Structural Engineering & Statics
where the load goes
Series

Natural period — the series

One essay so far on this idea, and more questions about it than one essay answers.
  1. Rayleigh's method: the frequency read off the deflection that was computed anyway. A 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.

    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.

    part 1 · dynamics

All series