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January 9th, 2018, 12:28 AM  #1 
Newbie Joined: Jan 2017 From: brussels Posts: 28 Thanks: 0  Thick and thin walled cylinders
A thick cylinder of 80mm internal radius and 120mm external radius is subjected to an internal pressure of 80 MN/m^2 and an external pressure of 25 MN/m^2, determine the hoop stress and radial stress on the inside and outside of the cylinder Can anybody give me the correct formulas to use to solve this, or help point me in the right direction please 
January 9th, 2018, 04:22 AM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 
What definitions and formulas do you have for "hoop stress" and "radial stress"? Those are not general "mathematics" terms but for a specific application.

January 14th, 2018, 09:33 AM  #3 
Newbie Joined: Jan 2017 From: brussels Posts: 28 Thanks: 0 
For hoop stress I have ÏƒH = Ïƒd/2t And I havnt got one for radial stress, can't seem to find a correct formula for it 
January 14th, 2018, 11:55 AM  #4 
Senior Member Joined: Jun 2015 From: England Posts: 915 Thanks: 271 
As Country Boy said, this is specialist stuff. You haven't provided anywhere near enough information to analyse a thick cylinder. For instance, What are the cylinder end conditions? What restraints are provided by the cylinder supports. Because of radial symmetry no shear stresses act on a volume element of the wall and normal stresses are a function of r alone. The stress is best analysed in cylindrical coordinates leading to a simple equation of equilibrium $\displaystyle \frac{{\left( {{\sigma _{rr}}  {\sigma _{\theta \theta }}} \right)}}{r} = \frac{{d{\sigma _{rr}}}}{{dr}}$ 
January 14th, 2018, 12:16 PM  #5 
Newbie Joined: Jan 2017 From: brussels Posts: 28 Thanks: 0 
Right after digging out a few textbooks I think I have found some sort of guidance At r=0.08m Ïƒ=60Mpa At r =0.12m Ïƒ=25Mpa I believe I then have to solve this as a simultaneous equation and plug the answers into this ÏƒH = p1r1^2  p2r2^2 / r2^2  r1^2  R1^2r2^2 (p2p1) / r^2 (r2^2  r1^2) I realise now my notes on this were lacking quite a bit of substance Does this look familiar to anyone? 
January 14th, 2018, 01:52 PM  #6 
Senior Member Joined: Jun 2015 From: England Posts: 915 Thanks: 271 
You mean these equations?

January 15th, 2018, 06:49 AM  #7 
Newbie Joined: Jan 2017 From: brussels Posts: 28 Thanks: 0 
Yes those are the ones. Pretty stuck on the simultaneous equation part of this question, it's been an awfully long time since I've done it and my mind needs refreshing 
January 15th, 2018, 08:30 AM  #8 
Senior Member Joined: Jun 2015 From: England Posts: 915 Thanks: 271 
Here is a derivation of your simultaneous equations, this time in English lettering.

January 15th, 2018, 08:57 AM  #9 
Newbie Joined: Jan 2017 From: brussels Posts: 28 Thanks: 0 
That is incredibly helpful, thank you very much


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cylinders, thick, thin, walled 
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