How many diagonal braces are needed to make a cube rigid?

Question

A guy welding together a large cube using angle iron for the edges notices that the cube is not very rigid. So he decides to weld on some diagonal braces, going from any one corner to another. How many braces does he need to make the cube rigid?

Note: Welded corners are notoriously non-rigid. Assume that they are flexible joints.

With completely flexible joints, a cube structure will fall flat on the ground, sometimes in interesting ways.

No fair depending on the ground for bottom flatness.

We can assume that the pieces themselves are rigid, even if the joints are flexible.

Answer 1

2 across the middle should do it I think. Oh, I was assuming the faces themselves were rigid.

If all the corners are completely limp, hmmm

You have 8 corner points. That's 24 degrees of freedom in 3 dimensions.

You have 12 edge pieces that fix the distance between a pair of points. That sucks up 12 degrees of freedom.

You don't care about overall position (3 degrees) or orientation (3 more degrees). The cube can be rigid and have those be whatever.

So 24 - 12 - 3 - 3 leaves 6.
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You can check this reasoning on some simpler structures like a triangle or a square.

A triangle has 3 corner points--9 degrees of freedom.
You don't care about 6 (overall position and orientation).
The three sides take care of 3 degrees.
9 - 6 - 3 = 0
A triangle is inherently rigid. Check.

A square has 4 corner points--12 degrees of freedom.
You don't care about 6.
The four sides take care of 4
12 - 6 - 4 = 2
You need two braces for a rigid square. Check.

Answer 2

(Shameless plagiarism follows)

You have 8 corner points. That's 24 degrees of freedom in 3 dimensions.

You have 12 edge pieces that fix the distance between a pair of points. That sucks up 12 degrees of freedom.

You don't care about overall position (3 degrees) or orientation (3 more degrees). The cube can be rigid and have those be whatever.

So 24 - 12 - 3 - 3 leaves 6.


Answer: 6 braces
http://www.robertinventor.com/cubeetc/cubetetrahedron.jpg

Answer 3

5 ... Last and final edit.

Looking at Alexander's picture of a cube, it is clear that you can clip out the two braces on the right hand side and replace them with an interior diagonal from the upper left to the lower right. This makes 5 braces.

[Note: I've also looked at cubes with three and four diagonals and they appear stable -- except they would be very vulnerable to torque so I discarded those.]

Answer 4

if u add the diagonal braces the cube will become an iindeterminate 3d truss.u can tell if the cube is rigid or not be finding the displacemnet
i think adding 2 diagonals at each face will make it veery rigid

Answer 5

Two per face is a must for large structure; however one each face may be enough for smaller ones.

Answer 6

1 acoss the internal space will do it