which the correction, by calculation, is 155 microstrain. The actual total unbalance is therefore -12 345 microstrain, and the actual applied strain is thus - 12 345 - (-4480) = -7865 microstrain.

Example (3) As a final example, consider a case in which the indicated initial unbalance after installing the strain gage was -2500 microstrain. Then the gaged member was installed in a structure with an indicated assembly strain of -45 500 microstrain. After taking this reading, subsequent loading produced an indicated strain change of 3000 microstrain in the tension direction. What corrections should be made to determine the actual tensile strain caused by loading the structure?

Prior to loading the structure, the Wheatstone bridge was unbalanced by an indicated -48 000 microstrain. By calculation, the correction is 2200 microstrain. Thus, the actual unbalance prior to loading was -45 800 microstrain. After loading the structure, the indicated unbalance in the Wheatstone bridge was -48 000 + 3000 = -45 000 microstrain. The correction for this indicated strain (by a second calculation) is 1940 microstrain, and the actual unbalance after loading was -43 060 microstrain. The applied tensile strain due to loading the structure was thus -43 060 - (-45 800) = 2740 microstrain. This example demonstrates that even with relatively modest working strains the nonlinearity error can be very significant (about 10% in this instance) if the Wheatstone bridge is operating far from its resistive balance point.

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