Problem $3$:

Below are the stresses at a particular point of interest in a structural system.

A$)$ Using the transformation equations, determine the principal angle and principal stresses. Show the results on a properly oriented element.

B$)$ Using the transformation equations, determine the maximum in$-$plane shear stress and associated angle, as well as the average normal shear stress. Show the results on a properly oriented element.

C$)$ Now plot the Mohr's circle equivalent of the stresses within the element shown below. Correctly label the principal stresses, the maximum shear stress, and the average stress.