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 • Welcome to Engineering! This looks like a homework question. In order for such questions to be answered in this site, we need you to add details describing the precise problem you're having. What have you tried to solve this yourself? Please edit your question to include this information.
– Wasabi
Nov 26 '17 at 20:20
• Can't be bothered to put my laptop on its side... Nov 26 '17 at 20:36
• Actually it's not homework. Preparing for exams. The reason I didn't mention the question is because I am only having problem in this part of the question. And the problem is the maths. Everything needed to solve is already there in the picture. Values of major and minor principal stresses are shown there in the picture.
Nov 26 '17 at 20:40
• @solar Mike there the picture is upright now.
Nov 26 '17 at 20:43
• The answer has already been given why would I come here if it was just for homework. I posted it here because I couldn't understand the solution (working) the writer has shown. It is missing crucial steps that's what I want help with
Nov 26 '17 at 20:50

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.

• Thanks for the answer. So is reduced von mises formula used in case of only ductile materials? What specific physical property are there.