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