The same thing that keeps the tension in them before it gets built: centripetal force.
Nope, that doesn't work like I said. When an object is in orbit, that is what maintains the tension because it turns the object while maintaining the tangential speed, i.e the tendency of the orbiting object to pull away from the earth absent that force. But with a solid loop structure around the earth, the object is NOT in orbit of the earth, it is merely in free drift above the earth. The earth's gravity acts on all points equally (assuming it is constructed such that all points are equidistant from the earth's surface), which means the radial force felt by the object has no effect on the tangential speed whatsoever. The object would eventually drift into the earth and break apart.































