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I Young's Modulus

  1. Apr 18, 2016 #1
    Suggest why a thin rod can bend more than thick rod without breaking
     
  2. jcsd
  3. Apr 18, 2016 #2
    If you look at the equation for stress: F/A, a thicker rod would have more stress for the same force. Thus it would bend less without breaking.

    This is just using the equation, I don't know why.
     
  4. Apr 18, 2016 #3
    For the same bending angle, the stress is less in the thinner bar.
    The breaking stress is a material characteristic so it is the same for two bars made from the same material.
     
  5. Apr 18, 2016 #4
    They are asking in terms of extensions (I wrote the same answer and got it wrong)
     
  6. Apr 18, 2016 #5
    Extensions and compressions are also less in a thin rod. They are proportional to the distance from the neutral axis.
    But how can be "wrong" to discuss it in terms of stress?
     
  7. Apr 18, 2016 #6

    cjl

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    You haven't really explained why the stress is lower in the thinner rod with just that answer. You should really mention that the stress is lower for a given bending angle because the strain is lower, and this is because of the distance from the neutral axis.
     
  8. Apr 18, 2016 #7
    The tensile strain at the outside of the bend is equal to the ratio t/R, where t is the distance from the neutral axis and R is the radius of curvature. So, in a thin rod having the same radius of curvature as a thick rod, the distance from the neutral axis at the outside of the bend is less and the tensile strain is less.
     
  9. Apr 21, 2016 #8
    Because the bending stress depends on the distance between it's neutral axis (which is in the center for common shapes in the case of pure bending). So a thicker rod will experience larger maximum bending stress than a slim one when subject to forces of the same magnitude.
    stress3.png
     
  10. Apr 21, 2016 #9
    M/I is the same thing as the elastic modulus E divided by the radius of curvature. So as I said in my post, for the same radius of curvature, with two rods of the same material, the thicker one will have a larger bending stress because it has material elements further from the neutral axis.
     
  11. Apr 22, 2016 #10
    same reason why a arc of small radius subtends a larger angle at center than a arc of same length and larger radius
     
  12. Apr 22, 2016 #11
    Please elaborate on how this answers the OPs question in terms of the stress required to cause the rod to break.
     
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