Buckling II: Instability of Slender Elastic Structures Under Compression

This lecture delves into the concept of buckling, focusing on the Euler buckling load for different beam constraints such as clamped-clamped, fixed-free, and clamped-pinned. The instructor explains the instability of slender elastic structures under compression, emphasizing the relationship between load and critical load for buckling. The lecture expands beam theory to allow compressive loads while assuming no compressive deformation, leading to the discussion of moment-curvature relations. Various boundary conditions are explored, including pinned-pinned and pinned-fixed configurations. The lecture also covers the moment-curvature relation and the ODE for general solutions. Additionally, the instructor introduces the concept of buckliphobia and buckliphilia, showcasing real-world applications of buckling phenomena in structures and aerodynamics.