In the class of axisymmetrically loaded members, the basic problem may be defined in terms of the radial coordinate. Typical examples are thick-walled cylinders, flywheels, press and shrink fits, curved beams subjected to pure bending, and thin-walled cylinders. This chapter concerns mainly “exact” stress distribution in this group of machine and structural members. The methods of the mechanics of materials and the theory of elasticity are applied. Consideration is given to thermal and plastic stresses, the material strength, and an appropriate theory of failure to obtain a safe and reliable design in Sections 16.6 and 16.7. We also discuss briefly symmetric bending of circular plates, axisymmetrically loaded shells, and filament-wound cylinders in Sections 16.9 through 16.14.

The buckling of thin-walled cylinders under axial compression and critical pressures in vessels are treated in the concluding section. There are several other problems of practical interest dealing with axisymmetric stress and deformation in a member. Among these are various situations involving rings reinforcing a juncture, hoses, semicircular barrel vaults, torsion of circular shafts of variable diameter, local stresses around a spherical cavity, and pressure between two spheres in contact (discussed in Section 3.14). For more detailed treatment of the members with axisymmetric loading, see, for example, [1-12].