Structural Engineering & Statics
where the load goes
Concept

Eigenvalue — where it appears

One of the discrete values at which a set of equilibrium equations goes singular, marking a natural frequency, a buckling load or a mechanism.

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

05010015020025001020304050brace stiffness (units of EI/L³)critical load (units of EI/L²)ideal stiffness ≈ 159 EI/L³21.839.5 — braced9.87 — unbraced

The brace that need not be strong

A brace holding a column at mid-height carries almost no force. What it has to be is stiff — and the stiffness required is exact, large, and reached at a knee past which more buys nothing at all.

stability · effective length five floors · 300 t eachmode 10.6 s · 1.65 Hz88.0% of the massno nodemode 20.21 s · 4.83 Hz8.7% of the massone nodemode 30.13 s · 7.61 Hz2.4% of the masstwo nodes

A structure has more than one period

One mass on one spring has one period. A building with eight floors has eight, each with a shape of its own, and the second one bends the building into a curve nobody drew. They are not harmonics, they do not interfere, and each behaves as though the others were not there.

dynamics · mode shapes

Named alongside it

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

BracingBuckled mode shapeCritical loadDegrees of freedomEffective lengthImperfectionLateral restraintModal analysisMode shapeNatural periodOrthogonalitySoft storey

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