Structural Engineering & Statics
where the load goes
Concept

Imposed load — where it appears

The load a structure carries because of what it is used for, as distinct from what it is made of. It is specified as a characteristic value with a small probability of being exceeded on one floor, which is why summing several of them over a column overstates the total and why a reduction is applied.

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

The envelope is not a state of the structure. Every arrangement of the imposed load on three spans — 8 of them, since each span is loaded or not — drawn faintly, with the greatest sagging and greatest hogging at each station drawn over them. Each faint curve is a real state of equilibrium and satisfies the free-moment identity exactly: mid-span ordinate minus the mean of the end moments is wL²/8, to 3e-16 of it. The envelope satisfies it nowhere, missing by up to 23% — because it is assembled from different load cases at different stations and no arrangement of load produces it. seven of the 8 arrangements are needed to build it; the rest never govern anywhere.

The envelope is not a structure

A continuous beam whose imposed load may sit on any span has eight load cases, and every one of them is a genuine state of equilibrium. The curve the design is made against is not one of them — it is assembled from different cases at different stations, and it fails the identity all eight satisfy exactly.

equilibrium · Load arrangement Independence, and the floor it never goes below. The reduction factor a column is allowed, two ways. The code's storey rule falls to 0.70 and stops. The independence argument — n bays each with a mean and a standard deviation, summed — gives (1 + zv/√n)/(1 + zv), which falls faster and stops at 0.503: a floor with no n in it at all, decided only by how variable the load is and how far out the fractile is drawn. The mean is never reduced away, because every bay really does carry its mean. At ten storeys the two differ by 10.0 points.

The load that is never all there at once

A column at the bottom of twenty storeys is designed for the imposed load of twenty floors added up, and twenty floors do not reach their own worst day together. The reduction that follows is not a discount on the safety margin. It is the central limit theorem, and it has a floor it never goes below.

equilibrium · Live load reduction

Named alongside it

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

Load combinationBending momentCharacteristic valueContinuityEnvelopeEquilibriumFractileFree bodyIndependenceIndeterminacyInfluence lineLive load reduction

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