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The cheapest materials would be what can be acquired in space without having to launch from Earth. As a result, you're going to want to build your O'Neill cylinder out of some combination of iron, aluminum, titanium, and silicon dioxide.
The last of which might be particularly useful, as it is the main ingredient of fiberglass while also being the most common substance on Moon and asteroids. As a result, you probably want to build your cylinder primarily out of fiberglass. You can get pretty decently sized cylinders, as fiberglass has a higher strength-to-weight ratio than steel. Apparently, 24km diameter is a viable figure. Scale up length the same way, and you'll get 96km. So a 24km x 96km O'Neill cylinder made out of fiberglass.
That would be about 7238 km^2 of usable surface area. Half that to 3619 km^2 to make room for windows (as originally envisioned by O'Neill), and assuming a density comparable to New York City (about 11,300 people/km^2), you'll get around 40 million people. Or about the population of Tokyo.
That's seems plenty for any sensible space colonization strategy we might adopt in the future. And what's best is that you don't really need any fancy technology. Just use solar power to power mass drivers and deliver raw materials from the moon or asteroid via electricity. And it won't be any special materials either. Raw regolith can be made into fiberglass, so cost can be kept surprisingly low. The only question is scaling it all up, which may unfortunately be too expensive or will take a very long time to happen. Ultimately, this is still sci-fi, albeit on the hard side of it, since no fancy new technology is require.
I'd like to see a pressure vessel made of fibreglass that size... Not happening. Wall thickness in pressure vessels scales
Simple calculator, assuming steel... a 24 km diameter pressure vessel at 15psi is over 13 metres thick steel wall to contain the pressure. https://checalc.com/calc/vesselThick.html
Just the volume of steel required would be astronomical. You might be able to do this out of a similar mass of fibreglass... But forget launching it from Earth (would have to be made in situ).
And, largely, forget the fantasy renderings of what O'Neill cylinders look like -- they are anything but lightweight.
This is sci-fi stuff. No one is seriously saying we could build this anytime soon. It will require a radical advancement in space travel capability. But the interesting part of this is that it doesn’t any new technology. It needs only the technology that we currently have, just scaled up massively.
As it is an O’Neill cylinder, the raw material needs will be truly huge. We’re literally building a city on the scale of Tokyo but in space. So we are just assuming that someday, we can move around that amount of stuff in space.
It's far more than building a city the size of tokyo. It's the mass required. If you weighed Tokyo, and then engineered a hypothetical Tokyo in space, you'd find that the mass of the equivalent materials would be orders of magnitude higher than even your worst estimates.
Back of the envelope, you put Tokyo in a cylinder with a similar surface area to actual tokyo, the volume of steel in the walls of the containing cylinder (just the pressure vessel) would be about ... 60 billion cubic metres, or something like 450 billion metric tonnes of steel. As a point of comparison, tokyo tower is... 4000 tonnes.
As another point of comparison: our global annual steel production is currently around 2 billion metric tonnes per year. It would take 200+ years worth of global production to build just the pressure vessel for a tokyo in space. Unless you're building this at your source of raw materials, it just doesn't happen.
Yes, that's the point. It's far beyond the actual city of Tokyo in terms of construction difficulty and scale. But it doesn't need any new technologies to be invented to be doable. Just the ability to build on that scale.
But the point is if you get your materials from the Moon, for example, it's vastly more economical to just build a Moon colony (or another Moon colony) than a space colony of the same size.
Then you'll have to deal with Lunar gravity, which may be unacceptable for long durations. Humans may have to live in giant space stations if we want to live in space. And since they can be truly massive, it may be more desirable than what some might think.
The ideal solution is probably not to build a colony in the middle of space, but rather find a celestial body with the necessary materials with gravity low enough to be acceptable.
Moon gravity too strong? Try smaller moons. Phobos? Europa? Charon?