Max Shear Stress in 3D Stress State?

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Discussion Overview

The discussion revolves around the determination of maximum shear stress in a three-dimensional stress state. Participants seek clarification on the applicability of certain equations related to shear and normal stresses, particularly in the context of 3D stress analysis.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions whether the equation for maximum shear stress, defined as (max normal stress - min normal stress)/2, is valid in a 3D stress state.
  • Another participant clarifies the need to distinguish between maximum and minimum normal stresses versus principal stresses when discussing shear stress calculations.
  • A later reply provides the equation for maximum shear stress as (max principal stress - min principal stress)/2, suggesting a focus on principal stresses in 3D analysis.
  • There is a query about how to determine shear and normal stress on a plane of arbitrary orientation using the three principal stresses aligned with Cartesian coordinates.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the applicability of the shear stress equations in 3D stress states, and multiple views regarding the definitions and calculations remain present.

Contextual Notes

There is ambiguity regarding the definitions of normal and principal stresses, and the discussion does not resolve how these definitions impact the calculations of shear stress in different orientations.

xJJx
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Hi, there's no particular question I need help on - just a few things I need clarifying. To determine the max shear stress, I know max shear stress = (max normal stress - min normal stress)/2, but are these equations true for a 3D stress state? (please look at attached image)
Thank you
 

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scottdave said:
Okay. That gives some perspective. How about your alumni association - see if there are any local chapters operating in Canada. Maybe you can connect with some people through LinkedIn. I'm just kicking some ideas around.
loool huh
 
xJJx said:
Hi, there's no particular question I need help on - just a few things I need clarifying. To determine the max shear stress, I know max shear stress = (max normal stress - min normal stress)/2, but are these equations true for a 3D stress state? (please look at attached image)
Thank you
Do you mean the difference between the maximum and minimum normal stress, or the difference between the maximum and minimum principal stress?
 
xJJx said:
loool huh
Whoops, I thought I was posting on another thread
 
scottdave said:
Whoops, I thought I was posting on another thread
haha, it's okay
 
Chestermiller said:
Do you mean the difference between the maximum and minimum normal stress, or the difference between the maximum and minimum principal stress?
The equation to determine max shear stress is: (max principle stress - min principle stress)/2
 
OK. Do you know how to determine the shear stress and normal stress on a plane of arbitrary orientation, given the magnitudes of the three principal stresses and assuming that they are aligned with the x, y, and z Cartesian coordinate directions?
 

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