Timothy A. Philpot - Mechanics of materials _ an integrated learning system-John Wiley (2017)

Torsion
CHAPTER
6
6.1 Introduction
Torque is a moment that tends to twist a member about its longitudinal axis. In the design of
machinery (and some structures), the problem of transmitting a torque from one plane to a
parallel plane is frequently encountered. The simplest device for accomplishing this function
is called a shaft. Shafts are commonly used to connect an engine or a motor to a pump, a compressor,
an axle, or a similar device. Shafts connecting gears and pulleys are a common application
involving torsion members. Most shafts have circular cross sections, either solid or
tubular. A modified free-body diagram of a typical device is shown in Figure 6.1. The weight
and bearing reactions are not shown on the diagram, since they do not contribute useful information
to the torsion problem. The resultant of the electromagnetic forces applied to the armature
A of the motor is a moment that is resisted by the resultant of the bolt forces (another
moment) acting on the flange coupling B. The circular shaft (1) transmits the torque from the
armature to the coupling. The torsion problem is concerned with the determination of stresses
in shaft (1) and the deformation of the shaft. For the elementary analysis developed in this
book, shaft segments such as the segment between transverse planes a–a and b–b in Figure 6.1
will be considered. By limiting the analysis to shaft segments such as this, the complicated
states of stress that occur at the locations of the torque-applying components (i.e., the armature
and flange coupling) can be avoided. Recall that Saint-Venant’s principle states that the effects
introduced by attaching the armature and coupling to the shaft will cease to be evident in the
shaft at a distance of approximately one shaft diameter from these components.
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