# Homework Help: [Material Science] Thin Walled Cylinders & Yield Criterion

1. Feb 13, 2012

### MarleyDH

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. Feb 14, 2012