For a given Cartesian coordinate system 0(x1, x2, x3), the state of stress at a point is given below.
Determine -
$[\sigma] = \begin{bmatrix} 2 & 1 & 3 \\ 1 & 2 & -2 \\ 3 & -2 & 1 \end{bmatrix}$
(a) Traction vector acting on a plane through the point whose unit normal is $\hat{n} = \frac{1}{3}\hat{e}_1 + \frac{2}{3}\hat{e}_2 - \frac{2}{3}\hat{e}_3$.
(b) Magnitude of traction vector acting perpendicular to the plane.
(c) Magnitude of shear component of traction on the plane.