Structural Engineering & Statics
where the load goes
Concept

Natural frequency — where it appears

The rate at which a structure oscillates when disturbed and left alone, set by its stiffness and its mass and by nothing else.

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

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

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.

dynamics · natural period 2345678910051015202530floor frequency (Hz)response factor1× pace2× pace3× pace4× pace4 Hz — R = 106 Hz — R = 7

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.

dynamics · floor vibration

Named alongside it

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

Modal massCharacteristic equationDampingDeflectionFloor vibrationFootfallMode shapeNatural periodRayleigh methodResonanceResponse factorServiceability

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