Page 279 - Introduction to Continuum Mechanics

The Elastic Solid 263

Therefore, the eigenvector is given by n = (V2/2)(ei - e 2). This normal determines a plane

perpendicular to the lateral face which makes a 45° angle with thejcj-axis. Frequently, a crack
along a helix inclined at 45° to the axis of a circular cylinder under torsion is observed. This
is especially true for brittle materials such as cast iron.

Example 5.13.2

In Fig, 5.11, a twisting torque M t is applied to the rigid disc A. Find the twisting moments
transmitted to the circular shafts on either side of the disc.

Fig. 5.11

Solution. Let MI be the twisting moment transmitted to the left shaft and M 2 that to the
right shaft. Then, the equilibrium of the disc demands that