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Bending moments at equillibrium

  1. Aug 28, 2016 #1
    "Consider a prismatic member AB possessing a plane of symmetry and subjected to equal and opposite couples M and M0 acting in that plane . We observe that if a section is passed through the member AB at some arbitrary point C, the conditions of equilibrium of the portion AC of the member require that the internal forces in the section be equivalent to the couple M"


    Could anyone provide me the proof of this? It seems little weird to me. if we applie bending moment on a beam, it would likely that each end side would experience greater moment(away from centre of mass).

    How could every cross section have the same moment?
     
  2. jcsd
  3. Aug 28, 2016 #2

    SteamKing

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    Have you constructed a free body diagram for the beam in this condition?

    Take a segment of the beam AC as described above, put all of the forces and moments which act on AC on a diagram, and see what must happen for segment AC to remain in equilibrium.
     
  4. Aug 29, 2016 #3

    simple-bending.png

    simple-bending.png

    I understand that it will balance out but I am confused with the physical interpretation.


    Should I interpret this in this way, just like stress, internal force will be distributed 'uniformly to counteract the moment?
     

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    Last edited: Aug 29, 2016
  5. Aug 29, 2016 #4

    SteamKing

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    Bending stresses are not distributed uniformly to counteract the bending moment, unless you mean that the stresses are distributed uniformly along the length of the beam (i.e., the stress in each cross section is the same, because the local bending moment is constant and equal to the applied couple M.)
     
  6. Aug 29, 2016 #5
    Thanks!
     
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