2) A state of stress at a point in a body is defined by the stress components $\sigma_{11} = 1000$, $\sigma_{22} = -1000$, $\sigma_{12} = 500$, $\sigma_{23} = -200$ and $\sigma_{13} = \sigma_{33} = 0$.
Consider a plane that passes through the point and has unit normal vector
$(1/10, 3/10, 3/\sqrt{10})$ relative to the Cartesian axes $X_1, X_2, X_3$
(a) Determine the $(X_1, X_2, X_3)$ components of the stress vector that acts on the
plane.
(b) Determine the magnitude of the stress vector of part (a).
(c) Determine the normal component of the stress vector of part (a)
(d) Determine the magnitude of the shearing stress that acts on the plane
3) Determine the principal stresses and principal directions for the stress tensor
in problem 2.
4) Using tensor notation write out $\sigma^*_{12}$ in terms of the $c_{ij}$ and $\sigma_{ij}$.
