The Giant Space Wheel (of Seveneves) is so much more attractive than space elevator. That is a large mass on geostationary orbit having smaller pods rotating at the end of ropes. Those pods can be lowered to atmosphere and synchronized with earth rotation. Elevator pod comes down and can stay down maybe couple of hours and then jerked back to heavens. All energy comes from the sun - collected at the center station. Safe because pods can be quickly reeled back to space and stay out of atmosphere until conditions are optimal.
Another inteersting idea is an orbital ring - basically a rotating cable around Earth in LEO, which is accelerated by a maglev-train-like platform. The platform travels "along" the ring at high speed, but it can be made to stay "at one place" from Earth surface perspective (i.e. geostationary). The cable ring is rotated at orbiting velocity (or higher), so the centrifugal force counteracts gravity, keeping it in place.
The mass of the pod is much less than the end-station of the space elevator. So the cable can be very thin at the far end. If the cable is tapering smoothly it weights 1/4, but it need not to do that, I think it tapers in some kind of exponential curve. So 1/16 might be quite reasonable assumption, but one needs recent college education to calculate that. On the other hand there are strong centrifugal forces, as the pod speeds up from standstill, which is also vividly described in Seveneves book.
