Notes From 3rd Annual Space Elevator Conference
colonist writes "The Space Elevator: 3rd Annual International Conference was held recently. Blaise Gassend, a PhD student at MIT, took notes. The main obstacle is still the material: transferring the strength of the nanotube to the ribbon. Other topics include: the nanotube tether Centennial Challenge; Elevator 2010, a challenge for a 250 kg climber to climb a 16 km tether; objections and refinements to Bradley Edwards' design; non-equatorial space elevators; replacing the term 'space elevator' with 'space bridge'; testing the space elevator material on cable cars; science; defense and economics."
This page seems to have some good links. Just check out the bottom of the page as it indicates if you're new to the idea of space elevators.
Wikipedia have a very good article on space elevators
That's why you need a really strong material for a space elevator - if it wasn't for the weight of the "rope" itself you'd only have needed a material strong enough to handle the weight of whatever you wanted to transport up it, but that is a miniscule amount of the total strain on the elevator.
Ignoring the weight of the rope itself, probably the main reason for this rule-of-thumb is the difference between dynamic loading and static loading.
If you (accidentally) get something bouncing on a short rope, the bounce will damp out pretty quicky and the period of oscillation is short. If you get something bouncing on a long rope, it will bounce for a while, and the rope is stretched for much longer with each bounce. It doesn't take all that much of a bounce to double the load on a rope, and perhaps take it past its elastic limit.
I'm guessing, but I think that pre-synthetic ropes probably can be briefly overstretched without losing strength because they knit back together again. If you continuously overstretch them, the fibres probably don't get a chance to recover before the slide past each other a little more, and so on.
So my guess is this doesn't apply nearly so much to modern synthetic ropes. In the case of a space elevator, I'd hope they'd try really hard to avoid excess dynamic loading.