Structural Engineering & Statics
where the load goes
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Fire — the series

3 essays on one idea, from the one that introduces it to the one that assumes the rest.
  1. 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.

    part 1 · materials
  2. 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.

    part 2 · materials
  3. A room's fire has a peak and an end, and the furnace has neither. Gas temperature in a compartment with 200 MJ/m² of fire load per square metre of its enclosing surface, linings of thermal inertia 1160 J/m²s½K and a medium growth rate, for opening factors of 0.02, 0.04, 0.08, 0.14 m½, against the standard furnace curve, dashed. At 0.02 the fire peaks at 841 °C after 120 minutes and is back at ambient by 435; at 0.04 the fire peaks at 944 °C after 60 minutes and is back at ambient by 171; at 0.08 the fire peaks at 1048 °C after 30 minutes and is back at ambient by 92; at 0.14 the fire peaks at 900 °C after 20 minutes and is back at ambient by 37, having used its fuel before the growth limit, so the fuel rather than the air decided it. A larger opening lets more air in: the fire burns hotter and gets through its fuel sooner. The furnace curve is still rising when every one of them is out.

    The fire that goes out

    The furnace curve rises for ever. A room's fire has a peak and an end, set by its window, its walls and its fuel, and a bigger window makes it hotter and shorter — which is worse for bare steel and better for protected steel. The protected member is hottest half an hour after the fire has started to die.

    part 3 · materials

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