Understanding Mohr's Circle: Shear Stress and Normal Stress Interactions

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Discussion Overview

The discussion revolves around understanding Mohr's Circle, specifically the interactions between shear stress and normal stress. Participants are exploring theoretical aspects related to the conditions under which shear stress becomes zero and the implications of average normal stress when determining maximum shear stress.

Discussion Character

  • Homework-related
  • Conceptual clarification
  • Technical explanation

Main Points Raised

  • One participant questions the existence of an angle (θp) where shear stress (τx'y') becomes zero, seeking proof for this phenomenon.
  • Another participant inquires why average normal stress is present when calculating maximum shear stress, suggesting a potential contradiction in the diagrams provided.
  • A later reply introduces the Cauchy stress relationship, indicating that it is relevant for determining stress components on surfaces of arbitrary orientation.
  • Some participants express unfamiliarity with the Cauchy stress relationship, raising concerns about their ability to understand stress vector components.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the questions raised, as there are differing levels of understanding regarding fundamental concepts like the Cauchy stress relationship and its application in the context of Mohr's Circle.

Contextual Notes

There are limitations in the discussion regarding the assumptions made about the stress conditions and the definitions of terms used, which may affect the clarity of the questions and responses.

chetzread
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Homework Statement


http://www.efunda.com/formulae/solid_mechanics/mat_mechanics/plane_stress_principal.cfm
in this notes , i couldn't understand that why there exists an angle (θp) where the shear stress (τx'y' ) becomes zero , (only normal stress acting )
is there any proof on this ?

for the second part , why when we find max shear stress , there's also average normal stress acting ?

Homework Equations

The Attempt at a Solution


is the second diagram wrong ? when we find max shear stress , there should not be average normal stress acting ...[/B]
 
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chetzread said:

Homework Statement


http://www.efunda.com/formulae/solid_mechanics/mat_mechanics/plane_stress_principal.cfm
in this notes , i couldn't understand that why there exists an angle (θp) where the shear stress (τx'y' ) becomes zero , (only normal stress acting )
is there any proof on this ?

for the second part , why when we find max shear stress , there's also average normal stress acting ?

Homework Equations

The Attempt at a Solution


is the second diagram wrong ? when we find max shear stress , there should not be average normal stress acting ...[/B]
Are you familiar with the Cauchy stress relationship?
 
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Chestermiller said:
Are you familiar with the Cauchy stress relationship?
no , i have never heard of that
 
chetzread said:
no , i have never heard of that
Then how can you possibly determine the components of the stress (traction) vector on a surface of arbitrary orientation?

The Cauchy stress relationship says that $$\tau=\sigma n$$
where n is a unit column vector normal to a surface of interest, ##\sigma## is the matrix of stress tensor components, and ##\tau## is the stress (traction) vector acting on the surface. Have you ever heard of anything like this?
 

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