Structural Engineering & Statics
where the load goes
Concept

Sparsity — where it appears

The property that almost every entry of a stiffness matrix is exactly zero, because a member reaches only the two nodes at its ends. The zeros are absences rather than small numbers, and they are what makes a large structural solution affordable.

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

36 × 36210 non-zerosof 1296 entriesbandwidth 13nullity 3before the supports go indense solve 16kbanded 6ka member reaches only its own two nodes

The matrix that replaced the hand methods

Moment distribution passes moments round a frame until they stop moving. Virtual work computes one deflection at a time. Both are exact and both stop scaling in the low tens of members. What replaced them adds no physics at all — the whole of the invention is the bookkeeping.

deflection · stiffness method 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

Named alongside it

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

CompatibilityDegrees of freedomAmplificationBandwidthBucklingCondition numberCritical loadDeterminacyEffective lengthEigenvalueEquilibriumFree body

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