Concept

Span scaling — where it appears

How a beam's quantities grow with its span at a constant load intensity and section. The load grows in proportion, the moment as the square, and the deflection as the fourth power. It is why a member long enough to be interesting is governed by stiffness rather than by strength.

Named by 3 essays across 2 fields — each of them below, with the objects they name alongside it.

11.522.530.40.50.60.70.80.91long span ÷ short spanshare taken by the short strips6 × 8 m: 76.0%by 2 : 1 it is a one-way slab

The slab that spans both ways

A panel supported on four sides sends its load in two directions at once, and the share is decided by a fourth power — so a panel a third longer than it is wide has already stopped being a two-way slab in any useful sense. What it does at collapse is a different calculation with a different answer.

structures · two way spanning
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.

Load pathFunicularMaterial indexMembrane actionSelf weightTributary areaArchCableCollapse mechanismDead loadDeflectionFixed point iteration

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