Membrane and Moment Shell Theories — Lesson 2

This lesson covers the concepts of Membrane and Moment Shell Theories, focusing on their application in the field of structural engineering. It delves into the basic formulation and special cases for spherical shell, cylindrical shell, circular plate, and rectangular plate. The lesson further explains how these theories apply to thin shells and their inability to sustain bending stresses or moments. It also provides examples of where these theories are applied and how they are used to solve problems in structural design. The lesson concludes with a discussion on the limitations of these theories and the need for numerical solutions in complex cases.

Video Highlights

02:37 - Governing equations for membrane theory of shells
10:58 - Solution for the generalized shell of revolution
18:56 - Application of the membrane shell theory
23:32 - Moment theory of circular cylindrical shell
32:31 - Boundary conditions for solving the 4th-order differential equation in moment shell theory

Key Takeaways

- Membrane Shell Theory applies to thin shells and can only take membrane loading, meaning it cannot sustain bending stresses or moments.
- Moment Shell Theory is used to find the boundary effect at junctions where shear forces and moments are generated, causing shear stresses and bending.
- The solution for a circular cylindrical shell is possible in some cases, but for complex cases, numerical solutions are required.
- The Membrane Shell Theory cannot predict the accurate behavior at junctions and supporting structures where the boundary conditions are expressed in terms of displacement.
- The Moment Shell Theory is used to find the boundary effect at the junctions, as small thickness or a small bending moment may cause large stresses in the shell.