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Stress tensors on a horizontal bar

  1. Mar 27, 2013 #1
    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.
     
  2. jcsd
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