Torsion of Non-Circular Shaft (Continued) — Lesson 2

This lesson covers the concept of torsion of non-circular shafts, focusing on the application of torsion and the resulting warping. It explains how shear stress acts parallel to the outer boundary of the section and introduces Prandtl’s stress function. The lesson further elaborates on how to calculate shear stress at a point and how it acts parallel to the boundary. It also discusses the relationship between the angle of twist per unit length, the cross-sectional dimensions, and the applied torque. The lesson concludes with examples of elliptical and triangular sections, demonstrating how to calculate the maximum stress and its direction.

Video Highlights

02:04 - Explanation of how shear stress acts parallel to the boundary in the case of torsion of non-circular components.
07:32 - Discussion on the direction of shear stress and how it aligns with the applied torque.
19:17 - Explanation of how to calculate the maximum shear stress on an elliptical section.
25:16 - Discussion on the distribution of stresses over the cross section of an elliptical component.
36:24 - Example of calculating shear stress on a triangular section.
46:12 - Explanation of how to calculate the maximum stress on a triangular section.

Key Takeaways

- Torsion of non-circular shafts results in warping, which is a solution of the Laplace equation.
- Shear stress acts parallel to the outer boundary of the section and cannot act normal to the boundary.
- Prandtl’s stress function helps in calculating the shear stress at a point.
- The angle of twist per unit length is related to the cross-sectional dimensions and the applied torque.
- The maximum stress and its direction can be calculated using the given cross-sectional dimensions and the applied torque.