Structural Engineering & Statics
where the load goes
Concept

Stiffness method — where it appears

Writing one equation per freedom and solving for displacements, with member stiffnesses scattered into a matrix indexed by the freedoms they touch. It adds no physics to the hand methods it replaced; the whole of the invention is the bookkeeping, which is why a machine can do it.

Named by 2 essays across one field — 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 0510152025-100-5050position along the beam (m)bending moment (kNm)-98.6-98.6hinges releasedsupports released

Choose what to take away

The other machine for a redundant structure works by removing restraints until what is left can be solved by statics, then putting back exactly enough force to close the gaps that opened. Which restraints are removed does not change the answer at all, and changes the arithmetic completely — one choice gives a tridiagonal matrix a person can solve on paper, and another gives a full one.

deflection · force method

Named alongside it

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

CompatibilityEquilibriumIndeterminacyMoment distributionVirtual workBandwidthBending momentCondition numberContinuous beamDegrees of freedomDeterminacyFlexibility

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