Concept

Material index — where it appears

A combination of material properties that ranks materials for one structural task, such as E to the half over density for a beam of free depth. The exponent comes from what is held constant and what shape is free, so a change of task reorders the materials without any property changing.

Named by 3 essays across 3 fields — each of them below, with the objects they name alongside it.

2.62.833.23.43.63.811.522.5density log₁₀(kg/m³)modulus log₁₀(GPa)mild steelhigh-strength steelaluminiumconcretetimbercast ironcarbon fibreglassE/ρ — a tieE^½/ρ — a beamE^⅓/ρ — a plate

The ranking belongs to the load case

Every table of material properties ever printed ranks by strength, and every one of them answers a question nobody asked. What a structure wants is the least mass for a stated performance, and the combination of properties that gives it changes with the shape of the member — so timber beats steel four to one as a beam and loses to it as a tie, without either material changing.

materials · material index
11.522.533.54050100150200250300span, relative to the first16×81×256×moment: the squareload: the first powerdeflection: the fourth

The weight that has to be known before it can be found

Every other load arrives from outside and can be looked up. A structure's own weight depends on how big it is, and how big it is depends on the load — so the first calculation on any project is a fixed point, and the fraction of a member spent carrying itself turns out to be the square of its span as a fraction of a span it can never reach.

equilibrium · dead load
0.511.520500100015002000depth of the truss1500857600429316the same moment, resisted by a longer lever arm

The same span, four ways

A beam, a truss, an arch and a cable can all cross the same gap under the same load, and the choice between them is usually described as a matter of judgement or of taste. It is neither. Each carries the load by a different mechanism, each mechanism has a different exponent, and an exponent decides the ordering at every span rather than at some spans.

structures · form selection

Named alongside it

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

FunicularLoad pathMembrane actionSelf weightSpan scalingStiffnessArchCableCarbon fibreCostDead loadDeflection

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