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January 9th, 2018, 01:28 AM   #1
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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
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January 9th, 2018, 05:22 AM   #2
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What definitions and formulas do you have for "hoop stress" and "radial stress"? Those are not general "mathematics" terms but for a specific application.
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January 14th, 2018, 10:33 AM   #3
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For hoop stress I have σH = σd/2t
And I havnt got one for radial stress, can't seem to find a correct formula for it
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January 14th, 2018, 12:55 PM   #4
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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


$\displaystyle \frac{{\left( {{\sigma _{rr}} - {\sigma _{\theta \theta }}} \right)}}{r} = \frac{{d{\sigma _{rr}}}}{{dr}}$
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January 14th, 2018, 01:16 PM   #5
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Right after digging out a few textbooks I think I have found some sort of guidance

At r=0.08m σ=-60Mpa
At r =0.12m σ=-25Mpa

I believe I then have to solve this as a simultaneous equation and plug the answers into this

σH = 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?
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January 14th, 2018, 02:52 PM   #6
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You mean these equations?
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File Type: jpg thickcyl1.jpg (93.6 KB, 3 views)
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January 15th, 2018, 07:49 AM   #7
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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
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January 15th, 2018, 09:30 AM   #8
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Here is a derivation of your simultaneous equations, this time in English lettering.
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File Type: jpg thickcyl2.jpg (98.9 KB, 5 views)
File Type: jpg thickcyl3.jpg (96.3 KB, 7 views)
File Type: jpg thickcyl4.jpg (98.8 KB, 4 views)
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January 15th, 2018, 09:57 AM   #9
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That is incredibly helpful, thank you very much
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