How much thickness for sphere to withstand atmospheric pressure?

In summary, the thickness required for a sphere to withstand atmospheric pressure depends on the material's strength and the sphere's diameter. Generally, thicker walls are necessary for larger diameters to maintain structural integrity. Engineering calculations, including factors like material yield strength and safety margins, are essential to determine the specific thickness needed for various applications, such as underwater or high-altitude environments.
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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.
 
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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:
 

FAQ: How much thickness for sphere to withstand atmospheric pressure?

How do you calculate the thickness required for a sphere to withstand atmospheric pressure?

The thickness required for a sphere to withstand atmospheric pressure can be calculated using the formula derived from the thin-walled pressure vessel theory: \( t = \frac{p \cdot r}{2 \cdot \sigma_{allow}} \), where \( t \) is the thickness, \( p \) is the external pressure (atmospheric pressure), \( r \) is the radius of the sphere, and \( \sigma_{allow} \) is the allowable stress of the material.

What factors influence the thickness needed for a sphere to withstand atmospheric pressure?

The factors that influence the thickness include the radius of the sphere, the material properties (specifically the allowable stress of the material), and the external pressure the sphere needs to withstand. Material properties such as yield strength, tensile strength, and safety factors are crucial in determining the thickness.

How does the radius of the sphere affect the required thickness?

The radius of the sphere is directly proportional to the required thickness. As the radius increases, the thickness needed to withstand the same external pressure also increases. This is because a larger radius results in a greater surface area that the pressure acts upon, requiring more material to resist deformation.

Why is it important to consider material properties when determining the thickness?

Material properties such as yield strength, tensile strength, and allowable stress are critical because they determine how much stress the material can handle before failing. Using materials with higher allowable stress can reduce the required thickness, whereas materials with lower allowable stress will require a thicker wall to withstand the same pressure.

Can the thickness requirement be reduced by using composite materials?

Yes, using composite materials can reduce the thickness requirement because composites often have higher strength-to-weight ratios compared to traditional materials like steel or aluminum. By using materials that have higher allowable stress, the required thickness to withstand atmospheric pressure can be decreased, leading to lighter and potentially more cost-effective designs.

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