I am trying to work out the size and (because this is among other things for populating a rotating habitat) weight of an arcology made to house, say, 5000 people - that seems a good number for a self-sufficient colony, large enough that you can avoid people you dislike, but small enough to still have a strong sense of community.
I assume you would (for civilian use) probably be able to get away with 20 m2 of personal habitation space per person - this is a room four meters by five meters, and while that is on the small side, it should be large enough not to feel cramped (source: My student apartment was about that big for a single person), so that gives 100,000 m2 for personal space. What I am a bit more lost on is how much space you'd have to allocate for workspaces and public space (I'd assume a few times as much as you have habitation space total, maybe 500,000 m2), hallways and elevator shafts (maybe on the same order as the amount of habitation space at most?) and also hydro-/aquaponics space to feed those 5000 people.
Assumptions I would be making for purposes of figuring out the size requirement of that and also the mass of the structure would be more or less near-future tech - meaning no bulk nanomaterials, but bulk availability of modern high-strength materials such as glass fibers or UHMWPE, and only mild genetic engineering of crops, as well as sufficient automation to run the aquaponics mostly automated, so that they can be run at the optimal environmental conditions for crop growth, without regards to human comfort.
The structure should be able to obviously withstand its own weight under 1 g of gravity, assuming a height of ~100 storeys, as well as (for use on Earth) moderate wind and seismic loads.