Critical Load for Portal Frame with Column Hinged at Base — Lesson 2

This lesson covers the derivation of the critical load for a portal frame with a column hinged at the base. It discusses both symmetric and anti-symmetric buckling modes. In symmetric buckling, the portal frame is not allowed to move sideways, while in anti-symmetric buckling, it is allowed to sway. The lesson also explains the concept of rotational spring constant and how it differs in symmetric and anti-symmetric buckling. It further provides a step-by-step guide on how to solve the boundary conditions to find the critical load. The lesson concludes with a comparison of the critical load of a hinged-hinged column to that of a portal frame.

Video Highlights

00:32 - Discussion on the boundary conditions to solve the fourth order differential equation
06:28 - Derivation of the rotational spring constant
17:57 - Discussion on the anti-symmetric type of buckling
23:16 - Explanation of how to solve the characteristic equation graphically for anti-symmetric buckling

Key Takeaways

- The critical load of a portal frame can be derived by considering both symmetric and anti-symmetric buckling modes.
- The rotational spring constant plays a crucial role in determining the critical load.
- The boundary conditions at the ends of the column are used to solve the fourth-order differential equation to find the critical load.
- The critical load of a hinged-hinged column can be compared to that of a portal frame to understand the effect of different buckling modes.