This chapter begins by discussing the design of shafts, making extensive use of the material from Sections 2.8 through 2.12 and Ch. 4 to develop stresses. The failure theories presented in Section 6.7 are used for static failure prediction in Section 11.2; the material in Ch. 7 is used to develop design rules for fatigue of shafts in Section 11.3. Here, combinations of loading are presented, whereas previously each type of loading was considered independently. It is important that this material be understood before proceeding with this chapter. The critical speed of rotating shafts is discussed in Section 11.5. The dynamics and the first critical speed are important, since the rotating shaft becomes dynamically unstable and large vibrations are likely to develop.