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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 ...
this brick has always annoyed me, when sorting my bricks
Just using bricks the cost argument becomes more important. Unfortunately large quantities of bricks really require that you deal with The Lego Group directly (and they're usually quite happy to deal). For rough price guides we can look at bricklink again. Sorting by quantity available from a single seller for some common parts (we don't care about price per ...
The key point that the team at The Open University calculated made was that while you could in theory build a tower about 3.5km high of bricks before the ones at the bottom would be crushed by the weight of the ones above - this was based on the load-bearing ability of a single 2x2 brick - they also stated that a 2x4 would fail sooner (less support on the ...
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