How Does Longitudinal Stress Affect a Body's Internal Tension?

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Homework Help Overview

The discussion revolves around the concept of longitudinal stress in a rod subjected to forces applied at both ends. Participants are exploring the relationship between external forces and internal stress, specifically questioning why the stress is defined as F/A rather than 2F/A when forces are applied at both ends of the rod.

Discussion Character

  • Conceptual clarification, Assumption checking, Mixed

Approaches and Questions Raised

  • Participants are attempting to reconcile the definition of stress with their understanding of forces acting on the rod. Questions are raised about the nature of tension and whether it should be considered as F or 2F. Some participants suggest using free body diagrams (FBD) to clarify the internal forces at play.

Discussion Status

The discussion is active, with multiple interpretations being explored regarding the definition of tension and stress. Some participants have offered clarifications about the nature of internal forces versus external forces, while others are questioning the conventions used in defining these terms. There is no explicit consensus, but productive dialogue is ongoing.

Contextual Notes

Participants are navigating a common misunderstanding regarding the application of forces and the resulting internal stress in materials. The conversation includes considerations of how forces are defined and the implications of these definitions on the understanding of tension in a rod.

  • #31
jbriggs444 said:
No. You misunderstand the proposal.

We are not messing with the definition of force. We are messing with the definition of stress, tension and pressure.

Right. Under the proposal, ##F=\frac{1}{2}P\ dV## and ##F=\frac{1}{2}Pa##. Meanwhile, atmospheric pressure, for instance, is doubled. As a result, forces and accelerations are unchanged.

No one is claiming that this is useful. Or even natural. Only that it is a possible convention.

You quoted me in post 28. I said that it was technically correct, but silly. I am not sure what you are trying to correct.

Knowing that continuum stresses and strains “look like” forces and displacements makes life simpler. One has to memorize fewer equations.

Or are we in violent agreement with each other.
 
Last edited:
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  • #32
Orodruin said:
Please show your attempt.
 

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  • #33
It is unclear from your diagram what forces are from the wall and what is the internal tension force. All forces have the same size F, but that comes later from the equilibrium equations. You should be calling the tension force something else, like T. I also suggest that you make the FBD of the part of the rod below some mid-point of the rod so that you have the internal force T rather than the force from the wall on the rod.
 
  • #34
The top blue and black arrows are reversed.
The force exerted by the bar on the wall (black arrow) is pulling on the wall rather than pushing in.
 
  • #35
Orodruin said:
It is unclear from your diagram what forces are from the wall and what is the internal tension force. All forces have the same size F, but that comes later from the equilibrium equations. You should be calling the tension force something else, like T. I also suggest that you make the FBD of the part of the rod below some mid-point of the rod so that you have the internal force T rather than the force from the wall on the rod.
Can you please show me the corrected version?
 

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