# Capped pressure vessel - strength and stability

• FEAnalyst
In summary, the conversation revolves around the availability of equations for stress and strain in closed cylindrical pressure vessels, both with capped ends and subjected to axial compression. It is mentioned that most mechanics of materials books only provide formulas for stress and strain in open vessels, but the 5th Edition of Roark's Formulas for Stress and Strain does have a section on this topic. The 9th Edition is recommended as a valuable resource. It is also suggested to look at Den Hartog's Advance Strength of Materials text for further discussion on this topic.

#### FEAnalyst

TL;DR Summary
What are the formulas for calculation of strengtg and stability of capped cylndrical pressure vessel?
Hi,
in mechanics of materials books one may easily find fomulas for stress and strain in thin- and thick-walled cylindrical pressure vessels subjected to internal pressure. However, it is assumed that they are open. So what are the formulas for stress and strain in capped vessels (with flat or hemi-spherical end caps)?

My second question is also related to cylindrical pressure vessels but subjected to axial compression. Again, books provide equations for critical buckling load in such case but can it be calculated for closed-end vessels too (like a soda can)?

My 5th Edition of Roark's Formulas for Stress and Strain has a whole section on exactly that problem. I see that the current 9th Edition has 300 more pages than the 5th Edition, so should be an even better resource. Given the questions you have been asking, I highly recommend that you get a copy of Roark for your library.

I already bought this book (newest version) and will get it soon. But, from what I’ve seen in older releases, there are only tables with formulas for open pressure vessels. Maybe capped ends are mentioned in the text before the tables. What about the buckling of closed cylindrical shell subjected to axial compression ? I’m almost sure that books provide equations only for open vessels. Especially that they are based on Timoshenko’s Theory of Elastic Stability where closed ends are not included, if I remember correctly.

I suggest the OP also look at Den Hartog's Advance Strength of Materials text. I seem to recall considerable discussion of this problem there.

FEAnalyst

## What is a capped pressure vessel and what is its purpose?

A capped pressure vessel is a container or vessel that is designed to hold pressurized fluids or gases. The cap, or end closure, is an important component that helps to maintain the pressure inside the vessel. These vessels are commonly used in various industries, such as chemical, pharmaceutical, and oil and gas, for processes such as storage, transportation, and reaction.

## How is the strength of a capped pressure vessel determined?

The strength of a capped pressure vessel is determined by the materials used in its construction, the design of the vessel, and the pressure and temperature conditions it is expected to withstand. The vessel must be able to withstand both internal and external pressure without deforming or rupturing. This is typically evaluated using calculations and simulations, and verified through testing and inspection.

## What factors affect the stability of a capped pressure vessel?

The stability of a capped pressure vessel can be affected by several factors, including the shape and size of the vessel, the pressure and temperature conditions, and the materials used. The design of the end closures, such as the shape and type of the cap, can also play a role in the vessel's stability. Additionally, the environment in which the vessel is used, such as corrosive or high-vibration environments, can also impact its stability.

## How can the safety of a capped pressure vessel be ensured?

The safety of a capped pressure vessel can be ensured through proper design, construction, and maintenance. The vessel should be designed and built according to industry standards and regulations, and undergo regular inspections and maintenance to ensure its integrity. It is also important to follow proper operating procedures and to have emergency plans in place in case of any issues or accidents.

## What are the potential risks associated with a capped pressure vessel?

The potential risks associated with a capped pressure vessel include rupture or explosion, which can result in injury or damage to property. Other risks include leaks, corrosion, and fatigue failure. It is important to properly design, operate, and maintain the vessel to minimize these risks and ensure the safety of those working with or around the vessel.