Thin Shells of Revolution — Lesson 1

This lesson covers the calculation of stresses in thin shells, specifically those with an axis of symmetry and small wall thickness. These shells can be cylindrical, spherical, conical, or toroidal. The lesson explains how to calculate stresses in these shells, with a focus on axial and circumferential stresses. It also discusses the concept of toroidal shells and how they are generated by the rotation of a circle about an axis of symmetry. The lesson further delves into the calculation of stresses in spherical and conical shells, and the differences in stress distribution in these shells. It concludes with a discussion on the calculation of stresses in toroidal shells and general membrane theory for doubly curved shells of revolution.

Video Highlights

01:08 - Explanation of toroidal shell and its generation by considering rotation of a circle about the axis of symmetry.
05:38 - Calculation of stresses in a conical shell and how to calculate the axial and hoops stress.
11:53 - Explanation of stresses in a toroidal shell and how to calculate the axial and circumferential stress.
29:30 - Discussion on the general membrane theory for W call shell and how to calculate the stresses.
41:06 - Solving examples on thin cylindrical shell and thin spherical shell using the derived formulas.
54:02 - Explanation of a problem involving a vessel filled with water and the calculation of the stress in the vessel.

Key Takeaways

- Thin shells with an axis of symmetry and small wall thickness can be cylindrical, spherical, conical, or toroidal.
- The calculation of stresses in these shells involves understanding axial and circumferential stresses.
- Toroidal shells are generated by the rotation of a circle about an axis of symmetry.
- The distribution of stresses in spherical and conical shells differs due to their shape.
- The general membrane theory for doubly curved shells of revolution provides a formula to calculate stresses in these shells.