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.