. The stress components relative to rectangular coordinate axes ( x 1 , x 2 , x 3 ) are, at a given point P in a medium, σ 11 = 0, σ 22 = 7 / 2, σ 33 = −7 / 2 , σ 23 = −1 √ 12 , σ 31 = 7 √ 2, and σ 12...

.
The stress components relative to rectangular coordinate axes (x1, x2, x3)
are, at a given

point
P
in a medium,
σ11 = 0,
σ22 = 7/2,
σ33 = −7/2, σ23 = −1

√

12, σ31 = 7

√

2, and

σ12 = −1/

√

6.

(a)
Determine the principal stresses and the maximum shearing stress. [Hint:
The principal

stresses are integers.] Consider axes
yα
obtained by a rotation relative to axes

xα

(b)
Determine the principal stresses and maximum shearing stress relative to axes
yα.