Problem $2$:

Setup: A piece of material is loaded as shown.

Find: The state of stress at a point is shown on the element. Determine $($a$)$ the principal stresses and $($b$)$ the maximum inplane shear stress and average normal stress at the point. Specify the orientation of the element in each case. ${?}^2$

Steps:

What is the necessary equation for the principal stresses?

What are ${}_x,{}_y,{}_{xy}?$

Plug them into the equation and solve for the principal stresses.

What is the orientation of the principal stresses?

What is the max shear?

What is the average stress?

What is the max shear orientation.