If one is on the surface of the Moon and you are 1734 km from the Moon's Center of gravity, at a distance of 1734 km over your head the Moon's gravity is 1/24th the Earth gravity. If you are half that distance up 869 km (540 miles), the Moon's gravity is 1/12th of Earth's. If 434.5 km (265 miles) the gravity is 1/8th Earth's.
As I said any non-tapered structure is limited by the it's compression strength if steel has an uniform compression strength of 150,000 psi, then it's maximun height is around 50 miles at the Moon's gravity which is about 1/6th of Earth's. At 1/8th gravity it's 66.6 or 200 miles if tapered/cone.
Hmm, I just checked, apparently the Moon is only 2 km offset from center of gravity [I had wondered if it might be more than that] http://www.exo.net/~pauld/activities/astronomy/planetshape.html
And also found out the mountains on the moon are only as high as Everst. Those were couple things was hoping which could be an advantage in the location of a tower, but it's appears they would have only a marginal effect. Btw, this post is a continuation from an eariler thread: http://www.habitablezone.com/space/messages/311753.html

Ok, so back to those stacked cones. One way I thought which improve the cone for this tower- is instead of having it solid, having it with a hole in the middle of it- so it's sort of a tapered pipe shape. In this first step, I'm not talking about removing any mass from the cone, nor *really* trying to increasing it's structural strength- it's mass from the center would be added to the walls of the "tapered pipe". For instance in the 48" by 24" by 50 mile pipe could have 12" hole from top to bottom & the mass of this 12" diameter by 50 mile rod would be added to the sides. Without doing the math but just guessing this could make the outside diameter instead about 50" by 30" (this is bad, instead we want more on the bottom say something more like 51 by 26). [So instead, perhaps it would better to take out a conic shape, like say 12" at bottom by 2" at the top, but if you think about this doesn't really help things.] Instead what you want is the wall of conical pipe to be wedge shape- flatter at the bottom & thiner at the top. Now, I've never seen or heard of such a thing before, so I'm going to call it a conical pipe.
To be continued...