Using mechanics of materials theory developed for axial members, torsion members, and beams, normal and shear stresses at a point can be computed in reference to an arbitrarily defined coordinate system, like the x-y coordinate system.
The material comprising a structural member will fail based on the magnitude and the direction of the largest stress. Designers have no assurance that stresses computed in either the x or y directions are in fact the largest stresses at the point. It is possible that the largest stress magnitudes at a point occur at orientations other than the arbitrarily chosen x and y directions.
Methods must be developed to find the critical stresses at a point in the material. These methods must consider any and all possible orientations.