Design of record-breaking builds
If you could design using Technic Axle 32 as your primary member that would probably be cheapest. You can get 500 of them for under $1 each on BrickLink, and making an Eiffel Tower shape out of those could be fairly strong. You'd be using axles in compression which isn't ideal so you'd need to be careful about bending forces, but in terms of cost per metre of height that's about as good as you can get. 32 studs is about 25cm, so your 40 metre tower is about 160 axles high. Assuming four legs (because Lego makes rectangles easier than triangles) you'd need 480 axles for the legs, plus another hundred or so for bracing. If you could work out a way to use only 3 legs the structure would be lighter.



You'd use axle connectors to join them end to end and either Technic liftarms or string for bracing (compression and tension respectively). There are Technic link parts in a few lengths that are lighter than liftarms, like this 15-long one and the tension member at the bottom would be a baseplate (or several baseplates)

If you made it modular using a "platform" that was, say, 16 studs square you'd end up with extra internal legs but a very easy to build structure. Say you make a tower that's two metres tall (8 axles) and tapers from 32x32 to a point. Four of those next to each other would support another similar tower on top of all of them. And so on, but the inside towers will end up with 2,3 or 4 towers sitting on top of them. A better design would make set of four symmetrically located parts "unique" and thus use fewer total parts but at the cost of the whole model being significantly more complex. On the other hand, I think you'd be able to get more than 2m out of each stage of such a tower.

I might have a go at a short version of this tonight if I can find my collection of long axles and see how stable it is. Somewhere in the garage is about 20 of them, so I should be able to get a metre tall fairly quickly and easily... if I can find those axles.

An alternative part that would involve a lot of SNOT techniques would be single train rails. Or even the modern click-together rails. I can't think of a good design for those off the top of my head, though.