You would have to have a super strong strand for this too. A captured asteroid would also work well for a Clarke elevator. a lot less to put into orbit.
This does not solve the issue of weight. The weight of the building would act as a force to sheer it
A Clarke elevator would be used to transport people and belongings to and from a geosynchronous orbit. The elevator-satellite would have no reason to have any substantial height at all, so no gravitational force acting to tear it apart.
The Clarke elevator isn’t all it’s commonly understood to be. It’s useless for building the satellite in the first place. All it does is allow a very cheap exchange of materials between the satellite and Earth. But you have to put mass up their to be exchanged in the first place.
Actually, I take it back about the Clarke elevator. You could use a giant rail gun to launch ballast into space. Such a rail gun involves accelerations that would obliterate anything useful. But once the ballast is in space, the elevator could exchange the mass of the ballast for more useful materials.