A How much thickness for sphere to withstand atmospheric pressure?

AI Thread Summary
To prevent a hollow sphere from crushing under atmospheric pressure when the air inside is evacuated, the thickness must be carefully calculated, considering the material's properties, such as elasticity. The Lame solution may be applicable for initial estimates, but Finite Element Analysis (FEA) is recommended for more accurate results due to the complexity of the stresses involved. Buckling presents a significant stability challenge, and manufacturing a perfectly shaped sphere with even thickness and welds is difficult. Internal stresses and uneven deformation are likely to occur during production. Therefore, it is crucial to incorporate a generous safety margin in the design calculations.
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TL;DR Summary
Hollow sphere withstanding the atmospheric pressure
Imagine a hollow sphere made of a material with high elasticity constant(e.g. steel). How much thickness should it have to prevent it from crushing when the air inside is pumped out?
Is it valid to use Lame solution to quantify the answer? What about Finite Element Analysis?
 
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This would be a stability problem involving buckling.
 
Manufacturing such sphere would be a difficult task.
The material would have internal stresses and would be unevenly deformed; therefore, even shell thickness and welds and perfect sphere shape would be difficult to achieve.
If built, the calculations should allow a generous safety margin.

Please, see:
https://www.sciencedirect.com/science/article/pii/S0020768318302592#:~:text=The classical buckling pressure of,shell thickness and its radius.

:cool:
 
This has been discussed many times on PF, and will likely come up again, so the video might come handy. Previous threads: https://www.physicsforums.com/threads/is-a-treadmill-incline-just-a-marketing-gimmick.937725/ https://www.physicsforums.com/threads/work-done-running-on-an-inclined-treadmill.927825/ https://www.physicsforums.com/threads/how-do-we-calculate-the-energy-we-used-to-do-something.1052162/
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