|Feb13-12, 02:33 PM||#1|
[Material Science] Thin Walled Cylinders & Yield Criterion
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 + σ1Ěσ2 + σ22 = σyield2
σhoop = PĚD/2Ět
σaxial = PĚD/4Ět
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)Ě(PĚD/4Ět)
When I use this equation, I get the correct answer.
I then reattempted my algebra and get to this:
(PĚD/2Ět)2 + (PĚD/2Ět)Ě(PĚD/4Ět) + (PĚD/4Ět)2 = σyield2
What am I missing here?
Any help would be appreciated.
|Feb14-12, 12:27 AM||#2|
|Feb14-12, 08:14 AM||#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!
|elasticity, materials, thin cylinders, yield, yield criterion|
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