Stress compound cylinder problem

[jakeward46]

Homework Statement

A tube 40mm inside and 60mm outside dia is to be reinforced by shrinking on a tube of 80mm outside diameter. The compound tube is subjected to an internal pressure of 50MPa and the shrinkage allowance is such that the final maximum stress in each tube is the same. Determine the maximum stress and the difference in tube diameter before shrinkage. E=207000 N/mm^2

Homework Equations

Lames equations:
Radial stress σr=A-B/r^2
Hoop stress σθ=A+B/r^2

The Attempt at a Solution

Ive attempted the first part of the question however i have ended up with a negative maximum stress which cannot be. If someone could point out my mistake or give advice that would be great :)

 

[SteamKing]

Usually, a negative stress indicates the member is in compression.

 

[jakeward46]

Ok thanks, so my answer is an acceptable one? I didn't think that would apply to cylinders.

 

[jakeward46]

I have just worked the calculation again and got A=16666687.5 and B=26666.7 and subbing into lames eqautuon for hoop stress in and out

σθin= 83.3MPa

σθout= 33.3MPa

this seems a more realistic answer, showing max stress is in the inside of the cylinder. ?

 

[sdaysley]

just looked at your working how did you now that the compound cylinder was made up of the same material, is that from the one value of young's modulus? also did you work out the stress produced from the shrink fit not just the internal pressure?

 

[jakeward46]

Yes as there is only one youngs mod given i would of thought it is the same material?

Ive been working on it and i have worked out the stress due to interference fit first and then calulated with internal pressure. not realising i had to to this at first.

:)