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Thickness of components for equal strength

  1. Aug 1, 2016 #1
    1. The problem statement, all variables and given/known data
    Givens:
    - Each of the 2 cylindrical posts are 0.5 inches thick.
    - The posts and chain links are made of galvanized steel of identical material composition.
    - The posts and chain links are solid.
    - Each post is permanently fixed to unbreakable surfaces. The surfaces will move in exactly opposite directions with infinite (unstoppable) strength.
    Problem:
    How thick must each chain link be, when the posts are pulled apart, so that the posts and chain links start to bend/break at the same time?
    2. Relevant equations
    What is/are the equation(s) to solve this problem?
    3. The attempt at a solution
    No idea what the equation(s) are.
     

    Attached Files:

  2. jcsd
  3. Aug 1, 2016 #2

    haruspex

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    I'm not too sure about this either, but "bend/break" is problematic. The posts will start to bend, and the chains stretch, straight away, so to make sense of the question I would delete "bend".
    Next, there's the question of compressibility. If the material is highly compressible then the posts can bend a long way without breaking, so maybe assume incompressible.
    Now it comes down to comparing tensions. The material will break at some tension per unit area.
    The chains are easy since the tension per unit area will be the same throughout. But in the posts the tension per unit area is not uniform across them or along their lengths.
    Where will it be greatest on the posts?
     
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