buckling of tube - shell thickness vs. momentum of inertia optimum is there any simple formula (perhabs semi emperical, or aproximatively derived model)  for buckling of tube under axial compression load given its crossection and wall thickness? ( and naturraly elastic modulus and length would also affect it ).
I mean - certainly there is a compromise between:


*

*maximizing area moment of inertia in euler formula for long rod.

*keeping walls thick enought to prevent local buckling of wall shell (such as Yoshimura / Donnell's buckling )


In case you want to keep weight (crossectional area) as low as possible ( let's say constant ) and achive maximal buckling-limited-strength of the tube under axial compression - to which extend it would be be better to increase diameter (moment of inertia) and thus decrease wall thickness until the problems with local buckling start to prevail.  
I would expect that in practical structural engeneering this should be very common problem, and there should be some well developed cook-book solution.
I found a lot of deep theoretical papers discussing various forms of local buckling from first principles and emperically, but I did not found simple Ready-to-wear prescription what parameters ideal thin-shell tubular pilar should have. 
 A: The go to formula in pressure vessel design is the semi-empirical NASA SP-8007.  Page 7, & 10 tell you most of the annotation used in the rest of the document, page 14 has the equation for isotropic cylinders.  Personally, I've mostly used the composites formulas in the back.
The long explanation is that due to poor experimental results, a cylinder will buckle at about 30% of the predicted value when using even the most conservative formulas.  The primary cause?  Deviations from a theoretical cylinder to a real cylinder.  These are called "imperfections", from the deviations of the cylinder thickness, thin and thick spots, etc.  The NASA guide takes this into account and delivers for all buckling methods of failure with an empirically determined knock down factor gamma, for each of the buckling methods of failure in the text.  The remainder is the "cookbook".
New research is trying to improve the knock-down factor with all kinds of crazy theories due to the imperfections, but the go to is still SP 8007
