Structural Engineering & Statics
where the load goes
Generator

The floor-response generator

Rendered here at the parameters it defaults to, with every essay that calls it — which is the same list as the blast radius of changing it.
Which floor frequencies a 2 Hz pace punishesThe 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.2345678910051015202530floor frequency (Hz)response factor1× pace2× pace3× pace4× pace

3 essays call floor-response. The drawing above is what it returns with no arguments at all; every call below passes it something, because a placement that passes nothing draws whichever member of the family the generator happens to default to rather than the one its essay argues about.

Where it is called

Changing this generator changes every one of these figures.

2345678910051015202530floor frequency (Hz)response factor1× pace2× pace3× pace4× pace4 Hz — R = 106 Hz — R = 7 Dynamics

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.

 020406080100120-0.015-0.01-0.0050.005people walking on the spantotal damping ratio0.60% damping · 0.5 Hz30.16 people — nothing leftbelow: a disturbance dies awayabove: the structure drives itself Dynamics

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.

 00.511.522.533.540510152025forcing frequency ÷ natural frequencyforce out ÷ force in√2 — nothing gained, at any damping2% damping5% damping20% damping Dynamics

The machine that shakes the building

Put a machine on springs to keep its vibration out of the floor, and below a frequency ratio of root two the springs make things worse. Every transmissibility curve ever drawn passes through exactly one at that ratio, whatever the damping — so a soft mount either works well or fails badly, with nothing in between.

The library, page 1 of 4 — where floor-response sits