Hypothetical Hollow Steel Sphere: collapse from outside pressure

In summary, the conversation discusses the collapse of a hollow steel sphere due to outside atmospheric pressure. The formula for buckling of spherical shells is mentioned, but its accuracy is questioned due to a lack of information on its derivation and assumptions. It is noted that the formula is a theoretical limit, and most actual spheres will fail at lower loads. Some resources for further research on the topic are provided.
  • #1
thedan16
4
0
Hello physics forums,

Say you had a hollow steel sphere of thickness 1 mm and diameter of 1 meter (from outside to outside)?

Inside the sphere is gas at 1 atm pressure. Outside is 1 atm of pressure. How much gas would I have to remove from the inside until the sphere collapsed from outside atmospheric pressure?

I'd have to use bulk modulus correct?
 
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  • #2
This http://www.engr.uconn.edu/~cassenti/AnsysTutorial/Modules_APDL/Module%205%20Buckling%20Sphere.pdf

gives a formula $$P = \frac{2Et^2}{r^2\sqrt{3(1-\mu^2)}}$$

But since it doesn't give any information about to how it was derived and what assumptions were made, I have no reason to believe it's correct. This is one of those problems which is very easy to describe, but very hard to solve.

The only thing one can say confidently is that it will collapse by buckling, not by compressive failure of the material.
 
  • #3
Yes, I'm curious to how this formula was derived! What about a cylinder or a cube?
 
  • #4
That is the the Zoelly-Van Der Neut formula for buckling of spherical shells and goes as far back as 1915. It is the theoretical limit to the buckling failure of a sphere, whereas from experimental data most actual spheres will fail with loads 1/3 to 1/4 of that value, due to say manufacturing and assembly defects giving a sphere different from that of a perfectly smooth one.

If your library has the book by Timoshenko, Theory of Elastic Stability, you will find a derivation using linear methods.
Nonlinear methods of solution for this problem are difficult to solve.

Research pays off and here are some pdf's of interest:
http://traktoria.org/files/pressure_hull/spherical/buckling_of_spherical_shells.pdf [Broken]
http://www.dtic.mil/dtic/tr/fulltext/u2/610809.pdf

The first link gives a different formula that is said to agree more with experimental results,
Pcr = 0.37E/ m^2

where m is the radius/thickness ratio.

The first formula in the same format becomes Pcr = 1.21 E / m^2, using a Poission ration of 0.3.

I suppose for your sphere, you will have to make some design choices on the differences fom an ideal shere
 
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  • #5


Hello,

Yes, to determine the amount of gas that needs to be removed for the hollow steel sphere to collapse from outside atmospheric pressure, you would need to use the bulk modulus. The bulk modulus is a measure of a material's resistance to deformation under pressure, and it is often used to calculate the collapse pressure of hollow structures such as pipes and spheres.

To determine the collapse pressure of the sphere, you would need to know the bulk modulus of steel and the dimensions of the sphere. Using the formula P = (4/3)E(t/R), where P is the collapse pressure, E is the bulk modulus, t is the thickness of the sphere, and R is the radius, you can calculate the collapse pressure for this specific scenario.

Once you have the collapse pressure, you can then compare it to the outside atmospheric pressure of 1 atm to determine how much gas needs to be removed from the inside of the sphere. Keep in mind that this calculation assumes ideal conditions and does not take into account any potential imperfections or weaknesses in the steel sphere.

I hope this helps answer your question. Let me know if you have any further inquiries.
 

1. What is a Hypothetical Hollow Steel Sphere?

A Hypothetical Hollow Steel Sphere is a theoretical object used in scientific experiments and calculations to represent the properties and behavior of a hollow steel sphere under specific conditions.

2. How does a Hypothetical Hollow Steel Sphere collapse from outside pressure?

The collapse of a Hypothetical Hollow Steel Sphere from outside pressure is a theoretical concept that depends on several factors such as the thickness and composition of the steel, the magnitude and direction of the pressure, and the structural integrity of the sphere. It is typically studied using mathematical models and simulations.

3. Why is the collapse of a Hypothetical Hollow Steel Sphere important to study?

Understanding the collapse of a Hypothetical Hollow Steel Sphere can provide valuable insights into the behavior of real-world objects, such as pressure vessels and storage tanks, made of similar materials. It can also help engineers and scientists design more resilient structures and predict their failure points.

4. Can a Hypothetical Hollow Steel Sphere collapse from internal pressure as well?

Yes, a Hypothetical Hollow Steel Sphere can collapse from both internal and external pressure. However, the mechanism and factors affecting the collapse may differ depending on the source of the pressure. For example, internal pressure may cause the sphere to expand and eventually rupture, while external pressure may cause it to buckle or collapse inward.

5. How can the collapse of a Hypothetical Hollow Steel Sphere be prevented?

To prevent the collapse of a Hypothetical Hollow Steel Sphere, engineers may use various techniques such as increasing the thickness or strength of the steel, reinforcing the structure with internal supports, or designing a more aerodynamic shape that can better withstand external pressure. The exact method used will depend on the specific scenario and desired outcome.

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