What Is the Practical Application of Mohr's Circle and Principal Stresses?

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Discussion Overview

The discussion revolves around the practical applications of Mohr's Circle and principal stresses in engineering design. Participants explore the relevance of these concepts in real-world scenarios, particularly in relation to material failure and stress analysis.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions the practical application of Mohr's Circle and principal stresses, suggesting that they may not be necessary beyond finding stresses for specific directions and understanding shear behavior.
  • Another participant argues that understanding shear failure is crucial, as materials often fail along planes of maximum shear, which can be analyzed using Mohr's Circle and transformation equations.
  • A follow-up inquiry is made regarding the different representations of von Mises stress, asking whether they are identical or if one is an approximation of the other, with a suggestion that substitution from Mohr's Circle could clarify this.
  • In response, a participant states that both equations for von Mises stress are exact, but one applies to all load states while the other assumes simplified loading conditions, prompting a request for clarification on the assumptions made.

Areas of Agreement / Disagreement

Participants express differing views on the necessity and application of Mohr's Circle in design, with some emphasizing its importance in understanding material failure while others question its practical relevance. The discussion on the equations for von Mises stress indicates a shared understanding of their validity but highlights differing interpretations of their applicability.

Contextual Notes

The discussion includes assumptions about loading conditions and the context in which von Mises stress is applied. There is also a lack of consensus on the practical necessity of Mohr's Circle in design, indicating potential gaps in understanding its applications.

Who May Find This Useful

Engineers, students of materials science, and professionals involved in structural design may find this discussion relevant, particularly those interested in stress analysis and material failure criteria.

sweetness2
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So I understand how to use Mohrs circle and the transformation equations to find principal stresses and stresses for a given plane, but what is the point? Is there a purpose to knowing this other than finding stresses for a given direction, the stress invariants or that shear does not occur on the principal directions? How are these things used in the real world / design?

Don't people usually use average stress when designing? I guess I just don't see a practical application.
 
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Hi sweetness2, welcome to PF. In metals, failure occurs due to shear. That doesn't mean a rod under normal axial load, for example, won't ever fail; it means that it will fail along a plane 45° from the load axis, because this is the angle of maximum shear. The transformation equations (and their graphical equivalent, Mohr's circle) can be used to analyze this and more complicated loading configurations.

People absolutely do not rely on average stress when designing. They need to know the location and magnitude of the maximum characteristic failure stress for that material (in metals, the von Mises stress).
 
Thank you for your answer Mapes. A follow up question: I have seen von Mises stress represented several ways,

1) vonMises = sqrt (((S1 - S2)^2 + (S2 - S3)^2 + (S1-S3)^2)/2)

where S# represents principal stresses (found from mohr's circle or transformation equations)


2) vonMises = sqrt (Sx^2 + 3*Txy^2)

where Sx is normal stress and Txy is shear stress.

Are these two equations identical or is one an approximation of true von Mises criteria? I suspect my answer would be solved by substituting expressions from Mohr's circle into the first equation...but I would also would like confirmation.
 
They're both exact, but the first equation applies to all possible load states, while the second assumes a more simplified loading. Can you tell which stresses have been assumed to be zero?
 

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