In this paper the problem of buckling of vertical risers due to an applied torque is solved. The vertical riser is modelled as a column, having axial, flexural and torsional stiffness. The column is subjected to gravity, hydrostatic loading, tension and a torsional moment. The general non-linear equilibrium equations are linearized around the vertical configuration and a system of coupled differential equations having variable coefficients is derived. A solution, expressed in terms of Airy functions, is found. Graphs of the critical torque, plotted against the length of the riser and the effective tension at the bottom, are presented. Several boundary conditions at the end of the riser are examined. The influence of the low bending stiffness of the structure is discussed and closed form asymptotic formulae are derived for this case. These results are compared against numerically obtained data using the Finite Element method.
The investigation of the behaviour of risers subjected to torsional loading has recently focused the attention of many researchers. During the operation of the riser many situations can occur, in which the torsional loading is significant and cannot be neglected, since it strongly influences the geometry of flexible pipes deployed in a lazy S configuration (O'Brien et al, 1992), or may result in global buckling of the structure, when "taut" configurations are considered. The torsional loading may occur at the top end, due to the rigid connection of the flexible riser to the vessel, or due to a distributed hydrodynamic loading along the length, as discussed by Chung et al (1994). Kodaissi et al (1992) presented the results of an experimental study performed on an elastic cable and an actual flexible pipe subjected to end torsion. The validation of computer codes based on this study was presented by ISSC (1994).