Structural Engineering & Statics
where the load goes
Concept

Critical temperature — where it appears

The temperature at which a steel member's reduced strength falls to the load it is carrying, so it is a property of the load ratio rather than of the steel. It converts a fire resistance period into a heat-transfer problem, and a member at half its cold capacity reaches it around 600 °C.

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

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

The hour that is really a temperature. The retention factors for carbon steel against temperature: the yield stress and the elastic modulus. The modulus falls away first — at 500°C the steel has kept 78% of its strength and 60% of its stiffness — so a member's failure mode can change during a fire. A member working at 60% of its cold capacity runs out of strength at 558°C, and out of the stiffness for the same ratio at 500°C, 58 degrees earlier. There is nothing about time in any of it: a fire rating is a temperature the member must not reach, converted into the minutes a particular fire takes to get it there.

The hour that is really a temperature

A fire rating is quoted in minutes and there is no time in the physics anywhere. What decides is a temperature, and the stiffness reaches its limit sixty degrees before the strength does — so the way a member fails can change while it is burning.

materials · Fire The fire is one curve, and the steel in it is several. Gas temperature and steel temperature against time in a standard fire. The gas curve is the same for every member in the compartment; the three bare steel curves are section factors of 76, 160 and 323 per metre, and they reach 558 °C at 17, 11, 8 minutes — a spread of a factor of two from geometry alone. The fourth curve is the middle section with 15 mm of board on it, which reaches the same temperature at 46 minutes. The kink near 735 °C on the bare curves is not a numerical artefact: steel's specific heat spikes there as its crystal structure changes, and the member spends several minutes absorbing heat at almost constant temperature.

The temperature is a shape

Two members of the same steel in the same compartment, under the same fire and the same load ratio, fail eight minutes apart. Nothing about the material differs and nothing about the fire does. What differs is a perimeter divided by an area, and it is the only number in the whole calculation that a designer chooses.

materials · Fire

Named alongside it

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

FireLoad ratioSection factorBucklingCreepElastic modulusEmissivityFire protectionHeat transferLimit stateProof stressRetention factor

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