Structural Engineering & Statics
where the load goes
Concept

Null space — where it appears

The set of vectors a matrix maps to zero. For a structure's equilibrium matrix those vectors are its mechanisms; for an unsupported stiffness matrix they are the rigid-body motions, three of them in a plane, and a fourth one means a restraint is missing.

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

a square with both diagonalss = 1 · m = 0Maxwell's count: +1nothing to stiffentwo bars in a straight lines = 1 · m = 1Maxwell's count: +0prestress stiffness +1.000

The forces that are there with nothing applied

Maxwell's count is the difference between two dimensions, and it knows neither of them separately. A frame can satisfy it exactly and still both fold and be prestressable — and when it does, the second of those is what stops the first.

structures · self stress 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.

DeterminacyBandwidthCable netCompatibilityCondition numberDegrees of freedomEquilibriumEquilibrium matrixFree bodyGeometric stiffnessGlobal stiffness matrixIndeterminacy

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