# Stress tensors on a horizontal bar

1. Mar 27, 2013

### dinospamoni

1. The problem statement, all variables and given/known data
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...........0

and

σ_b = 0.................-10F/(3 pi c^2).......0
.......-10F/(3 pi c^2)........0..................0
.............0.....................0..................0

Since 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.

2. Relevant equations

3. 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.