At the end of this section you should be able to:

1. Construct stress element in arbitrary orientation

2. Find maximum and minimum normal stresses (principal stresses) and angle (principal direction) 

3. Find maximum shear stress and angle

4. Understand the utility of principal stresses

Stress Transformations explains how the stress state at a point changes when the stress element is rotated to a new orientation. You will construct a stress element in an arbitrary orientation, compute the normal and shear stress components on a selected plane, then find the maximum and minimum normal stresses (principal stresses) and the corresponding principal direction. You will also determine the maximum shear stress and the angle where it occurs, and learn why principal stresses are useful for interpreting combined loading and supporting strength and failure checks. Mathematica code resources are included for efficient solving and verification.