Structural monitoring
Strain gauges: making the reading still mean something next year
On a bridge or a building, the hard part is not acquiring the bridge voltage — it is that lead resistance, gauge apparent strain and excitation self-heating all drift with temperature, and they drift more than the strain you are trying to see.
Bridge arithmetic for quarter, half and full configurations; excitation current and self-heating; why lead resistance appears in the reading and how wiring changes it; gauge apparent strain; and the resolution a narrow input range buys you.
Structural monitoring is a different discipline from machine vibration, and the difference is time. A machine test lasts minutes and the question is what is happening now. A structural installation lasts years and the question is whether this year differs from last year — which makes drift, rather than bandwidth, the thing that decides whether the data is worth keeping.
Bridge arithmetic, in one table
| Configuration | Output per 1000 µε (GF = 2) | What it gives you |
|---|---|---|
| Quarter bridge, one active gauge | 0.5 mV/V | One measurement axis. Needs three completion resistors, and it is the configuration most sensitive to lead wire and to temperature. |
| Half bridge, two active gauges | 1.0 mV/V | Twice the output. If the two gauges see opposite strains — bending on either face of a beam — the strain adds and the thermal apparent strain largely cancels. |
| Full bridge, four active gauges | 2.0 mV/V | Four times the output of a quarter bridge and the best thermal behaviour, at the cost of four gauges to install and a placement error that no amount of signal processing will remove. |
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The thermal argument for the full bridge is the one that decides most structural installations. On a long-term job, the difference between a quarter bridge and a full bridge is usually the difference between needing a temperature channel next to every gauge and not needing one — and the difference between re-deriving the baseline every season and not needing to.
Excitation: more voltage is not free
Bridge output is proportional to excitation, so raising the excitation is the obvious way to get more signal. It also raises the power dissipated in the bridge, and that power has nowhere to go except into the gauges and the structure they are bonded to.
| Excitation | Current through a 350 Ω bridge | Power dissipated in the bridge |
|---|---|---|
| 2.5 V | 7.1 mA | 17.9 mW |
| 5 V | 14.3 mA | 71.4 mW |
| 10 V | 28.6 mA | 286 mW |
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Going from 2.5 V to 10 V multiplies the signal by four and the self-heating by sixteen. That heat raises the gauge temperature, the gauge temperature changes the gauge's own apparent strain, and the loop closes as a drift that looks exactly like slow structural movement. On a bonded installation where the gauge cannot shed heat into a large mass, low excitation and a longer averaging time is usually the better trade.
Lead resistance appears in the reading
In a quarter bridge, the two wires running to the gauge are in series with the active arm. They are not part of the strain, but the instrument cannot tell the difference, so their resistance desensitises the reading and their temperature coefficient appears as apparent strain.
The size of both effects is worth working through once with the numbers from a real installation. Take a 350 Ω gauge, and 20 m of 0.5 mm² copper twin lead — about 0.7 Ω per conductor, so 1.4 Ω in the loop.
- Sensitivity. The active arm is now 351.4 Ω instead of 350 Ω, so the same strain produces a slightly smaller output. The reading is low by 350 / 351.4, which is 0.4% — about 4 µε on a 1000 µε reading. Small, but known and correctable.
- Apparent strain from lead temperature. Copper changes resistance by roughly 0.4% per °C, so 1.4 Ω of lead moves by about 5.6 mΩ per °C. Against a 350 Ω arm that is about 16 ppm per °C, which the instrument reports as strain — of the order of 8 µε per °C with a gauge factor of 2.
The second number is the one that matters outdoors. A structure that swings 20 °C over a day will show on the order of 160 µε of apparent strain that has nothing to do with load. If the effect you are monitoring is smaller than that, the lead wire is currently the dominant sensor.
Three-wire connection is the standard answer. It puts an equal lead into the adjacent arm of the bridge, so the two leads' thermal resistance changes push the bridge in opposite directions and largely cancel. The residual sensitivity error is roughly halved rather than eliminated, and the correction above still needs to be applied — but the temperature term, which is the large one, goes away.
