Structural Engineering & Statics
where the load goes
Concept

Scaling — where it appears

How a structural quantity changes when a dimension is multiplied, which is usually a power rather than a proportion. The exponent is the whole result: a deflection carrying a fourth power and a stress carrying a first behave completely differently as the same structure grows.

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

11.522.533.54050100150200250300span, relative to the first1×5×16×81×256×moment: the squareload: the first powerdeflection: the fourth

Span to the fourth, which is why spans are short

Doubling a span multiplies its deflection by sixteen. No other relationship in ordinary structural work is that steep, and it is the reason long spans are always a different kind of structure.

deflection · span scaling 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

Named alongside it

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

StiffnessCarbon fibreCostDensityDesignDimensional analysisElastic modulusFourth power lawMaterial indexMaterial selectionSecond momentSecond moment of area

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