FE Mechanical Measurements, Instrumentation, and Controls Practice Problems

The current FE Mechanical specification assigns 5-8 of the 110 exam questions to Measurements, Instrumentation, and Controls. Form A contains 6 original problems in this area. The sample below is published in full, with the same worked-solution format used throughout the book.

A single active foil gauge of gauge factor 2.10 is bonded along the axis of a steel tie rod ( $E = 200$ GPa) and wired as one arm of a quarter-bridge excited at 10.0 V DC. The bridge is balanced at no load; under load the bridge output is 1.05 mV. The axial stress in the rod is most nearly:

(A)20 MPa
(B)40 MPa
(C)84 MPa
(D)176 MPa

Show worked solution

Answer: (B)

The bridge output corresponds to 200 microstrain in the active arm, or 40 MPa of axial stress in the steel rod.

A single active arm unbalances the bridge by one quarter of the fractional resistance change, so the output-to-excitation ratio carries a factor of four.

\frac{V _{o}}{V _{e x}} = \frac{GF \cdot ϵ}{4}

ϵ = \frac{4 ( 1.05 \times 1 0 ^{- 3} )}{2.10 ( 10.0 )} = 2.00 \times 1 0^{- 4}

Hooke's law in uniaxial tension converts the surface strain to stress, since the rod remains elastic.

σ = E ϵ = (200 \times 1 0^{9}) (2.00 \times 1 0^{- 4}) = 40 \times 1 0^{6} Pa

FE Reference Handbook — Instrumentation, Measurement, and Controls: Strain Gauge and Wheatstone Bridge

Why the other choices appear

(A)Uses the half-bridge factor of 2 instead of 4, giving 100 microstrain and 20 MPa.
(C)Omits the gauge factor entirely, giving 4(1.05 mV)/(10.0 V) = 420 microstrain and 84 MPa.
(D)Multiplies by the gauge factor instead of dividing, giving 882 microstrain and 176 MPa.