Poisson's ratio for a rigid rod

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Discussion Overview

The discussion revolves around the concept of Poisson's ratio in the context of a rigid rod subjected to thermal stress. Participants explore the implications of thermal expansion and mechanical strain when the rod's ends are constrained, questioning how transverse strain can occur without longitudinal strain.

Discussion Character

  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant expresses confusion about how transverse strain can occur in a rigid rod under thermal stress when there is no longitudinal strain due to the constraints at the ends.
  • Another participant suggests a thought experiment where the rod is heated with free ends, then compressed back to its original length, implying that this process illustrates Poisson's effect.
  • A subsequent reply challenges the thought experiment by arguing that the initial longitudinal expansion would offset any subsequent compression, resulting in no net mechanical strain in the transverse direction.
  • Another participant asserts that heating a rod with no constraints leads to equal strains in all directions, resulting in a new stress-free configuration.
  • The original poster questions how this applies to their scenario with longitudinal constraints, seeking clarification on the mechanical contribution to transverse strain despite the absence of longitudinal strain.

Areas of Agreement / Disagreement

Participants do not appear to reach consensus, as there are competing views on the relationship between thermal expansion, mechanical strain, and Poisson's ratio in the context of a constrained rod.

Contextual Notes

Participants express uncertainty regarding the assumptions of the thought experiments and the definitions of thermal and mechanical contributions to strain in the context of Poisson's ratio.

westmckay99
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I have a conceptual misunderstanding it seems. Poisson's ratio is the ratio of elastic strain deformation of the transverse and longitudinal components. That being said, if I were to induce thermal stress (heating up) to a rod by keeping its ends (longitudinal component) rigid, would there be a mechanical contribution to the transverse strain on top of the thermal one? My textbook solutions manual seems to think so however I don't understand how you can have a transverse strain when you have no longitudinal one (no change in length since the rod is maintained rigid throughout the thermal stress exposure).

Any insight on this would be greatly appreciated.
 
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Imagine a process wherein you heat the rod with the ends free, and then later, while it is hot, compress it back to its original cool free length. I think you will see where the Poisson expansion comes from in this.
 
OldEngr63 said:
Imagine a process wherein you heat the rod with the ends free, and then later, while it is hot, compress it back to its original cool free length. I think you will see where the Poisson expansion comes from in this.

Hi, thanks for the reply! I completely understand that thought experiment, however I see a flaw: the imaginary step of letting it expand longitudinally offsets the compression afterwards, ie it may expand in the transverse direction when you compress it back down but it had already contracted by the same amount originally when you let it expand i the longitudinal direction (net effect of mechanical strain in the transverse direction is null).
 
When you heat it with no constraint, it expands with equal strains in all directions to a new stress-free configuration.

Chet
 
Last edited:
Chestermiller said:
When you heat it with no constraint, it expands with equal strains in all directions to a new stress-free configuration.

Chet
Hi, Thanks for the reply! However, I'm unsure as to how your comment applies to my question. The scenario I refer to has longitudinal constraints. The thermal expansion in the radial direction I understand but how is it there's also a mechanical contribution (they use the poisson ratio times the thermal stress/modulus of elasticity) when there's is no longitudinal strain to begin with. Refer to my previous reply to OldEngr63 to see my counter argument to the hypothetical thought experiment of assuming it had been free to expand then applying a compression strain to return the expansion to the original length.

Cheers
 

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