Structural Engineering & Statics
where the load goes
Generator

The energy-loop 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.
Where the energy goes: one loop in force against displacementThe force the supports feel — the spring's and the damper's together — against the displacement, for one mechanism. yielding at 182.53 kN, enclosing 22.35 kJ over the record drawn. The yielding loop is a parallelogram whose area does not depend on how fast it is traced, and every circuit leaves the structure displaced from where it began.-40-202040-200-100100200displacement (mm)restoring force (kN)yielding at 182.53 kN — 22.35 kJ

3 essays call energy-loop. 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.

00.511.522.530510152025forcing frequency ÷ natural frequencyamplitude ÷ static deflection1% damping — 50× at the peak2% damping — 25.01× at the peak5% damping — 10.01× at the peak10% damping — 5.03× at the peak Dynamics

The only thing that stops it

Drive a structure at its own frequency and the amplitude grows without limit unless something takes energy out. What takes it out is damping, and damping is the one structural property that is never designed, never drawn, and never known until the thing is built.

 02468101214161820-60-40-20204060time (s)displacement (mm)a ground motion of 3.5 m/s² peakelastic, and the same frame at a 4th of its strengthelastic: peak 57.71 mmyielding: peak 65.46 mmleft 14.13 mm off plumb Dynamics

The earthquake asks for a displacement

A structure a quarter as strong as the elastic demand does not deflect four times as far. It deflects almost exactly as far, yields on the way, and survives — which is why no ordinary building is designed for the force an earthquake would apply if it stayed elastic.

 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 energy-loop sits