Different theories of failure have their own allowable limits. If a limit is defined as yield (from a simple tension test), then the maximum shear stress approach would predict failure (of any, more complicated load set) when the maximum shear stress (the radius of the largest "Mohr's Circle") exceeds one half of the material yield stress. When using distortions energy, octahedral shearing stress, or equivalent stress (all three terms are "identical"), failure is predicted when the calculated stress exceeds SQRT(2)/3 times the material yield stress.

The piping codes have their own defined stresses and limits and I do not get uncomfortable when one of these "non-code" stresses exceed the code-defined allowable limits.