Structural Engineering & Statics
where the load goes
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Floor vibration — the series

2 essays on one idea, from the one that introduces it to the one that assumes the rest.
  1. Which floor frequencies a 2 Hz pace punishes. The response factor of a floor of 12 tonnes modal mass and 3.0% damping, against its own natural frequency, under a walker at 2 steps per second. The peaks are at 2, 4, 6, 8 Hz — the harmonics of the pace — and they fall away sharply: four peaks, each smaller than the one below it, because the harmonics of walking get smaller. A floor at 2 Hz reaches R = 31 and one at 8 Hz reaches 6. Between them the floor is quiet.

    The floor that is strong and unusable

    A floor can satisfy every strength check, deflect less than the limit, and still be rejected by the people who work on it — because somebody walking across it at two steps a second happens to be exciting it at exactly the rate it likes to move.

    part 1 · dynamics
  2. The rates a seated crowd makes worse. The stand's steady rms acceleration under 40 people jumping, against the rate they jump at, for a stand of 30 t modal mass at 6 Hz with 2 per cent damping, empty and with 15 t of spectators sitting on it. Empty, the worst rate is 3.00 Hz, where the second harmonic of the jump lands on the stand's own frequency, and the stand reaches 2.54 m/s², 25.9 per cent of gravity. Occupied, the worst anywhere from 1.5 to 3.5 Hz is 0.49 m/s² at 3.50 Hz. But from 1.64 to 2.32 Hz, shaded, the occupied stand responds more than the empty one — 1.6 times as much at 2.00 Hz.

    The crowd that is also the structure

    A crowd jumping to music loads a grandstand with harmonics several times those of walking, and nothing about their size is measured: they follow from a pulse that has to average one body weight. But the people who jump arrive with the people who sit, and the seated crowd is mass, stiffness and damping bolted to the stand. It lowers the worst case by a factor of five and makes the most common jumping rates worse.

    part 2 · dynamics

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