- #1

- 16

- 0

## Homework Statement

If [tex] \sigma_{ij} = \begin{pmatrix}

3 & 3 & 3 \\

3 & 3 & 3 \\

3 & 3 & 3

\end{pmatrix} [/tex] 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:

[tex] \lambda_1 = 9 , \lambda_2 = 0 , \lambda_3 = 0 [/tex]

[tex] v_1 = \begin{bmatrix}

1\\

1\\

1

\end{bmatrix} ,

v_2 = \begin{bmatrix}

-1\\

1\\

0

\end{bmatrix} ,

v_3 = \begin{bmatrix}

-1\\

0\\

1

\end{bmatrix}

[/tex]

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

Last edited: