Nonlinear stability of thin elastic cylinders of different length under global bending

Many thin-walled cylindrical shells are used in structural applications in which the dominant loading condition is global bending. Key examples include chimneys, wind turbine support towers, pipelines, horizontal tanks, tubular piles and silos. The buckling behaviour of these structures in bending is complex due to the coupling between cross-section ovalisation and local bifurcation buckling. Analytical treatments of this problem have a history going back almost a century and still constitute an active and challenging research area. This paper investigates in detail the effect of cylinder length on the nonlinear elastic buckling behaviour of clamped cylindrical tubes under global bending, covering a very wide range of lengths. It is found that the behaviour may be classified into four distinct length-dependent domains with clearly-defined boundaries which have here been assigned the names ‘short’, ‘medium’, ‘transitional’ and ‘long’. Algebraic characterisations of the computed nonlinear moment–length relationships are proposed for design purposes.