1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: [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


    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!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook