Structural Engineering & Statics
where the load goes
Concept

Moment distribution — where it appears

A hand method for a continuous frame: lock every joint, release them one at a time, and pass each out-of-balance moment to its neighbours. The corrections shrink at every cycle, it converges on the exact elastic answer, and the sequence shows where the moment travels on the way there.

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

012345678020406080cycles of distributionmoment at the support (kNm)exact: 64.0all joints clamped

Solved by passing it around

An indeterminate structure needs simultaneous equations, and for thirty years engineers solved them without writing any down. Clamp every joint, release one, share out what is left over, pass half of it along, and repeat — and the answer walks in, three figures correct after four cycles.

deflection · moment distribution 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.

IndeterminacyBandwidthCarry overCompatibilityCondition numberContinuityDegrees of freedomDeterminacyDistribution factorEquilibriumFixed end momentFree body

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