For the stress matrix below, the two principal stresses are given as \(\sigma_{3}=-3\) and \(\sigma_{1}=2\), respectively. In addition, two principal directions corresponding to the two principal stresses are also given below.

a. What are the normal and shear stresses on the plane whose normal vector is parallel to

\((2,1,2)\) ?

b. Calculate the principal stress \(\sigma_{2}\) and the principal direction \(\mathbf{n}^{2}\).

c. Write the stress matrix in the new coordinate system that is aligned with \(\mathbf{n}^{1}, \mathbf{n}^{2}\), and \(\mathbf{n}^{3}\).

Transcribed Image Text:

2 [102 ,n' = 20-2 1 , and n: SNOST