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Elasticity problem

  1. Jan 7, 2013 #1
    Hello, I am struggling with this problem. It is probably the easiest problem ever...

    [​IMG]

    What I did: The plane has 2 stress components. σn and σs.

    σn is a multiple of (l, m, k) vector. For σs, I made up a vector (a, b, c) which is orthogonal to (l, m, k). And I equated all vectors.

    I'm probably doing something wrong. Any help is appreciated!
     
  2. jcsd
  3. Jan 7, 2013 #2
    1. The problem statement, all variables and given/known data

    [​IMG]

    2. Relevant equations

    General plane formulas.

    3. The attempt at a solution

    I thought that the plane has 2 stress components. σn and σs.

    σn is a multiple of (l, m, k) vector. For σs, I made up a vector (a, b, c) which is orthogonal to (l, m, k). And I equated all vectors.

    I'm probably doing something wrong. Any help is appreciated!
     
  4. Jan 7, 2013 #3
    Hello, I am not an expert on elasticity but this really looks quite straightforward. Let's first find the stress vector T (I'm using T instead of σ to avoid confusion with the stress tensor). You will get it by multiplying the (diagonal) stress tensor by your normal vector as T=(σ1l, σ2m, σ3n). It has two components as you wrote, Tn and Ts. The magnitude of Tn is simply the dot product of T and n and its direction is along n as you wrote. Vector Ts has to be the complement to the total stress vector.
    And for the second part - the shear stress will be maximum if vector T lies in your plane, e.g. the dot product of T and n is zero.
     
    Last edited: Jan 7, 2013
  5. Jan 7, 2013 #4
    Whilst this thread properly belongs in the homework section, this needs comment.

    What is a stress vector?
     
  6. Jan 7, 2013 #5
    Aha, he's probably talking about the traction vector.

    However, this was very helpful. Thanks
     
  7. Jan 7, 2013 #6
    We defined it similarly like the article on wiki does, so I won't rewrite it...Stress on Wikipedia
    Most likely there are other methods or other terminology, I'm not a native speaker so i can't tell the subtle differences that well, sorry about that.
     
  8. Jan 7, 2013 #7
    Thanks Zirkus!
     
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