stress Tensor transformations

by ArticMage
Tags: stress, tensor, transformations
ArticMage is offline
Sep15-13, 01:56 PM
P: 13
Given the stress tensor σ = {0,2,0;2,0,0;0,0,0}

i) Find the principal stresses and their associated directions,
ii) find the surfaces on which the maximum tangential traction occurs, and the value of this traction.

For i) I found the eigen values and eigen vectorsto be λ = 2,-2,0 and for λ= 2 the vector is [1,1,0] for λ= -2, [-1,1,0] and for λ= 0, [0,0,1]. Now in order to populate the principal stress tensor do I know which value goes where based on the vectors? Trying that I get {2,0,0;0,-2,0;0,0,0} is this correct?

for ii) I know that this should occur at 45 to the principal stress, but I'm not sure how to apply that, or how to populate the stress tensor.

Any help, especially on ii, would be appreciated. Also if possible use an example of a matrix with less zeros in it. I feel this problem is simplified so I want to be sure I understand the operations.

EDIT: I now realized this is the wrong place to post this. I had just searched fora similar thread and posted where they posted. I dont know how to move this or delete it.
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