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Tension on the ring

  1. Jan 29, 2010 #1
    Imagine a ring; the image below shows the top cross section of the ring -


    The arrows represent forces which is acting towards the inner side of the ring cause of a pressure which applies towards it's inner side.

    Assuming the ring to be made up of a material having a plastic property, I want an expression for the tension produced in the ring.

    Attached Files:

  2. jcsd
  3. Jan 29, 2010 #2


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    Do you own a copy of Roark? This looks like a ring under internal pressure. Actually, the load case you probably want is a simple shell of revolution under internal pressure. In my version its Chapter 13 load case 1b.
    Hoop stress:
    \sigma = \frac{qR}{t}
  4. Jan 29, 2010 #3


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    That is pretty much the definition of the hoop stress.
  5. Jan 29, 2010 #4
  6. Jan 29, 2010 #5
    I did some calculations and found that the stress should be ~63.7% of 1/4th of the total force applied by the pressure.
  7. Jan 29, 2010 #6


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  8. Jan 29, 2010 #7


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    I understood 1/4th of 63.7% of that post. Care to rephrase this or tell us what you are getting at?
  9. Jan 29, 2010 #8
    is this a good book for the "techno savy" non engineer?

    I would like to find a good formula book that was not a novel in "techno-ese" just formulas
    (especially pressure and temp related)

  10. Jan 29, 2010 #9
    Roark's book is pretty good. If you are crafty enough with mathematics you can derive some of the formulas in Roark with the help of Timoshenko's book "Plates and Shells" but you better be good.:biggrin:

    To answer your question:

    Roark's book is good for the non-engineer. The hard part is knowing that you have the right boundary conditions specified.

    Here is a link to it.


    Be cautious of the online calculator.

  11. Jan 29, 2010 #10


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    It is but you do have to have a basic understanding to fully understand it. The beginning sections of each chapter cover theory. However, it is, essentially, a book divided into different tables covering load/support scenarios with associated equations covering that scenario. I attached a typical page so you can see it.

    Attached Files:

  12. Jan 29, 2010 #11
    aaa...just forget the 63.7% part...I'll work on it later.

    Point is hooks stress is no different from normal stress right?...I mean if hook's stress comes as 500 mega pascals, then the stress in the material is 500 mega pascals right?
  13. Jan 29, 2010 #12
    The hoop stress is very easy to derive for this type of setup. There is no need for any fancy elasticity theory.
    Last edited: Jan 29, 2010
  14. Jan 30, 2010 #13


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    dE_logics: That is correct. Hoop stress is normal stress. Very good.
  15. Jan 30, 2010 #14
    Sounds sarcastic.

    Is there a conversion or something?
    Last edited: Jan 30, 2010
  16. Jan 30, 2010 #15


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    No. He was being serious. The hoop stress is the same thing as the normal stress because of the direction on an element that is perpendicular to a line around the circumference at some radius.


    Attached Files:

  17. Jan 30, 2010 #16
    Oh...ok, thanks a lot people.

    Need it urgently.
  18. Feb 1, 2010 #17
    thanks for the book review
    I'll add it to my "wish list" when I go to the used book store
    if not, it looks like it is worth the $70 anyway

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