9. For the stress matrix below, the two principal stresses are given as 03 = —3 and crj = 2, respec¬

tively. In addition, the two principal stress directions corresponding to the two principal stresses are also given below.

¦ 2 " " 1 "

1 0 2 V5 V5 0 1 0 i n1 = 0 and n3 = 0 2 0-2 1 -2

-Vsl

(a) What is the normal and shear stress on a plane whose normal vector is parallel to (2, 1, 2)?

(b) Calculate the missing principal stress <12 and the principal direction n2.

(c) Write stress matrix in the new coordinates system that is aligned with n1, n2, and n3.