Stairway to Heaven
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@Jolly I think it was in one of Alastair Reynolds' books (Chasm City?) where such an elevator becomes the target of a terrorist group. It's a minor plot point, but he does a nice job of describing what would happen if the cable were snapped. Given the centripetal force of the "station," the gravitational pull on the cable, etc, it presents some interesting thoughts on how one could survive a breach of the cable if it happened below you on the way up.
