The Span

What the bridge is actually doing

1. 01

   Every member is a spring

   A member of length L pulls or pushes with a force of EA/L times however far it has been stretched or squashed — stiffer the shorter it is, exactly like the real thing. Joints are pins: they carry no bending, so the only thing a member can do is pull its two ends together or shove them apart.

2. 02

   Nothing is rigid

   Forces are summed at every joint, divided by the mass hanging on it and integrated forward three hundred times a second, with a little damping along each member so the structure settles instead of ringing. That is why the bridge sags visibly before the load has even set off: it is finding its own equilibrium, not being placed in one.

3. 03

   Long members buckle

   In tension a member holds until it reaches its breaking force. In compression it also has to beat Euler: capacity falls off as 1/L², so a nine-metre timber strut gives up at half the load a four-metre one will take. Held over capacity for a thirtieth of a second, it goes — and everything it was carrying goes to its neighbours, which is how one bad member takes a bridge down in stages.

Why the gorge is always crossable

Dealing a gap at random and asking you to bridge it on a fixed budget is only fair if the page knows it can be done. So before any of this is drawn, four standard lattice trusses — timber and steel, four and eight metres deep — are built against today's gorge and each one is put through the entire crossing headlessly: settle under its own weight, take the load on at one end, carry it across, put it down on the far bank. The cheapest one that survives becomes the reference, your budget is that cost plus forty-five per cent, and Show me one that works hands you the reference itself. If none of the four survive the gorge is narrowed by four metres and the whole thing is dealt again, which over three hundred gorges has not once been needed — though on forty-eight of those three hundred, exactly one of the four was still standing at the end. It costs about eight milliseconds to find out, which is why you did not notice it happening.

None of that makes your bridge a good one. The reference is a dull, heavy, over-braced lattice with two diagonals in every panel where one would mostly do. Measured against it: an ordinary Pratt truss — verticals at every panel point, single diagonals leaning in towards the middle so they are pulled rather than pushed — gets the load across a hundred and thirteen of a hundred and twenty gorges, and where it works it does the same job for about seventy-three per cent of the reference's price. The budget is the ceiling, not the target.

Two things worth knowing before you start. Wire rope really will not push: a cable asked to take compression simply goes slack and carries nothing, so a cable-stayed deck needs a mast standing on solid ground to hang from. And the roadway is not scenery — it is four-metre panels with a breaking force like everything else, and an unsupported panel with two tonnes standing on it is the usual way this ends. A roadway that has dropped two and a half metres counts as failed whether anything has snapped or not, on the grounds that it is no longer a road. For what it is worth, the reference trusses sag about half a metre at worst.

The same date integer that draws the flow field on the front page cuts this gorge, and it is doing eighteen other jobs besides — it grows the Garden, writes the Chimes, deals the Lattice, files the Almanac, scatters the Observatory, raises the Atlas, breeds the Menagerie, lights the Orrery, invents the Codex, runs the Chronicle, builds the Folly, cuts the gears of the Engine, threads the Loom, opens the Exchange, invents the rules of the Gambit, locks the doors of the Warren and arranges the corridor in the Inquest. Nothing here is saved between visits. Tomorrow the gorge is somewhere else and your bridge is not.