Page 201 - Introduction to Continuum Mechanics

186 Stress

the characteristic equation has the form

Therefore A = 0 is an eigenvalue and its direction is obviously n = 63. The remaining eigen-
values are

To find the corresponding eigenvectors, we set (7/j-A(5,y)n^ = 0 and obtain for either
A = TI or T 2,

see
The third equation gives n>$ = 0. Let the eigenvector n = cosflej+sin^ ( F*g- 4.7). Then,
from the first equation

Fig. 4.7

(b) Since the third eigenvalue is always zero, the maximum shearing stress will be the greatest
of the value
IT- I T" I