My Math Forum Thick and thin walled cylinders

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 January 9th, 2018, 01:28 AM #1 Newbie   Joined: Jan 2017 From: brussels Posts: 26 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, 05:22 AM #2 Math Team   Joined: Jan 2015 From: Alabama Posts: 2,919 Thanks: 785 What definitions and formulas do you have for "hoop stress" and "radial stress"? Those are not general "mathematics" terms but for a specific application. Thanks from greg1313
 January 14th, 2018, 10:33 AM #3 Newbie   Joined: Jan 2017 From: brussels Posts: 26 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, 12:55 PM #4 Senior Member   Joined: Jun 2015 From: England Posts: 715 Thanks: 203 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, 01:16 PM #5 Newbie   Joined: Jan 2017 From: brussels Posts: 26 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 (p2-p1) / 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, 02:52 PM   #6
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You mean these equations?
Attached Images
 thickcyl1.jpg (93.6 KB, 2 views)

 January 15th, 2018, 07:49 AM #7 Newbie   Joined: Jan 2017 From: brussels Posts: 26 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, 09:30 AM   #8
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Here is a derivation of your simultaneous equations, this time in English lettering.
Attached Images
 thickcyl2.jpg (98.9 KB, 5 views) thickcyl3.jpg (96.3 KB, 6 views) thickcyl4.jpg (98.8 KB, 4 views)

 January 15th, 2018, 09:57 AM #9 Newbie   Joined: Jan 2017 From: brussels Posts: 26 Thanks: 0 That is incredibly helpful, thank you very much

 Tags cylinders, thick, thin, walled

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