Advanced Strength and Applied Elasticity, Fourth Edition

Chapter 8 Axisymmetrically Loaded Members

8.1 Introduction

There are numerous practical situations in which the distribution of stress manifests symmetry about an axis. Examples include pressure vessels, compound cylinders, clad reactor elements, chemical reaction vessels, heat exchanger tubes, flywheels, solid or hollow spherical structures, turbine disks, and components of many other machines, from aerospace to household in application.

Consider a large thin plate having a small circular hole subjected to uniform pressure, as shown in Fig. 8.1. Note that axial loading is absent and therefore σ_z = 0. The stresses are clearly symmetrical about the z axis, and the deformations likewise display θ independence. The symmetry argument also dictates ...