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Help - Thick Walled Cylinder Using Von Mises

Help - Thick Walled Cylinder Using Von Mises

Help - Thick Walled Cylinder Using Von Mises

(OP)
I am working on calculations based on a thick walled cylinder with open ends (longitudinal stress = 0).

The situation is you have a known bore diameter (1 to give an answer in a ratio), yield, known internal bore pressure (15ksi), so using Von Mises theory can a relationship be determined for a known bore to give the outer diameter based on a ratio. If I simply calulate the outer diameter and plot the relationship for outer diamter/bore diamter I get a consistent value of 1.14, but I want to prove this mathmatically, hopefully someone can help.

I have achieved this using Roark's but struggling with Von Mises.

so starting with

2yield^2 = (s1-s2)^2 + (s2-s3)^2 + (s3-s1)^2

How can I re-arrange this down to make the outer diameter the subject? Any help would be great, I am sure I am missing something straight forward........

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