Maximum Shear Stress and Octahedral Shear Stress, Deviatoric and Hydrostatic Stresses — Lesson 5

This lesson covers the concept of determining planes of maximum shear stresses at a point. It explains the principal stresses and their directions, and how to find out a plane that will have the maximum shear stress. The lesson also discusses the concept of tractions in reference directions and how to calculate the normal stress. It further explains the concept of octahedral shear stress and octahedral planes. The lesson concludes with the explanation of the Deviatoric and Hydastatic stress tensors and their roles in deformation and volume change of an element.

Video Highlights

01:02 - Explanation of how to determine the principal stresses, sigma 1, sigma 2, sigma 3, and their directions
08:45 - Explanation of how to calculate the shear stress on the plane.
19:21 - Explanation of how to solve for l and m using the equations obtained
34:21 - Explanation of the concept of octahedral shear stress and octahedral planes
41:04 - Explanation of how to calculate the shear stress on octahedral planes
49:36 - Explanation of how to break up the total stress tensor into Deviatoric and Hydastatic stress tensors

Key Takeaways

- The principal stresses at a point are determined by the tensor sigma i j.
- The plane with the maximum shear stress can be determined by calculating the tractions in the reference directions.
- The Deviatoric part of the stress tensor is responsible for the deformation of the element, while the Hydrastatic part is responsible for the change of volume of the element.
- The octahedral shear stress is an invariant quantity and can be calculated using the stress invariants.
- The total principal stress can be obtained from the principal stresses arising out of the Hydrastatic part and after adding the mean stress.