Torsional Buckling — Lesson 2

This lesson covers the concept of torsional buckling, focusing on St. Venant torsion, uniform and non-uniform torsion. It explains the derivation of the governing differential equation for torsion and the expression for strain energy stored when torsion is applied to any member. The lesson further simplifies the governing differential equation by deriving the expression for torque per small length. It also discusses the critical load of torsional buckling for a cruciform section and a case where the ends of the bar cannot rotate and are free to warp.

Video Highlights

01:02 - Explanation of the term torque per small length dz in the governing differential equation
09:01 - Explanation of the moment about the longitudinal axis of the fictitious lateral load for a small element of length mn
16:43 - Explanation of the standard expression for torsional buckling
21:22 - Explanation of how to find the critical torsional buckling load

Key Takeaways

- The governing differential equation for torsion holds for any symmetric shape of cross-section as long as the shear centre and centroid coincide.
- The torque per small length can be derived by considering a cruciform section.
- The critical load of torsional buckling for a cruciform section can be found using the derived equations.
- In a case where the ends of the bar cannot rotate but are free to warp, the critical stress for torsional buckling can be calculated.