von-mises stress for axisymmetric problem

Can someone help me to understand how the von-mises stress might be computed for the following axisymmetric plate bending problem in cylindrical co-ordinates:

u_r(r) u_theta = 0 u_z(r)

So, the following strains are non-zero: e_rr, e_theta_theta, e_rz

This gives the following non-zero stress components: sigma_rr, sigma_zz, sigma_theta_theta, sigma_rz

Once I have the values for the above 4 stress components at a point, how do I proceed to compute the von-mises stress at that point. How do I go about computing all three principal normal stresses at that point?

Any help/clarifications are appreciated

~ankush