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Scale changes everything — page 3

Essays 49 to 53 of 53 on this thread, in the same order.
11.522.533.54050100150200250300span, relative to the first16×81×256×moment: the squareload: the first powerdeflection: the fourth Equilibrium

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.

0.511.520500100015002000depth of the truss1500857600429316the same moment, resisted by a longer lever arm Structural form

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.

0102030405060strength (N/mm²)mean 30characteristic 23.2design 15.5one specimen in 155,818 falls below the design value Materials

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.

600 kN180 kN·mresultant at e = 300, outside the platemiddle third154.42 kNBolts engagedbearing over 150.88 mm at 20 N/mm² · 100% of 20 Connections

The failure that is in the concrete

An anchor bolt is a steel component and its capacity is usually decided by something else entirely — a cone of concrete pulled out around it, failing in tension, in a material every other calculation on the project has assumed cannot take tension at all. The exponent in the capacity says so: it is not the square the geometry implies.

0123400.20.40.60.81liquid depth ÷ radiusfraction of the liquidwith the wallslosheslever ÷ Hthis tank: H/R = 1.33, 65% impulsive Dynamics

The liquid has a period of its own

Shake a tank and its contents do not all go with it. Part of the liquid moves as though it were bolted to the wall and part sloshes at a period fixed by gravity and the radius, which the tank's stiffness has no influence over whatever. The split is decided by one proportion, and the two parts then take entirely different amounts of the earthquake.

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