The gauge itself moves with temperature
Even with perfect wiring, a bonded gauge reads a nonzero strain on an unloaded structure when the temperature changes. The gauge alloy and the structure expand by different amounts, and the gauge factor itself varies with temperature. This is apparent strain, and its curve against temperature is not a straight line — it is specific to the gauge type and the material it is bonded to, and the manufacturer publishes it.
- The dependable approach on a long-term installation is a dummy gauge: an identical gauge bonded to an unstrained piece of the same material, in the same thermal environment, wired into the adjacent bridge arm. It measures the apparent strain directly, and subtracting it is exact rather than modelled.
- The second-best approach is a temperature channel bonded alongside the gauge, with the manufacturer's apparent-strain curve applied afterwards. This works, and it depends on the curve staying valid — which it does not if the bonding adhesive or the structure's surface treatment differs from the coupon the curve was measured on.
- What does not work is re-zeroing whenever the temperature changes. That removes the thermal term from the data and removes the load-induced term with it, and there is no way to tell afterwards which was which.
Resolution: choose the narrow range
The same arithmetic that applies to every other low-level signal applies here. A full bridge at 1000 µε produces 2 mV/V, so at 5 V of excitation the output is 10 mV. On the ±0.2 V input range, where one LSB is 6.1 µV, that 10 mV spans about 1640 codes — roughly 0.6 µε per LSB.
Compare that with the same signal left on the ±10 V range at 305 µV per LSB, where 1000 µε is only 33 codes and each one is about 30 µε. Both are the same module. The difference is entirely in the range selection, and it is the reason a structural channel left on the default range will look noisy when it is not.
Logging for a year changes the requirements
Once the deployment is measured in months, the parameters that matter are different from a laboratory test. Bandwidth stops being interesting — strain under traffic is slow, temperature is slower — and what takes its place is clock stability, power, and the ability to prove the system was alive.
- Sample fast for the transient and log the average for the trend. Traffic events and thermal movement want different rates, and a system that records only the 1 Hz average will lose the event that caused the crack.
- Keep a free-running sample even when nothing happens. A gap in the record is indistinguishable from a period of zero strain unless the system says otherwise.
- Give every structure a temperature channel. It is the single most useful channel for explaining a slow change, and it costs one input.
- Plan for the clock. Over a year, a drifting host clock puts events in the wrong order relative to each other and relative to the inspection records they will be compared against.
The standards that apply
A few references are worth knowing because they define what a deliverable looks like, not because they prescribe a sensor. ISO 16587 covers performance parameters for condition monitoring of structures. ISO 18649 addresses the evaluation of measurement results from dynamic tests and investigations on bridges. ISO 10137 deals with serviceability — the vibration levels that affect the people using a structure rather than the structure itself. And where a fatigue assessment is the point of the exercise, ASTM E1049-85 (reapproved 2023) is the reference for cycle counting, which is the rainflow method most fatigue analyses assume.
Choosing the module
| The job | Part | Why this one |
|---|---|---|
| A dense array of gauges and temperature channels on one structure | USB-6225 | 80 single-ended / 40 differential inputs at 250 kS/s. With 80 channels the rate per channel is still about 3 kS/s, which is ample for strain and far more than temperature needs. |
| Fewer channels, but with a mix of strain, accelerometer and actuation | USB-6212 | 16 differential inputs, 32 digital lines and two 80 MHz counters, so a strain installation can also count axle passes or read a limit switch. |
| A small, low-power logger at a remote location | USB-6003 | Four differential inputs at up to 100 kS/s in a bus-powered package, for a handful of channels where the enclosure, not the channel count, is the constraint. |
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Errors that take a season to notice
- Two-wire quarter bridge with long leads, and a reading that tracks sunlight.
- Re-zeroing whenever the temperature changes, which deletes the load signal along with the thermal one.
- Raising excitation to 10 V for more signal, and adding 286 mW of self-heating to the structure.
- Leaving every channel on the ±10 V range and concluding the gauges are noisy.
- Recording only a 1 Hz average, and losing the traffic event that started the crack.
- Citing a bridge-design code as if it were a measurement standard, without checking that it says what the specification claims.
Every figure in this note is either arithmetic from published resolution and sample-rate specifications, or a value stated by the standard it cites. Where a number depends on a particular module, confirm it against that module datasheet before design freeze.