Equilibrium Equations in 2-D Polar Coordinates Plane Stress and Plane Strain Conditions — Lesson 5

This lesson covers the concept of equilibrium equations in 2-D polar coordinates. It explains the derivation of these equations and their application in geometries with circular shapes. The lesson also discusses the equilibrium conditions for small elements and how to calculate the stresses present in these elements. It further elaborates on the equilibrium equations in radial and tangential directions and the equilibrium moment at a point. The lesson concludes with a discussion on plane stress and plane strain conditions, their relationship with stress and strain, and their applications in real-world scenarios.

Video Highlights

00:59 - Derivation for the 2-D polar coordinates
10:13 - Explanation of the equilibrium equation in the radial direction
17:52 - Explanation of the equilibrium equations in the Tangential direction
22:05 - Explanation of the moment equilibrium equation
28:57 - Introduction to plane stress and plane strain conditions
33:10 - Explanation of the relationship between stress and strain in plane stress condition
46:54 - Explanation of the relationship between stress and strain in plane strain condition

Key Takeaways

- In a thin plate-like object loaded in its own plane, a plane stress condition is observed.
- Plane stress and plane strain conditions are characterized by three non-zero components of stresses.
- Under loading, equilibrium conditions are maintained at every point in the body.