Stress tensors on a horizontal bar

[dinospamoni]

Homework Statement

A horizontal support bar has a downwards force F =
450 N applied near one end, as shown. The radius of the bar
is c = 4 cm, and the length L = 1.2 m. The stress tensor σ
at any point describes the components of stress in a particular
coordinate system. For the coordinate system shown, the stress
tensors at points A and B are given by:

(sorry for how I'm about to write these matrices!)

σ_a = 4LF/(pi * c^2)...0...-2F/(pi*c^2)
...0...0...0
...-2F/(pi*c^2)...0...0and

σ_b = 0....-10F/(3 pi c^2)...0
...-10F/(3 pi c^2)...0.....0
....0.....0.....0Since each σ is symmetric, there must exist a ’principal’ coordinate system for each point in which the
stress tensor is diagonal. Determine the components
of stress at point A in its principal coordinate system, and list them from most negative to most positive.

Homework Equations

The Attempt at a Solution

I have no clue, but I'm pretty sure in the "principle" coordinate system the main diagonal of the matrix has values and everything else is zero.

 

[lippyka]

So for A I would haveσ_a = -4LF/(pi * c^2)...0...0...0...2F/(pi*c^2)...0...0...0...2F/(pi*c^2)So the components of stress from most negative to most positive would be -4LF/(pi*c^2), 2F/(pi*c^2), 2F/(pi*c^2). For B I would haveσ_b = -10F/(3 pi c^2)...0.....0...0...0.....0....0.....0.....10F/(3 pi c^2)And the components of stress from most negative to most positive would be -10F/(3 pi c^2), 0, 10F/(3 pi c^2). Is this correct?