It's one thing to build a 15km high vertical structure, but it's much harder to build a 15km high horizontal structure.
You have to remember that at that scale, even metal behaves like soggy paper.
Either you'd need thousands of support columns (and each one would be a huge project to build), or you'd need a crazy way to keep the whole thing in the air.
Here's a crazy idea for how to keep it in the air: Make the whole thing a giant glider.
It has lots of pairs of wings, and on a windy day the entire thing will be lifted up.
Ailerons on the wings would allow the structure to make itself as straight as possible, since the wind would be different depending on the altitude.
I don't think it'd need to be anywhere near 1000km (20km long would be plenty) but if it was 20km then it'd need a circle of clear and flat land 20km in radius.
Could work in Africa.