7.Data Reduction

Readings in position E on geokon’s readout boxes are displayed directly in microstrain based on the theoretical equation:

µε_theory = 0.391 (f ² x 10^–3)

Equation 5: Theoretical Microstrain

Where με is the strain in the wire in microstrain and f is the resonant frequency of the vibrating wire.

7.1Conversion of the Readings to Strain Changes

In practice, the method of wire clamping effectively shortens the vibrating wire slightly, causing it to over-register the strain. This effect is removed by applying the batch gauge factor (B) from the calibration report supplied with the gauges.

µε_apparent = (R₁ – R₀)B

Equation 6: Strain Calculation

Where R₀ is the initial reading on position E and R₁ is a subsequent reading.

Note: When (R₁ – R₀) is positive, the strain is tensile.

The value obtained from the above equation is required for computing stresses in equations steps two through four in Appendix B. The stresses thus computed are the total of those caused by both construction activity and by any temperature change that may have occurred.

7.2Converting Strains to Stresses

Strain gauges measure strain or deformation of the structure, however, the designer is usually more interested in the structural loads or stresses. This requires a conversion from the measured strains to computed stresses.

Stresses are computed by multiplying the measured strain by the Young's modulus for steel, which varies between 190 to 206 Gpa, (28 to 30 x 106 psi). Loads are computed by multiplying the stress by the cross-sectional area of the steel member.

Strain changes are computed from strain gauge readings taken at various times, and by comparison with some initial readings taken at time zero. This initial reading is best taken when the structural member is under no load, i.e., the gauges should be mounted while the member is still in the steel yard or warehouse.