Determine the principal stresses and show these on a sketch of an element in the correct orientation relative to the x axis.

Determine the principle of stresses

a.      Determine the magnitude and direction of stresses

According to this case, the vertical angle is given by 30 degree

Magnitude is given by

(b) Determine the direct (normal) stress acting at the surface of the shaft in the axial direction (the x-direction) and in the circumferential direction. That is, determine the values of 𝜎𝑥 and 𝜎𝑦.

Given