Normal Stress/Shear Stress from stress tensor

[muskie25]

Homework Statement

If $$\sigma_{ij} = \begin{pmatrix}<br /> 3 & 3 & 3 \\<br /> 3 & 3 & 3 \\<br /> 3 & 3 & 3<br /> \end{pmatrix}$$ represents a stress tensor, on what plane(s) will the normal stress be a

minimum? On what plane(s) will the shear stress be a maximum?

Homework Equations

The Attempt at a Solution

The first two parts to the question asked for the eigenvalues and eigenvectors, which are:
$$\lambda_1 = 9 , \lambda_2 = 0 , \lambda_3 = 0$$

$$v_1 = \begin{bmatrix}<br /> 1\\<br /> 1\\<br /> 1<br /> \end{bmatrix} ,<br /> <br /> v_2 = \begin{bmatrix}<br /> -1\\<br /> 1\\<br /> 0<br /> \end{bmatrix} ,<br /> <br /> v_3 = \begin{bmatrix}<br /> -1\\<br /> 0\\<br /> 1<br /> \end{bmatrix}$$

I don't understand how these relate to the normal min, shear max.

 

[Orodruin]

What is the normal/shear stress on planes with these vectors as normal vectors? How does the stress change as you make a rotation from one to the other?

Otherwise, a good place to start is reading up on Mohr's circle: http://en.wikipedia.org/wiki/Mohr's_circle