How Do You Calculate Principal Stresses and Orientations in a 2D Stress State?

[rock.freak667]

Homework Statement

In an element of material, subjected to general two-dimensional stress one axial stress is 66N/mm² (tensile) and the shear stress is 48N/mm². Calculate the values and directions of the principal stresses and the normal and shear stresses on planes equally inclined to the axes if the other axial stress of 22N/mm² is a) tensile and b)compressive.

Homework Equations

\sigma_n=\frac{1}{2}(\sigma_x+\sigma_y)+\frac{1}{2}(\sigma_x-\sigma_y)cos2\theta+\tau_{xy}sin2\theta

\tau_n= \frac{1}{2}(\sigma_x-\sigma_y)sin 2\theta-\tau_{xy}cos2\theta

The Attempt at a Solution

Well I used the fact that the principal stresses are given by

\sigma_1,\sigma_2=\frac{1}{2}(\sigma_x+\sigma_y) \pm \sqrt{(\sigma_x-\sigma_y)^2+4\tau_{xy}^2

and got the values to be 96.8 N/mm² and -8.80N/mm²

Then I used the fact that

tan2\theta=\frac{2\tau_{xy}}{\sigma_x-\sigma_y}

and got \theta=32.69. That part I got out, but I don't know how to get the normal and shear stresses on planes equally inclined to the axes.

I am not sure about what the question means by equally inclinded to the axes.

EDIT:solved.