Discussion Overview
The discussion revolves around the naming convention for shear stress (\tau_{ij}) in the context of a cylindrical shaft subjected to torque. Participants explore how to assign indices to shear stress components and the implications of using different coordinate systems, particularly in relation to differential elements versus entire cross sections.
Discussion Character
- Exploratory
- Technical explanation
- Debate/contested
Main Points Raised
- One participant questions how to assign indices i and j for shear stress in a circular shaft under torque, suggesting it relates to the plane containing the cross-section.
- Another participant asks why the naming convention for shear stress would differ from that of normal stress.
- A participant references a 3D infinitesimal element and describes the shear stress components as off-diagonal elements, proposing a mnemonic for remembering the index assignment.
- Some participants suggest that using cylindrical coordinates might simplify the discussion, while noting that the differential element in cylindrical coordinates still resembles a square.
- One participant expresses confusion regarding an instructor's definition of shear stress indices, indicating that it may only apply to differential elements rather than the entire cross section.
- Another participant clarifies that stress states are defined for differential elements to maintain equilibrium, suggesting that trying to define a single stress state for the entire cross section leads to confusion.
- Participants discuss the shear stress induced by torque, with one noting that it can be expressed as \tau_{z\theta}=\tau_{\theta z} proportional to the applied torque.
Areas of Agreement / Disagreement
Participants express varying interpretations of the shear stress naming convention, with some agreeing on the need to focus on differential elements while others remain uncertain about the application of definitions to entire cross sections. The discussion does not reach a consensus on the correct approach.
Contextual Notes
Participants highlight the limitations of applying definitions to entire cross sections, emphasizing that stress states are typically defined for differential elements. There is also mention of the potential confusion arising from different coordinate systems.
