Max Shear Stress in 3D Stress State?

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SUMMARY

The maximum shear stress in a 3D stress state is calculated using the formula: max shear stress = (max principal stress - min principal stress)/2. This equation is applicable for determining shear stress in three-dimensional scenarios. The discussion also highlights the importance of distinguishing between normal stress and principal stress when calculating shear stress on an arbitrary plane. Understanding these concepts is crucial for accurate stress analysis in engineering applications.

PREREQUISITES
  • Understanding of 3D stress states
  • Familiarity with principal stress concepts
  • Knowledge of shear stress calculations
  • Basic grasp of Cartesian coordinate systems
NEXT STEPS
  • Study the derivation of the maximum shear stress formula in 3D stress states
  • Learn how to calculate shear and normal stress on arbitrary planes
  • Explore Mohr's Circle for visualizing stress states
  • Investigate the effects of different loading conditions on principal stresses
USEFUL FOR

Mechanical engineers, structural analysts, and students studying material mechanics will benefit from this discussion, particularly those focused on stress analysis in three-dimensional contexts.

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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