Structural Engineering & Statics
where the load goes
Concept

Crowd loading — where it appears

The forces a crowd applies to a structure when its people move together, walking, swaying or jumping to a beat. It is not their weight times their number, because people fall in and out of step, and a crowd's timing decides which harmonics of its motion survive to reach the structure.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

The damping a crowd leaves behind, and the number of people that uses it up. Total damping ratio against pedestrians, for a structure with 0.60% of its own and a modal mass of 120 tonnes at 0.5 Hz. Each person walking laterally puts a force in phase with the deck's velocity into it — about 300 N·s/m per person — so the crowd subtracts from the damping, and at 30.16 people what is left is nothing. Below the threshold a disturbance dies away. Above it, the structure feeds itself and the motion grows out of nothing at all — which is what makes this a different mechanism from resonance rather than a severe case of it.

The bridge that was pushed by its own sway

A crowd walking on a bridge that moves sideways adjusts its footing to stay balanced, and the adjustment pushes the bridge the way it is already going. The crowd is a damper with the sign reversed, and past a certain number of people the total damping is negative.

dynamics · Crowd synchronisation 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.

dynamics · Floor vibration

Named alongside it

The objects these essays reach for when they reach for this one.

DampingFloor vibrationFootbridgeLateral vibrationModal massNatural frequencyNegative dampingResonanceSelf-excitationServiceabilityStability thresholdTuned mass damper

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