A closed-form solution for elastic buckling of thin-walled unstiffened circular cylinders in pure flexure

• The difference in strength between a cylindrical shell under uniform axial compression and that under pure bending is not well understood.
• A closed-form solution for the elastic buckling strength of unstiffened circular cylinders under pure bending is presented.
• Two types of analyses are presented for cylinders with large and medium diameter-to-thickness ratios.
• A unique testing rig was used to experimentally verify the new theory using a Moiré fringe film.
• The current design rules for CHS are compared, and the newly derived design curve was found in a good agreement with the test results.

To date, despite the significant development in the field of structural mechanics, there still remains a paradox in the solutions available for a classical shell buckling problem. The difference in strength between a cylindrical shell under uniform axial compression and that under pure bending is not quite well investigated. This lack of research is reflected in the wide variations in the elastic bending strength and the slenderness limits given in current international design standards. The discrepancies in the available classical solutions and hence the design rules have initiated the current research. The main aim of this paper is to present a closed-form solution for the elastic buckling strength of unstiffened circular cylinders under pure bending using a new simplified energy approach employing the well-known Ritz method. Two types of analyses are presented for cylinders with large (D/t>200) and medium (100