Structural Engineering & Statics
where the load goes
Generator

The rayleigh-shape 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.
Rayleigh's method: the frequency read off the deflection that was computed anywayA simply supported beam of 8 m, sagging 13.08 mm under its own weight, sampled at 21 stations. Rayleigh's quotient over those deflections gives 4.91 Hz against the exact 4.91 Hz — 0.119% high, and high rather than low because an assumed shape is a constraint and a constraint stiffens. The rule of thumb, 18 divided by the square root of the deflection in millimetres, gives 4.98 Hz.8 m simple span · sag 13.08 mmthe static shape, not an eigenvectorω² = g · Σ(w·δ) ⁄ Σ(w·δ²)Σ(w·δ) = 197.3 · Σ(w·δ²) = 2.030Rayleigh, from the static shape: 4.915 Hzexact, from the characteristic equation: 4.909 Hz18/√δ with δ in mm: 4.977 Hz

2 essays call rayleigh-shape. 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.

8 m simple span · sag 13.08 mmthe static shape, not an eigenvectorω² = g · Σ(w·δ) ⁄ Σ(w·δ²)Σ(w·δ) = 197.3 · Σ(w·δ²) = 2.030Rayleigh, from the static shape: 4.915 Hzexact, from the characteristic equation: 4.909 Hz18/√δ with δ in mm: 4.977 Hz Dynamics

The period nobody chose

Every structure has a natural period, it decides the answer to every question in this field, and no drawing anywhere records it. It is a consequence of a mass picked for one reason and a stiffness picked for another — and it has already been computed, by the serviceability check.

 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.

The library, page 3 of 4 — where rayleigh-shape sits