Application of Beam on Elastic Foundation Analysis to Pressure Vessels for Calculation of Discontinuity Stresses — Lesson 3

This lesson covers the application of beam on elastic foundation analysis to pressure vessels. It discusses the deformation of a cylindrical vessel subjected to radially distributed loading, and how this deformation can be analyzed by considering a sector of the vessel like a beam on an elastic foundation. The lesson also explains how to calculate the constants needed for this analysis, such as the modulus of rigidity of the beam and the resistance of the beam to deflection. It further explores the impact of forces on the deformation of a sector, and how these forces can be visualized and calculated. The lesson concludes with a discussion on discontinuity stresses at the junction of a cylinder and a sphere, and how these stresses can be calculated and analyzed.

Video Highlights

00:39 - Introduction to the application of beam on elastic foundation analysis to pressure vessels.
05:16 - Discussion on the deformation of a sector of a shell and the calculation of parameters like k and beta.
08:16 - Explanation of the calculation of the vertical force resisting the movement due to loading.
12:12 - Discussion on the extra rigidity in a sector of a shell due to the continuity of the shell all over the circumference.
16:36 - Explanation of the calculation of the discontinuity stresses at the junction of a vessel subjected to forces.
24:16 - Discussion on the application of the derived formulas to a bimetallic joint.
45:51 - Explanation of the calculation of the discontinuity stresses at the cylinder-sphere junction.

Key Takeaways

- The deformation of a cylindrical vessel subjected to radially distributed loading can be analyzed by considering a sector of the vessel like a beam on an elastic foundation.
- The modulus of rigidity of the beam and the resistance of the beam to deflection are key constants in this analysis.
- Forces acting on the deformation of a sector can be visualized and calculated.
- Discontinuity stresses occur at the junction of a cylinder and a sphere, and these stresses can be calculated and analyzed.