Stability of a tower of blocks

A single stack of rectangular blocks is a relatively simple statics problem.

You just need to check at each level that the area immediately bellow the combined centre of gravity of the blocks above is supported, not hanging in space.

stacks with multiple blocks on a layer or where blocks are not rectangular makes things much more complicated as will outside forces other than gravity acting on the stack.

-- Jonathan

Barnes's theorem; for every foolproof device there is a fool greater than the proof.

To reply remove AT

Hi Tom:

If I undertand you correctly I think you need to look up information on calculating the center of gravity of your tower. When the center of gravity reaches a point where it is outside the base of your structure it will tip (provided it's not bolted to the ground).

Don

It's a nice problem to solve with recursion. For prismatical blocks with parallel tops and bottoms, it's not really a 3D problem anyway.

For one block, Find the location in arbitrary Cartesian coordinates of the center of gravity of the block, for simple blocks its centroid in the XY plane, as modified by a compressive force from above at a given XY location. The compressive force from above is the weight of all the blocks in the stack but the current one, and the given XY location is the CG of that stack. Start at the top of the stack, with zero blocks above, and recurse your way down until you run out of blocks.

Exit at any point where the computed XY location falls outside the perimeter of the current block. If the block has edges that are curved inward, that exit criterion must be modified a bit. Anytime the net CG falls outside the perimeter of a string stretched around the block's perimeter, the tower will topple.

-Mike-

As stated, and with the assumptions everyone seems willing to leap to (rigid blocks on a rigid platform), this is a pretty uninteresting problem. Are you sure there's no elastic foundation or elastic blocks?

Fred Klingener

Not at the moment, I'm planning to get the basics sorted out and working and then add to it. :-) The tower problem is actually part of a complete game and there are other things that I need to concentrate on as well.

Thanks everyone for the help,

Tom

If these are rigid rectangular block, if they are neatly stack, if their is now wind, then the height is unlimited. If you want to model the real world, and have a limited height, then you need to consider at least one of those factors. So you might say that each block is out of alignment by a random amount, or a fixe amount. Or you might use elastic block, so they will eventually buckle like a tall collumn. Or their might be wind.

There is something that would cause neatly stacked rigid blocks to fall, and this is the base not being level, so that's another option, a base that is x degrees from horizontal.

Mitchell Timin

If these are rigid rectangular blocks, if they are neatly stacked, if there is no wind, then the height is unlimited! If you want to model the real world, then you need to consider at least one of those factors. So you might say that each block is out of alignment by a random amount, or a fixed amount. Or you might use elastic blocks, so they will eventually buckle like a tall collumn. Or there might be wind.

I forgot one other thing that would cause neatly stacked rigid blocks to fall, and this is the base not being level, so that's another option, a base that is x degrees from horizontal. Deviations from perfect right angles in the blocks themselves would have a similar effect.

In the real world we have all of them simultaneously: imperfect blocks, slightly tilted base, wind, mis-aligned blocks, and slightly elastic blocks.

Mitchell Timin