Structural Engineering & Statics
where the load goes
Concept

Characteristic value — where it appears

The value of a load or strength that has a stated small probability of being exceeded, or of not being reached — usually a 95th or 5th percentile. Design starts from it, so how it is defined decides what a sum, an average or a reduction of such values means.

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

Also named here as independence, live load reduction — the same set of essays touches all of them, so they are one junction rather than several.

Independence, and the floor it never goes below. The reduction factor a column is allowed, two ways. The Eurocode 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 The floor under the reduction rises with the correlation. The least factor a column carrying ever more floors may take, against the correlation between floors, for an office imposed load with a coefficient of variation of 0.6, its characteristic value the 95th percentile, loads normal: (1 + zv√ρ)/(1 + zv). With independent floors it is 0.503, the floor the independence argument found; at a correlation of 0.1 it is 0.660, at 0.3 0.775, at 0.5 0.855. EN 1991-1-1's storey rule falls to ψ₀ = 0.70 (dashed), and the two cross at a correlation of 0.157: floors that move together any more than that make the rule's tall-building reduction larger than the averaging can pay for.

The floors that fill up together

A column may be designed for less than the sum of its floors' imposed loads because the floors do not reach their worst day together — an argument that assumes each floor's load is independent of every other's. Let any two floors be correlated, and the reduction the averaging can pay for shrinks, and stops shrinking at a higher floor. At a correlation of 0.16 that floor reaches the 0.7 the storey rule falls to. One tenant on five floors halves what twenty floors can average away.

equilibrium · Live load reduction

Named alongside it

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

FractileImposed loadIndependenceLive load reductionLoad combinationTributary areaLoad pathReliability

All concepts