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[Material Science] Thin Walled Cylinders & Yield Criterion

  1. Feb 13, 2012 #1
    1. The problem statement, all variables and given/known data

    A long cylindrical boiler shell is 1.75 m in diameter and has a wall thickness of 12 mm. Treating the boiler as a thing shell, predict what internal pressures will produce yield in the shell according to the: (a) Rankine, (b) Max. Principal Strain, (c) Tresca and (d) Von Mises Criteria.

    σyield = 300 MPa, E = 200 GPa, v = 1/3)

    2. Relevant equations

    The only issue I am having here is with the Von Mises criteria, which states for plane stress:

    σ12 + σ1·σ2 + σ22 = σyield2

    σhoop = P·D/2·t
    σaxial = P·D/4·t

    3. The attempt at a solution

    So all good and well, I attempt the solution but get a value of 3.11 MPa, which is incorrect according to the answer. (4.75 MPa)

    I then rechecked my results and did a google search. This lead me to a site which boiled the math down to a similar problem to:

    σyield = sqrt(3)·(P·D/4·t)

    When I use this equation, I get the correct answer.

    I then reattempted my algebra and get to this:

    (P·D/2·t)2 + (P·D/2·t)·(P·D/4·t) + (P·D/4·t)2 = σyield2

    What am I missing here?

    Any help would be appreciated.

    Thank you,

    - MarleyDH
     
  2. jcsd
  3. Feb 14, 2012 #2

    nvn

    User Avatar
    Science Advisor
    Homework Helper

    Wrong. Read more carefully.
     
  4. Feb 14, 2012 #3
    Ah right. Saw my mistake, the cross terms should be a preceded with a minus sign. Thanks for the assistance once again nvn. Now its on to failure criterion!
     
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