Young's Modulus

[Faiq]

Main Question or Discussion Point

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

 

[Flyx]

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.

 

[nasu]

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.

 

[Faiq]

They are asking in terms of extensions (I wrote the same answer and got it wrong)

 

[nasu]

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?

 

[cjl]

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.

 

[Chestermiller]

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.

 

[DanielSauza]

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.

 

[Chestermiller]

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.

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.

 

[hackhard]

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

 

[Chestermiller]

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.