Torsion of Non-Circular Shaft — Lesson 1

This lesson covers the concept of torsion of non-circular shafts, focusing on the distribution of stresses when such shafts are subjected to twist. The lesson explains how a non-circular shaft undergoes deformation, leading to shear stresses that act parallel to the boundary. It further discusses the concept of warping of the cross-section and introduces the Prandtl stress function and the Saint Venant's warping function. The lesson also explains how to calculate the strains and stresses using these functions. For instance, it uses an elliptical or rectangular shaft as an example to illustrate the concepts.

Video Highlights

00:28 - Explanation of shear stress distribution in a circular shaft
09:49 - Calculation of the strains and stresses using Hook's law
16:02 - Explanation of the equilibrium equations and their satisfaction in the problem of torsion
37:25 - Introduction to the Prandtl stress function and its relationship with the warping function
42:00 - Explanation of the properties of the Prandtl stress function and its role in calculating the torque capacity of the shaft

Key Takeaways

- Non-circular shafts undergo deformation when subjected to twist, leading to shear stresses that act parallel to the boundary.
- The warping of the cross-section, a type of section deformation, is a crucial concept in understanding the behavior of non-circular shafts under torsion.
- The Prandtl stress function and the Saint Venant's warping function are essential tools for calculating the strains and stresses in non-circular shafts.
- The torque capacity of a non-circular shaft can be determined from the volume bounded by the phi surface and the section or x-y plane.