Measurement Principles, Sensors & Transducers Notes

Last reviewed 30 Sept 2026 · 8 min read

Why measure a bridge

A bridge designer works with assumed loads and material properties; instrumentation shows what the bridge actually does. Measurements verify the design, check construction stages, reveal deterioration, decide whether a bridge can carry a heavier train or vehicle, and warn of trouble early. Good measurement depends on understanding what a sensor can and cannot tell you.

Basic measurement concepts

Term	Meaning
Range	The span between the smallest and largest value the instrument can measure
Accuracy	How close the reading is to the true value
Precision (repeatability)	How close repeated readings are to each other
Resolution	The smallest change in the quantity that produces a change in the reading
Sensitivity	The change in the output per unit change in the input (e.g., mV per µε, mV/V per kN)
Linearity	The closeness of the input–output relation to a straight line
Hysteresis	The difference in reading for the same input when approached from above or from below
Drift	A slow change in the output with time when the input is constant (temperature and ageing)
Zero offset and span error	Errors in the reading at zero input, and in the slope of the calibration
Response time and frequency response	How fast the instrument follows a changing input; a static sensor cannot record vibration

Accuracy and precision are different: an instrument can be very precise (repeated readings identical) but inaccurate (all wrong by the same offset).

Errors and uncertainty

Systematic errors — repeatable and correctable: calibration error, zero drift, temperature effect, a wrong gauge factor.
Random errors — scatter due to noise; reduced by averaging and better shielding.
Gross errors — mistakes: wrong connection, a damaged cable, a loose sensor.
Uncertainty combines the contributions of all sources into a range within which the true value is expected (for independent random errors, the root-sum-of-squares $u = u_{1}^{2} + u_{2}^{2} + \dots$ ).

Strain gauges

Electrical-resistance strain gauge: a thin metal foil grid bonded to the structure. When the surface is strained the grid is stretched, and its resistance changes in proportion:

\frac{Δ R}{R} = GF ε

$GF$ = gauge factor (about 2.0 for common foil gauges), $ε$ = strain. A change of 500 µε in a 120 Ω gauge gives $Δ R = 120 \times 2.0 \times 500 \times 1 0^{- 6} = 0.12$ Ω — tiny, so it is measured with a Wheatstone bridge.

Wheatstone bridge

The gauge forms one arm (quarter bridge) — or two, or four — of a bridge circuit excited by a voltage $V_{e x}$ . The output for a quarter bridge is

V_{o u t} = \frac{V _{e x} GF ε}{4}

Worked ExampleExample — quarter-bridge output

$V_{e x}$ = 10 V, $GF$ = 2.0, $ε$ = 500 µε:

$V_{o u t} = \frac{10 \times 2.0 \times 500 \times 1 0 ^{- 6}}{4} = 2.5 mV$ — the signal must be amplified (typically ×100 to ×1000) before it is digitised.

Bridge	Arrangement	Advantage
Quarter	One active gauge; 2 (or 3) fixed resistors	Simple; temperature effect needs a dummy gauge
Half	Two active gauges (e.g., tension and compression on opposite faces)	Twice the output; temperature compensated
Full	Four active gauges	Four times the output; best compensation; used in load cells

Temperature compensation is crucial: a temperature change alone gives an apparent strain. It is cancelled with a dummy gauge (same type, same temperature, unstressed) in the adjacent arm, or by using a half/full bridge. Lead-wire resistance is compensated by a three-wire connection. Gauges are bonded with epoxy and protected by coatings against moisture and mechanical damage; for embedment in concrete, sealed gauges are used.

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