(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

3.) Stress analysis at a critical point in a machine member gives the three-dimensional state of stress in MPa as the following:

y =

[ 105 0 0

0 -140 210

0 210 350 ]

Using the eigenvalue formulation to find the principal stresses (eigenvalues) and principal directions (eigenvectors). Show these stresses on a properly oriented element. Use the three-dimensional Mohrâ€™s circle to obtain the maximum shear stress and show this on a properly oriented element. Repeat this problem using MATLAB.

2. Relevant equations

I can do all except finding the directions. I'm not sure how to find that. Do i just plug back my eigenvalues into mhy homogeneous eqn?

3. The attempt at a solution

skipping some steps:

det( 105 - s 0 0

0 -140 - s 210 = [0]

0 210 350 - s )

Solving for S (using characteristic eqn): S = 105, 427.68, -217.68

These are my eigenvalues.

In a previous step, my homogeneous eqn was:

[ 105 - s 0 0

0 -140 - s 210 * [l;m;n] = [0]

0 210 350 - s ]

If i plug my S values back in, i dont know how to solve.

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# Homework Help: Eigenvalue formulation to find the principal stresses, directions

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