Stress Distribution in Thick Cylinder — Lesson 3

This lesson covers the determination of stresses in thick cylinders and rotating discs. It explains the concept of stresses in thin cylinders, where the thickness divided by the internal radius of a cylinder is less than about 0.1. The lesson further elaborates on the circumferential stress or hoop stress and axial stress in thin cylinders. It also discusses the stress distribution in thick cylinders, the existence of radial stress, and the distribution of hoop stress and axial stress. The lesson provides examples of thick cylinders in real-life situations such as domestic gas cylinders, oxygen gas cylinders, water or gas pipelines, and the body of a submarine. It also explains the connection between thick cylinders and rotating discs, and the calculation of stresses due to rotation in the case of a rotating shaft or a grinding wheel.

Video Highlights

00:56 - Explanation of thin cylinder and its properties.
05:44 - Explanation of the stress distribution in thick cylinders.
09:45 - Discussion on the stresses developed in a rotating disc.
13:36 - Explanation of the displacement pattern in a thick cylinder
23:06 - Discussion on the equilibrium equations in a thick cylinder.
36:58 - Explanation of the stress distribution in a thick cylinder subjected to internal and external pressure.
46:19 - Discussion on the variation of stresses in a thick cylinder.
54:10 - Explanation of the maximum hoop stress in internally pressurized and externally pressurized cylinders.

Key Takeaways

- The thickness divided by the internal radius of a cylinder determines whether it is a thin or thick cylinder.
- In thin cylinders, the circumferential stress or hoop stress and axial stress are present.
- In thick cylinders, the distribution of hoop stress, axial stress, and the existence of radial stress are considered.
- The stresses in a rotating disc or a grinding wheel due to rotation are calculated for design purposes.
- The sum of radial and circumferential stresses in a thick cylinder is constant and independent of the radius.