What is the significance of the octahedral shear stress?
- AIt is always the maximum shear stress in the material
- BIt is used in the von Mises yield criterionCorrect
- CIt occurs only in planar stress state
- DIt is the average of all shear stresses in the material
Solution
Concept
Significance of octahedral shear stress
Formula
NONE
Step-by-step solution
1. Octahedral shear stress acts on planes equally inclined to all three principal stress axes. 2. It plays a significant role in distortion energy calculations and yield criterion formulations. Answer: B
Explanation
Octahedral shear stress acts on planes that are equally inclined to all three principal axes. The magnitude of this stress is directly proportional to the distortional strain energy and forms the basis for the von Mises yield criterion used to predict yielding in ductile materials. Consequently, option B correctly states its primary significance.
Why the other options are wrong
A) Maximum shear stress occurs on 45-degree planes, which differs from octahedral shear stress. C) Octahedral shear stress applies to 3D stress states acting on planes equally inclined to principal axes.
Shortcut
Octahedral shear stress represents distortion energy and forms the basis of the von Mises yield criterion.
Common mistake
Assuming octahedral shear stress is equivalent to the absolute maximum shear stress in the material and selecting option A.
Correct answer: B) It is used in the von Mises yield criterion