Solve the rotating disk problem of Example 8.11 for the case of an annular disk with inner radius a and outer radius b being stress free. Explicitly show that for the case b >> a, the maximum stress is approximately twice that of the solid disk.

Data from example 8.11

Transcribed Image Text:

As a final example in this section, consider the problem of a thin uniform circular disk subject to constant rotation ), as shown in Fig. 8.37. The rotational motion generates centrifugal acceleration on each particle of the disk, and this then becomes the source of external loading for the problem. No other additional external loadings are considered. It is convenient to handle the centrifugal force loading by relating it to a body force density through the disk. For the case of constant angular velocity, the body force is only in the radial direction given by F = pwr (8.4.73) where p is the material mass density. This problem is axisymmetric, and thus the equilibrium equations reduce to do, or - 08 + dr r +pwr=0 (8.4.74)