Normally, the specification for the steel will show the yield stress OR the yield point, and you use whichever one you have. Normally, a steel specification, such as ASTM A36, will require a minimum yield strength, IE, it will specify which one is measured, and no one checks the other one.
And, in many cases, if you're designing to some standard or code, allowable stress is specified. In those cases, you don't fool with theories of failure, just maximum tensile or compressive or shear stress.