Radial stress in pressure vessels

In summary, the conversation discusses the concept of stress in pressure vessels, specifically axial, hoop, and radial stress. Hoop stress is the stress in the direction along the circumference, while radial stress is a stress in the radial direction. In thick-walled vessels, the tangential and radial stress are highest at the inner surface, but for thin-walled vessels, the hoop stress is the driving design factor. The radial stress is negligible for thin-walled vessels, and when there is no external pressure, it is equal to the internal pressure on the inside surface and zero on the outside surface.
  • #1
jayanth nivas
15
0
Hi all,
I have started with my understanding of pressure vessels and i have some queries on the topic.

1) I understand the part of axial stresses.When a cylinder capped at both ends is subjected to internal pressure,it tends to increase the length of the shell,and therefore a resistance is offered by pressure vessel,which is measured by load (Internal pressure X circular area )/ the cross sectional area of Pressure vessel (One between I.D & O.D of the vessel)

2) To some extent,I understand the concept of hoop stress.The internal pressure inside the cylinder tries to displace the circumferential elements farther (Increasing the diameter of the cylinder).Therefore the hoop stress is measured by load (internal pressure X projected area )/ cross sectional area of pressure vessel (one which is the product of thickness and length considered)

3) My query now is,what is radial stress?.And what is the load for it and what is the area resisting it?.In what way it tries to deform the pressure vessel ?.And why do we
neglect it for thin walled pressure vessels and consider it for thick walled pressure vessels ?

4) Also are both hoop and radial stress a response to diametrical deformation ?

My understanding on this topic is elementary and I apologize if I have misstated something.

Thanks for going through the post.
 
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  • #2
Circumferential (hoop) and radial stresses are responses to diametrical deformation. To state just for completeness, the hoop stress is stress in the direction along the circumference, and radial stress is a stress in the radial direction. For a internally pressurized cylinder, the hoop stress is generally a tensile stress along the circumference of the cylinder, while a radial stress is usually a compressive stress between the outer and inner surfaces of the cylinder. These radial and hoop stresses can be formulated as a function of internal and external pressure and the inner and outer radii, so no "area" calculations are necessary.

In thick-walled vessels, there is a distribution of tangential and radial stress across the thickness of the cylinder. Generally, the stresses are highest for both radial and tangential (hoop) stress at the inner surface of the cylinder. However, when the wall thickness of the cylinder is less than 1/20th the radius (according to Shigley), the distribution has a valid approximation of an average tangential stress. As well, the radial stress tends not to matter much because it's so small when compared to the hoop stress. That's also why we can use plane stresses when talking about thin-walled cylinders. The tangential stress then becomes your driving design factor for thin-walled vessels.
 
  • #3
Have you noticed that for a uniform cylinder under pressure, the hoop stress is twice the axial stress. That explains why pipes split along their length when they burst.
 
  • #4
On the inside surface of the cylinder, the radial stress is the same as the internal pressure. On the outside, it is the same as the external pressure (often atmospheric pressure, 14 psi or 0.1 MPa). Through the thickness of the cylinder, it varies almost linearly between those values.

For a thin cylinder the radial stress of the order of P is negligible compared with the other stress components with are of the order of Pr/t or Pl/t, and for a thin cylinder r/t and l/t are big numbers.
 
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  • #5
If there is no external pressure and all pressure is applied internally would that mean that the radial stress is 0?
 
  • #6
OKaraali said:
If there is no external pressure and all pressure is applied internally would that mean that the radial stress is 0?
In this case, the radial stress is zero on the outside surface. It is still equal to the pressure on the inside surface.
 

1. What is radial stress in pressure vessels?

Radial stress in pressure vessels is the stress that is exerted on the walls of the vessel due to the internal pressure. It is perpendicular to the surface of the vessel and is responsible for the expansion or contraction of the material.

2. How is radial stress calculated in pressure vessels?

The radial stress in pressure vessels can be calculated using the formula σr = pr/t, where σr is the radial stress, p is the internal pressure, and t is the thickness of the vessel's walls. This formula is derived from the principles of mechanics and is widely used in engineering calculations.

3. What factors affect the magnitude of radial stress in pressure vessels?

The magnitude of radial stress in pressure vessels is affected by several factors, including the internal pressure, vessel geometry, material properties, and operating conditions. Higher internal pressures, thinner walls, and weaker materials can result in higher radial stress levels.

4. How does radial stress impact the design and safety of pressure vessels?

Radial stress is a critical factor in the design and safety of pressure vessels. If the stress exceeds the yield strength of the material, it can lead to deformation or failure of the vessel. Therefore, engineers must carefully consider the radial stress in their designs and ensure that it is within safe limits.

5. Can radial stress be reduced in pressure vessels?

Yes, radial stress can be reduced in pressure vessels by increasing the thickness of the walls, using stronger materials, or reducing the internal pressure. However, these solutions may have drawbacks, such as increased weight and cost. Alternatively, designers can use stress-relieving techniques, such as adding reinforcement or changing the vessel's shape, to reduce radial stress levels.

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