Tighten a string and the pitch goes up. Loosen it and the pitch drops.
A guitarist hears the frequency and knows when the tension is right.
A stay cable works the same way.
It is just a 200 m guitar string carrying hundreds of tonnes.
The Vibration Method (Accelerometer)
This is the most widely used method on site.
1) Clamp a small accelerometer to the cable a few metres above the deck.
2) Let wind and traffic pluck the cable, with no shaker needed.
3) Run an FFT on the signal and clear peaks appear at f1, 2f1, 3f1 and so on, evenly spaced like the harmonics of a guitar.
4) Convert frequency to force with taut string theory:
T = 4mL²(fn/n)²
m = mass per metre, L = free length, fn = nth natural frequency
For example, a 200 m cable at 80 kg/m with f1 = 0.6 Hz carries about 4.6 MN, roughly 470 tonnes.
Tension goes with frequency squared, so a 1% error in frequency becomes a 2% error in force.
A real cable is also not a perfect string.
Bending stiffness matters on short cables, sag matters on long ones, and dampers near the anchorage change the effective length.
That is why we calibrate the model against a direct measurement.
Back when I was a young engineer, I spent a whole month measuring tension, and apparently I got to the point where I could tell how many tonnes of load had been applied just by placing my hand on the cable and feeling the vibrations…
Take it or leave it.
The Other Methods
Load cell: a ring sensor at the anchorage gives a direct and continuous reading.
It must be installed during construction and is costly, so usually only a few cables get one.
Lift off test: a hydraulic jack pulls the anchor head until it just lifts off the bearing plate.
The jack force at that moment is the cable force.
It is the reference method, but it is slow and needs access to the anchorage.
Laser: a laser Doppler vibrometer reads the cable vibration from the ground with no contact.
It uses the same frequency method, with no climbing needed.
EM sensor: a coil around the cable reads how the magnetic properties of the steel change with stress.
It suits monitoring over many years, but it must be calibrated for the steel grade and temperature.
In Practice
On site, we rarely rely on one method.
Lift off tests and load cells set the reference on a few cables.
Vibration measurements then check every cable quickly, during construction and for decades after.
So the next time you tune a guitar, you are doing what bridge engineers do, just on a smaller scale.
Which method do you trust most on site?
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