Structural Engineering & Statics
where the load goes
Concept

Rayleigh quotient — where it appears

The ratio of a structure's strain energy to its kinetic or geometric energy for an assumed deflected shape, giving a frequency or a buckling load. It is stationary at the true mode, so a crude shape gives a good number, and it is always an upper bound because an assumed shape is a constraint.

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

5010015020000.20.40.60.811.2slenderness (effective length ÷ radius of gyration)they cross at λ = 85squashingEuler bucklingreal columns, which are neither

The stiffness the load takes away

Buckling is usually taught as an event — a critical load, a bifurcation, a mode. Written as a matrix it stops being an event at all. A compressive load subtracts a stiffness from the structure, the subtraction grows with the load, and the critical load is simply where what is left reaches zero.

stability · geometric stiffness 0123four nodes, three freedoms eachthe marked member touches six of the twelvethe global matrix, twelve by twelvethirty-six entries added in; the rest untouched

The answer that depends on how it was divided

Every computed answer in this collection came out of a structure chopped into pieces — elements, strips, stations, trial positions. The chopping is invisible in the result and it is not neutral: some divisions give the exact answer, some give one that is always too stiff, and one of them changes nothing but the cost of getting there.

deflection · discretisation

Named alongside it

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

CompatibilityDegrees of freedomEigenvalueStiffness matrixAmplificationBandwidthBucklingConvergenceCritical loadDiscretisationEffective lengthFlexibility

All concepts