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Bending stress

  1. Aug 11, 2016 #1
    1. The problem statement, all variables and given/known data

    https://en.wikipedia.org/wiki/Bending

    form the link, we know that σ represent the bending stress, I'm wondering can I call the bending stress as normal stress act at the cross sectional area of beam?


    2. Relevant equations


    3. The attempt at a solution
    IMO, they are not the same....Because the normal stress act on the cross sectional of beam will only cause the beam to elongate or shorten, it will not cause it to bend , so they are not the same....
     

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  2. jcsd
  3. Aug 11, 2016 #2
    If there is tensile stress perpendicular to the beam cross sections in the upper half of the beam, and compressive stress in the bottom half of the beam, the upper half of the beam will get longer and the bottom half of the beam will get shorter. This geometrically means that the beam is bent.
     
  4. Aug 11, 2016 #3
    I agreed, but, it only means the beam is sheared , but not bent like U shape, right?
     
  5. Aug 11, 2016 #4
    why you said that it's bent?
     
  6. Aug 11, 2016 #5
    The key assumption involved here is the flat cross sections of the beam remain flat after the deformation has occurred. Can you tell me how the cross sections can remain flat while the upper part of the beam gets longer and the bottom part of the beam gets shorter without the beam developing curvature (i.e., bending)?

    Your reference fails to mention this key assumption (that is actually observed in practice). Therefore, I can see the source of your confusion regarding the deformation being shear. "Shear bending" does actually occur in very short beams, but in long slender beams, the dominant mode of deformation is "normal bending".
     
  7. Aug 11, 2016 #6
    initially, i was thinking that the author mean this, so the object is sheared , but not bent (figure above)
    But, it should look like this,right? (figure below)
     

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  8. Aug 11, 2016 #7
    Yes.
     
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