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Homework Help: Pressure vessel expansion

  1. Sep 1, 2010 #1
    1. The problem statement, all variables and given/known data
    The inner diameter of a spherical gas container is 5m, has a wall thickness of 24mm and it is made of steel for which E=200GPa and v=0.29. Knowing the guage presure in the container is increased from zero to 1.8MPA determine:
    a) The maximum normal stress in the container,
    b) The increase in the diameter of the container


    2. Relevant equations



    3. The attempt at a solution
    a) I used the equation stress = pr/2t and got an result of 187.5MPa. Does this seem correct?

    b) Its this part I am stuck on. I cannot find an equation for calculating the change in diameter or circumference of a spherical container. Can anyone point me in the direction of some reading material or post some up here? http://ocw.mit.edu/courses/materials-science-and-engineering/3-11-mechanics-of-materials-fall-1999/modules/pv.pdf" [Broken] is the best I could find and it seems to only show the chance in circumference of a pipe.

    Thanks in advance guys.

    Adam
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Sep 1, 2010 #2

    rock.freak667

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    Homework Helper

    This should be correct.

    That formula should work. I assume it is the same as you using the normal stress (hoop stress) and longitudinal stress, with Hooke's law to get the hoop strain and then use that to get the change in radius (which is the increase in the radius).
     
    Last edited by a moderator: May 4, 2017
  4. Sep 1, 2010 #3
    Thanks for that.

    So is it correct to assume that in this case a spherical container can be treated the same as a cylinder with open ends?

    Cheers,
    Adam
     
  5. Sep 1, 2010 #4

    rock.freak667

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    Homework Helper

    I believe it can be.
     
  6. Sep 1, 2010 #5

    stewartcs

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    A cylinder with open ends will not hold any internal pressure! Pressure vessels are closed.

    The hoop stress in a cylinder is twice as much as the hoop stress in a spherical vessel.

    CS
     
  7. Sep 1, 2010 #6

    stewartcs

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    You're on the right track...take a look here:

    http://www3.esc.auckland.ac.nz/People/Staff/pkel015/SolidMechanicsBooks/Part_I/BookSM_Part_I/04_LinearElasticity%20I/PDF/Linear_Elasticity_05_Presure_Vessels.pdf [Broken]

    CS
     
    Last edited by a moderator: May 4, 2017
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