# Help with assumption (thick walled theory)

In summary, the thick walled theory is a mathematical model used to analyze the stress and strain distribution in thick-walled structures. It is important in scientific research as it allows scientists to understand and predict the behavior of these structures under different conditions, aiding in the design of safe and efficient engineering systems. The theory assumes homogeneous, isotropic, and elastic materials, and is applied in real-world scenarios through mathematical equations and numerical methods. Limitations of the theory include its assumptions and its applicability to only certain types of structures. However, current developments aim to improve its accuracy, such as incorporating advanced materials and considering complex factors.
Hello!

I have a solid cylindrical shaft with a mounted ring on it.
My ring is subjected to a point load, I have with this load and the geometry of the ring used a special beam theory called Winkler Bedding. By using that theory I get the deflection of my "beam". This deflection is the deflection of the ring.

Now for my question:
Can I use this deflection as a radial mismatch between the shaft and the ring so that I can derive the hoop stress ?
this gives me pretty good results, with a applied force of 200 kN for a certain geometry I should get around 100 MPa in hoop stress. This I know from testing and experience.
Now with my assumption that the deflection as a radial mismatch I get 100 MPa from my derived equations

Does anybody know if my assumption is correct or is it completely wrong?

Hello there!

Your assumption may be partially correct, but there are a few factors that need to be considered before using the deflection as a radial mismatch to derive the hoop stress. First, the Winkler Bedding theory assumes that the load is evenly distributed along the length of the beam, which may not be the case for your mounted ring. Additionally, the Winkler Bedding theory does not take into account the effects of shear stress, which can significantly affect the hoop stress in your ring.

Furthermore, the geometry and material properties of your shaft and ring also play a significant role in determining the hoop stress. It is important to consider these factors and possibly conduct further testing or analysis to accurately determine the hoop stress in your system.

In summary, while your assumption may provide a rough estimate of the hoop stress, it is not a reliable method for accurate calculations. It is always best to consider all factors and conduct thorough analysis to ensure the accuracy of your results.

## What is the "thick walled theory" and why is it important in scientific research?

The thick walled theory is a mathematical model used to analyze the stress and strain distribution in thick-walled structures, such as pipes or cylinders. It is important in scientific research because it allows scientists to understand and predict the behavior of these structures under different conditions, which is essential for designing safe and efficient engineering systems.

## What are the assumptions made in the thick walled theory?

The thick walled theory assumes that the material used in the structure is homogeneous, isotropic, and elastic, meaning that it has the same properties in all directions and can return to its original shape after deformation. It also assumes that the structure is subjected to internal or external pressure, and that the thickness of the wall is relatively small compared to the overall dimensions of the structure.

## How is the thick walled theory applied in real-world scenarios?

The thick walled theory is applied in real-world scenarios through the use of mathematical equations and numerical methods to calculate the stress and strain distribution in thick-walled structures. This information is then used to design and optimize structures for different applications, such as pipelines, pressure vessels, and hydraulic systems.

## What are the limitations of the thick walled theory?

Some limitations of the thick walled theory include the assumption of homogeneous and isotropic materials, which may not accurately represent the actual properties of the structure. It also does not take into account the effects of temperature, fatigue, and other external factors that may affect the behavior of the structure. In addition, it is only applicable to structures with relatively small wall thicknesses, and may not accurately predict the behavior of very thick-walled structures.

## What are some current developments in the thick walled theory?

Some current developments in the thick walled theory include the incorporation of advanced materials, such as composites, which may have anisotropic properties. There is also ongoing research to improve the accuracy of the theory by considering more complex factors, such as non-linear material behavior and the effects of temperature and fatigue. Additionally, advancements in computer technology have enabled more sophisticated numerical methods for analyzing thick-walled structures, allowing for more accurate and efficient predictions.

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