Young's Modulus

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  • #1
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Main Question or Discussion Point

Suggest why a thin rod can bend more than thick rod without breaking
 

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  • #2
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Suggest why a thin rod can bend more than thick rod without breaking
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.
 
  • #3
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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.
 
  • #4
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They are asking in terms of extensions (I wrote the same answer and got it wrong)
 
  • #5
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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?
 
  • #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.
 
  • #7
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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.
 
  • #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
 
  • #9
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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
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.
 
  • #10
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Suggest why a thin rod can bend more than thick rod without breaking
same reason why a arc of small radius subtends a larger angle at center than a arc of same length and larger radius
 
  • #11
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same reason why a arc of small radius subtends a larger angle at center than a arc of same length and larger radius
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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