This problem is applicable to aerostructures and mechanics of materials courses. Principal stresses are the components of the stress tensor when the basis is changed in such a way that the shear stress components become zero. Principal stress is the maximum normal stress a body can have at its some point such that it feels no shear stress. It represents purely normal stress. If at some point principal stress is said to have acted it does not have any shear stress component. Rather than use stress invariants and complex calculations that do not require Matlab, using Eigen values takes 9 equations and makes the problem into two lines of code to return these stresses. Once the values of tensile/compressive stress and shear stress are known, they are plugged into a matrix, where shear stress in the XY plane is equivalent to shear stress in the YX plane, creating a symmetric matrix. Once the stress tensor is created, taking it’s Eigen values will reveal its principal stresses. For the maximum shear force experienced by the cube, take the difference of the highest and lowest principal stress and half it.
