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March 19th, 2012, 01:09 PM   #1
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3d Matrix problem

Hello,

Can anyone help me solving the following math/physics problem.
The problem should be solved with a matrix.

An architect wants to decorate a building by using open cubes, with a diagnal stand compare the body vertical diagonal, between the pillars.

The diameter of all bars is the same: A = 400mm2 steel: E = 200 kN = mm2. The length of the
ribs, a = 1m. The rotational stiffness of the vertices of the cube can be neglected.
Therefore, the rigidity cube retrieves from among the eight plane diagonals, also with surface area of ??the cross-section of:
Ad = 400mm2, and of a length of P2A.
The tilting of the cube is not considered. The cube is vertically loaded (Force direction 0,0,0 to 1,1,1)

1. What is the efective rigidity of the cube? Or when it is loaded with a vertical force
Fz what is the vertical displacement z?
2. Now the architect the thick plane diagonals not so beautiful and she wants thinner than the
original Ad = 400mm2. Derive a formula for the stiffness of the cube as a function of
The surface area Ad of the cross section of the surface diagonals.

I couldn't add a picture of the cube. I hope the coordinates help.

bar/diagonal, P1,P2, X, Y, Z, X,YZ
V1 A D 0 0 0 1 0 0
V2 A B 0 0 0 0 1 0
V3 A W 0 0 0 0 0 1
S1 D B 1 0 0 0 1 0
S2 B W 0 1 0 0 0 1
S3 D W 1 0 0 0 0 1
W1 B C 0 1 0 1 1 0
W2 C D 1 1 0 1 0 0
W3 D T 1 0 0 1 0 1
V1' V U 1 1 1 0 1 1
V2' V T 1 1 1 1 0 1
V3' V C 1 1 1 1 1 0
S1' C U 1 1 0 0 1 1
S2' T U 1 0 1 0 1 1
S3' T C 1 0 1 1 1 0
W1' T W 1 0 1 0 0 1
W2' W U 0 0 1 0 1 1
W3' U B 0 1 1 0 1 0
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