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

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TORSION
A positive internal torque T in a shaft or other torsion member tends to rotate in a
right-hand rule sense about the outward normal to an exposed section. In other words, an
internal torque is positive if the right-hand thumb points outward away from the sectioned
surface when the fingers of the right hand are curled in the direction that the internal torque
tends to rotate. This sign convention is illustrated in Figure 6.11.
mecmovies 6.3 presents an
animation of the sign conventions
used for internal torques, shaft
element twist angles, and
rotation angles.
Outward
normal
+T
FIGURE 6.11 Sign convention for internal torque.
+ T
Outward
normal
Sign convention for Angles of Twist
The sign convention for angles of twist is consistent with the internal torque sign convention.
A positive angle of twist φ in a shaft or other torsion member acts in a right-hand rule
sense about the outward normal to an exposed section. In other words,
• At an exposed section of the torsion member, curl the fingers of your right hand in
the direction of the twisting deformation.
• If your right-hand thumb points outward, away from the sectioned surface, the angle
of twist is positive.
This sign convention is illustrated in Figure 6.12.
Outward
normal
Outward
normal
+φ
+φ
FIGURE 6.12 Sign convention for angles of twist.
Sign convention for Rotation Angles
Let the longitudinal axis of a shaft be defined as the x axis. Then, a positive rotation angle
acts in a right-hand rule sense about the positive x axis. For this sign convention, an origin
must be defined for the coordinate system of the torsion member. If two parallel shafts are
considered, then the two positive x axes should extend in the same direction. This sign
convention is illustrated in Figure 6.13.
y
+
x
+φ
FIGURE 6.13 Sign convention for rotation angles.