How to Spot a Psychopath

A reader writes:

Could you build a tabletop cathedral out of sugar cubes?

What I mean is, of course you could build one out of soapstone, or soap, or wax, or whatever, but all of those are so strong you can get away with pretty much anything. Snow is weak but so light you can build a shelter out of it with no particular concern for architecture (though I once had an unpleasant surprise when it got warm overnight - "wait, should I really be seeing stars? and what's this weight on my legs?"). But sugar cubes are both heavy and fairly crumbly.

So could you build a cathedral of reasonable size and have to deal with similar engineering difficulties to those medieval stone-cathedral builders did?

Anne

Never having tried it myself, and not even having any sugar cubes in the house, I reckon you could build something pretty impressive with them. I think they may indeed be quite good analogues for unreinforced historic masonry, at around a 1:100 scale. And yes, this could be quite instructive, like the classic spaghetti-bridge exercise that also forces the architect to work with a material that behaves in small scale not unlike real construction materials at full scale, neutralising the square-cube law that tends to make models unrealistically sturdy.

(Look at this enormous model, for instance. It's held together with glue, which may reinforce the cubes significantly, or may not.)

The compressive, and tensile, strength of materials is defined in pascals, one pascal being one newton of force applied over an area of one square metre. Because of this rather large area, even quite feeble materials achieve strength scores up in the kilopascals (kPa).

If your sugar cube is, for the sake of argument, one centimetre square, its share of a 1 Pa pressure over a square metre would be only one ten-thousandth of a newton, which is the kind of pressure a marshmallow could withstand without visible deformation. Crank the pressure up to 10,000 Pa (ten kilopascals, kPa) and the sugar cube will be supporting a whole Newton, equal to a weight of about 100 grams under normal Earth gravity. This seems a plausible sort of strength for a sugar cube to manage.

The compressive strength of modern bricks and concrete blocks is up in the single-digit megapascals (or considerably higher, if the bricks or blocks don't have the usual holes through them); some natural stones are much stronger (granite manages around 200 MPa), but natural stone is likely to contain cracks and fissures that make the safe load limit considerably lower.

If sugar cubes turn out to actually be feeble, it might not actually matter that much, because the full compressive strength of masonry is surprisingly unimportant a lot of the time. You could build the Empire State Building out of stone, or possibly even ordinary bricks, and be in no danger of crushing the bottom blocks with the weight of the rest. That building would be spectacularly unsafe - even with a big reinforced concrete foundation to prevent it from subsiding into the earth, tilting and then toppling, things like wind stress and very minor seismic events could destabilise a giant stone tower very easily. (There is a reason why the longest-lived colossal stone structures in the world are approximately the shape that collapsing stonework naturally creates.) But compressive strength, at least, would not be a problem.

The centuries-old cathedrals that survive are, generally speaking, well engineered, but this is because they're the ones that didn't fall down. A lot did. Pre-scientific architecture was a trial-and-error, evolutionary process, in which people built things that looked as if they'd stay up, and then hoped that if the roof did fall in, it wouldn't be on a full Easter congregation. Sometimes there's evidence of a forced design review in the middle of a building's construction; the Bent Pyramid probably looks the way it does because it became clear to the builders half way through that they were making something too tall and pointy to stay up.

Very few collapses had anything to do with masonry being crushed by its own weight, though, except when some genius decided to use masonry like wood and, say, try to bridge pillars with a slab of stone (the ancient Greeks did this sort of thing quite often, which is why the Parthenon is as ruined as it is. There's a fabulous stack of broken lintels hidden inside the Great Pyramid, too; one broke, they put another one on top, it broke, they put another one on, that one burned down, fell over, and then sank into the swamp...).

Another great way to accidentally put masonry in tension is to put a darn great dome on your building, which will push down and out all around its base. Masonry must then be tricked into keeping force paths safely within the stone by contrivances like, for instance, flying buttresses. If you must have a huge dome, you either need a lot of these tricks, or a circle of very stout iron chain hidden inside the dome's base.

Getting back to sugar cubes, they're not actually all that dense, since they're a porous sintered aggregate of sugar particles (which is essential; a solid cubic crystal of sugar would look pretty neat, but you'd be waiting a while for it to dissolve in your tea). The density of sucrose is only about 1.6 grams per cubic centimetre in the first place.

So if we ballpark the mass of each once-centimetre cube as one gram, and set the ceiling supportable weight as 100 grams, we can stack 100 cubes on top of each other before the one at the bottom is under unacceptable strain. I've no idea how close these numbers actually are to reality, though, and there are no doubt considerable variations between different brands of sugar cubes (some of which are rectangular cuboids, not cubes at all), how they've been packed and otherwise treated, the same sugar cubes under different conditions (humidity, mainly), and so on. I invite actual experimental evidence from readers below; stack things on sugar cubes until they're crushed, and tell us how much weight your cubes can stand!

(In the above blather about historical architecture, any seeming brilliance on my part was actually just relayed from the author of two of my favourite books in the whole world, J.E. Gordon. The relevant book here is "Structures, Or Why Things Don't Fall Down", but "The New Science of Strong Materials, or Why You Don't Fall through the Floor" is also essential reading for anybody who, on reading those titles, realises that they don't really know why these unfortunate events do happen so seldom in the modern world.)

Psycho Science is a regular feature here. Ask me your science questions, and I'll answer them. Probably.

And then commenters will, I hope, correct at least the most obvious flaws in my answer.