Structural Engineering & Statics
where the load goes
Concept

Scatter — where it appears

The spread of measured values about their mean in a set of nominally identical tests. It is what separates a characteristic strength from an average one, and a wider scatter lowers the design value even when the mean is unchanged.

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

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

The characteristic strength, which nothing was measured at. A lognormal population of strengths with a mean of 30 N/mm² and a coefficient of variation of 0.15. The characteristic value is the 5% fractile — 23.2 N/mm², which is 77% of the mean, and which need not be the strength of any specimen that was tested. Dividing it by 1.50 gives 15.5, and the shaded sliver below that is the fraction of the population that would fail to reach it: 6.4e-6, or one in 155,818. A factor applied to a fractile is not covering the scatter, because the scatter has already been spent getting to the fractile.

The strength no specimen had

A material property is written into a calculation as a number, and a material does not have one. It has a population of strengths with a mean and a spread, and the number used is a low fractile of that population — a value that need not have been measured, that most of the material exceeds, and whose distance below the mean is decided entirely by the scatter.

materials · Characteristic strength Three specimens cannot see the tail. The factor k applied to the sample's own scatter when a characteristic value is estimated from n specimens. With the scatter known in advance it is z·sqrt(1 + 1/n) and barely moves; with the scatter estimated from the same n results it is the Student t quantile instead, and it runs from 7.73 at two specimens to 1.73 at 30. At n = 4 the characteristic strength comes out at 23.8 N/mm² against 27.9 for a population known exactly — 15% lower, for a material that is identical. A small test programme does not report a worse estimate of the strength; it reports a worse strength.

The strength that belongs to the test programme

A characteristic strength is a fractile of a distribution, and a distribution estimated from four specimens is not the same object as one known exactly. The same material tested four times reports a strength 15 per cent below what it reports when its scatter is known — and nothing about the material differs.

materials · Characteristic strength

Named alongside it

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

Characteristic strengthFractilePartial factorReliabilitySize effectTestingCoefficient of variationDuctilityEffective depthFractureFree bodyLognormal

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