Q:

Machine design problem

I am getting confused with the maths in the max distortion strain energy part of the question.  Plus there is a misprint as the formula for distortion should be a^2 +b^2-2ab=(yield stress)^2, here they have missed the 2 in 2ab.  Or maybe I am wrong
Can someone please solve it correctly showing the working(maths).  I just need a step by step working as I am making some error solving it myself.  And the one solved here is missing steps. 
*F.S=1 that's why not mentioned. 
Thanks

A:

Maximum distortion strain energy formula from your example is reduced von Mises formula,
 so the calculation should be correct.  It does not comply the binomial theorem because of specific physical properties of material and stress tensor components relations.  
It's very easy ask google question.  Though always check wikipedia's answer and try finding some lecture notes or other literature if possible peer reviewed.