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Stress on an Axially Loaded Beam

  1. Aug 19, 2009 #1
    1. The problem statement, all variables and given/known data
    Consider a cantilever beam of length L where a force F is applied in compression at the bottom of the beam. (An off-center axial point load.) Determine the stress at the top and bottom of the beam at x=L/2.

    2. Relevant equations

    There is both compressive and bending stress in the beam. The compressive stress is -F/A and the bending stress is My/I, where F is the force, A is the cross sectional area, M is the applied bending force, y is the distance to the neutral axis, and I is the second moment of area.

    3. The attempt at a solution

    Applying this force is the same as a pure bending moment, except you gain additional compressive stress. Thus, at all points in the beam, the stress is:

    S = -F/A + My/I

    Most of the beam will be in compression, and a smaller part of the beam will be in tension.

    My difficulty is determining what M is. In cantilever problems with transverse loads, M = M(x) = F*(L-x). I have a feeling M is not a function of x, but is constant over the whole beam. I think its F*d, where d is the thickness of the beam, but I'm not really sure why this is the case.
     
  2. jcsd
  3. Aug 19, 2009 #2

    Mapes

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    Agreed. Could the lever arm that produces M have something to do with the nature of the off-axis load...?
     
  4. Aug 19, 2009 #3
    Yes. The moment is produced due to the lever arm. I suppose the lever arm appears as the force drifts from the center. So the lever arm must be the distance to the center of the beam, or half the thickness.

    Good?
     
  5. Aug 20, 2009 #4

    Mapes

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    Sounds good.
     
  6. Aug 20, 2009 #5
    Thanks ;)
     
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