# Shell thickness of a pressure vessel required subjected to a cyclic pressure

In summary, the conversation discusses the use of a thin-walled pressure vessel as a pressure accumulator in various situations. The vessel is made of pressure vessel steel with specific yield, failure, and endurance stresses. It has been determined to be safe for all proposed stress situations, but further analysis is needed to determine its safety from fatigue failure under specific cyclic pressure conditions. Two specific scenarios are mentioned, with the minimum required shell thickness being calculated using the Hopp stress equation. Assistance is requested for further guidance.

I was wondering if anyone could help me with the following question, please:

A thin walled pressure vessel is to be used as a pressure accumulator in a number of situations all involving a number of different operation conditions some of which create cyclic stresses. The dimentions of the vessel are 600mm long (not including end caps) and a shell outside diameter of 60mm. The material which the vessel is made from is pressure vessel steel, with a yield of 510 MPa. A failure stress of 630 MPa and an Endurance stress of 400 MPa. Static stressing has shown that the vessel is safe for all the stress situations proposed and it must now be determined if the vessel is safe from fatigue failure for the following situations:

1. If the vessel is subjected to cyclic pressure of 0 and 400 bar, determine the minimum shell thickness of the vessel to give infinit life.

2. If the vessel is subjected to cyclic pressure of 50 to 600 bar, determine the minimum shell thickness of the vessel to give infinit life.

Show us an attempt and we can steer you in the right direction.

For the first part, I thought of using Hopp stress equestion σ = p d / 2 t and taking Endurance stress (400 MPa) as the value for σ since in the cyclic pressure is 400 bar which less that Endurance stress, thus:

4 x 10^8 = [(4 x 10^7)(60x10^-3 - t)] / 2t

t = 0.003 m

Anybody goin to "steer me in the right direction" now ?

I would approach this question by first considering the factors that contribute to fatigue failure in a pressure vessel. These include the material properties, the applied cyclic pressure, and the geometry of the vessel.

Based on the given information, the material used for the vessel is pressure vessel steel with a yield strength of 510 MPa, a failure stress of 630 MPa, and an endurance stress of 400 MPa. This means that the vessel can withstand a maximum stress of 630 MPa before failure, but it is recommended to keep the stress below 400 MPa for extended periods to avoid fatigue failure.

Next, I would analyze the applied cyclic pressure in each situation. In the first situation, the vessel is subjected to a cyclic pressure of 0 and 400 bar. This means that the pressure alternates between 0 bar (no pressure) and 400 bar (maximum pressure). In the second situation, the pressure ranges from 50 to 600 bar. This is a wider range of pressure and may cause more stress on the vessel.

To determine the minimum shell thickness of the vessel for infinite life, I would use the ASME Boiler and Pressure Vessel Code, specifically Section VIII Division 2 for pressure vessels subjected to cyclic loading. This code provides equations for calculating the required shell thickness based on the material properties, applied pressure, and geometry of the vessel.

Using these equations, I would calculate the minimum shell thickness for each situation and compare it to the current thickness of the vessel. If the calculated thickness is greater than the current thickness, then the vessel is safe for infinite life. If not, modifications may need to be made to the vessel to ensure its safety.

In addition, I would also consider other factors such as weld quality, surface finish, and any potential stress concentrations in the vessel design. These can also affect the fatigue life of the vessel and should be taken into account in the analysis.

Overall, with proper analysis and consideration of all factors, it is possible to determine the minimum shell thickness required for a pressure vessel to withstand cyclic pressure without fatigue failure.

## 1. What factors affect the required shell thickness of a pressure vessel subjected to cyclic pressure?

The required shell thickness of a pressure vessel subjected to cyclic pressure is affected by several factors, including the material properties of the vessel, the design pressure and temperature, the type of cyclic loading, and the expected life of the vessel.

## 2. How is the design pressure and temperature determined for a pressure vessel?

The design pressure and temperature for a pressure vessel are typically determined by considering the intended purpose of the vessel and the materials it will be containing. This information is then used to calculate the maximum operating pressure and temperature that the vessel will experience.

## 3. What is considered a cyclic pressure in relation to pressure vessels?

Cyclic pressure refers to a fluctuating or repeating pressure that a pressure vessel is subjected to during its operation. This can be caused by various factors such as changes in temperature, changes in the volume of the contained material, or external forces acting on the vessel.

## 4. How does the type of cyclic loading affect the required shell thickness of a pressure vessel?

The type of cyclic loading can greatly impact the required shell thickness of a pressure vessel. For example, a pressure vessel subjected to high-frequency cyclic loading will typically require a thicker shell compared to one subjected to low-frequency loading, as the higher number of cycles can lead to fatigue failure.

## 5. How does the expected life of a pressure vessel impact the required shell thickness?

The expected life of a pressure vessel is an important consideration in determining the required shell thickness. A vessel with a longer expected life will require a thicker shell to withstand the higher number of cycles it will experience over its lifetime. On the other hand, a vessel with a shorter expected life may be able to tolerate a thinner shell.