[Scourge of Ages]

In my concept, the structure does not spin. So does that mean that it is in no danger of tearing itself apart?

I don't have any fancy "math" or "science" to back this up, but I would imagine that without at least some centrifugal (centripetal? I can never remember) force from rotation, the structure would collapse under it's own weight, not unlike an onion ring.

[FlamingCobra]

....................................................does that mean the space elevator would have to spin too?

[Dragon]

Larry Niven provided such a material in scrith, an ultra-tensile-strength material that is 50,000 times more resilient than the toughest steel alloy. The material seems to somehow tap into the strong nuclear force that binds the particles in atomic nuclei together, and extends it onto a macroscopic scale.

This reminds me of neutronium, a superdense material composed entirely of neutrons bound by the strong nuclear force. Neutron stars are made out of it. Scrith looks like neutronium with gravity somehow altered not to crush the inhabitants of the Ringworld.

....................................................does that mean the space elevator would have to spin too?

Space elevator isn't subject to that kind of forces due to it being very small compared to a planet. It's strong and light enough not to collapse under it's own weight (it's essentially a cable hanging from the sky, light enough for it's own gravity not to be a factor).

[Polpolion]

At these scales without spinning the force of gravity on a point of the ring due to the rest of the ring (see my previous post) is small (ie < 0.00001 N, it's another pretty trivial calculation I'll let you guys verify) and decreases linearly with the ring's radius. If it were a problem, then spinning the ring would actually help fix it, to a certain (small) rotational speed. A much more pressing concern would be the force of gravity of other large bodies, namely the sun.

Also please note that collapsing under your own weight =/= collapsing under your own gravity. What I described above was an investigation to see if the ring would collapse under its own gravity, by which I mean the force produced by itself and acting upon another part of itself. Collapsing under your own weight means that there is an external gravitational field strong enough to `break' objects that aren't strong enough. For example, if I suddenly gained 500 pounds of fat, I would collapse under my own weight, lacking body strength to support my mass. Alternatively if you created two massive slabs of material seperated by a short twig (in SPACE), the system would collapse due to its own gravity.

EDIT:

You could argue that you could balance the sun's gravity and your object's with a spin. This isn't possible with a dyson sphere because your two poles would still need to collapse; they would likely collapse inward while the equator would collapse outward. It's slightly more reasonable with a ring. Slightly. The radius of the ring would have to be many times greater than that of the sun, and the sun would need always be very close to the solar system's barycenter.

[Enzo03]

This reminds me of neutronium, a superdense material composed entirely of neutrons bound by the strong nuclear force. Neutron stars are made out of it. Scrith looks like neutronium with gravity somehow altered not to crush the inhabitants of the Ringworld.

And this reminds me of a book where the author took the challenge of creating creatures which could live on neutron stars.  I forget the book and author name, never actually read the book, just read about it on writesf.com