Does anyone know how big we could builds a torus colony. 600 miles across, 100 miles thick, built like a continuous suspension bridge, 1/4 gee gravity due to centrifugal force on the inside surface. Could we build this with current technology

With current technology yes, with current politics no. To make it self-sufficient would require quite a lot of R&D.

 

We could build them as big as could be afforded; it just spins slower (less RPM but faster velocity).

Hmm...

 

Scaling up a torus: we increase diameter, then the length of the torus increases linearly (length = 2*pi*r) as a function of the diameter. Assuming that we don't make the torus any thicker with increasing diameter, then it only becomes longer, so the weight also increases linearly. Assuming we build spokes (like on a bicycle wheel) to keep it together, the amount of spokes that we can build also increases linearly.

The only non-linear aspect that I can find off the top of my head is the weight of the spokes. Those increase in number, but also in length.

 

So, unless we're talking about some ridiculously large monster torus, I see little limitations to scale up a simple ring to a large scale.

 

The only factor that I dare not say something about is the thickness of the ring itself. You propose a 100 miles thick ring, which makes it larger than almost anything man made. How would you solve the force balance of such a ring to see if it can keep itself together? Afinite element analysis of the forces involved?

Although we could do this, it seems like it would be easier to just focus on colonizing mars and the moon right now.