Structural Engineering & Statics
where the load goes
Concept

Degrees of freedom — where it appears

The independent displacements a structural model allows, one per direction of movement at each node. Their number sets the size of the stiffness matrix, and a structure with more of them than its supports restrain has a rigid-body motion in that matrix's null space.

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

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 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

Named alongside it

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

BandwidthCompatibilityCondition numberDeterminacyEigenvalueEquilibriumFree bodyGlobal stiffness matrixIndeterminacyModal analysisMode shapeMoment distribution

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