# Capped pressure vessel - strength and stability

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)?

Mentor
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.

FEAnalyst
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.

Dr.D
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