(adsbygoogle = window.adsbygoogle || []).push({}); 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.

σ_{yield}= 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:

σ_{1}^{2}+ σ_{1}·σ_{2}+ σ_{2}^{2}= σ_{yield}^{2}

σ_{hoop}= P·D/2·t

σ_{axial}= 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:

σ_{yield}= 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}= σ_{yield}^{2}

What am I missing here?

Any help would be appreciated.

Thank you,

- MarleyDH

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

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