The Effects of Yielding on Suspended Pipelines Under Tension Using a Trilinear Momentes Curvature Approximation
Authors: Serpas Raymond , Wilhoit J.C. , Merwin J.E. 
Published: October 2008

ABSTRACT
This paper reports the effects of horizontal tension and angle of lift off from a support stinger on a suspended pipeline which is allowed to yield if the curvature becomes large enough. The effect of yielding over a support stinger, which results in a residual moment at the lift-off point, is also investigated. The technique developed for the solution of the suspended pipe problem employs a numerical procedure using Taylor series and a trilinear approximation to the moment vs curvature diagram for the pipe. A 16-in diameter pipe is used in the computations and the results are presented graphically. It is concluded that allowing the pipe to yield either in the suspended portion or over a support stinger does not significantly affect the depth attainable and horizontal tension can be used to control yielding.

INTRODUCTION
The methods used to lay underwater pipelines subject the pipe to large angle deflections, which result in large curvatures in the suspended portion (see Fig. 1). Consequently, the geometry that the pipeline deflects to, due to the forces of its own weight and tension along its axis, has been under study.
The governing equations for this large angle deflection problem are nonlinear and, therefore, there is no simple solution. Many investigators have approached the problem using different methods. Ovune and Mallareddyl used a stiffness matrix method, which was an iterative technique that adjusted the forces on and geometry of the pipeline until equilibrium was attained. Wilkins2 used a finite-element procedure, while Dareing and Neathery3 used Newton's method to linearize the governing equations. Palmer, Hutchinson, and Ells4 used a boundary value-finite difference method.
Garcia, Merwin and Wilhoit5 used a finiteelement initial value approach that employed a Taylor series solution. This is also the proct;ldure used in this report. Powers and Finn6 used a finite-element method too. The convergent method developed by Brando and Sebastiani7 for use with their finite-element approach is also employed here for cases of extreme bending.
LeBlanc8 was the first to include the possibility of yielding in the suspended portion and residual moments at the lift off from the support stinger due to previous yielding.
The main interest in determining the geometry is to prevent buckling of the pipe at the point of maximum curvature or to determine the state of stress throughout the pipe due to a particular set of conditions at the departure point from the stinger. It was found that the application of tension reduces the curvature along the pipeline without increasing the overall stress since the order of magnitude of the bending stresses is usually two or three times that of the axial stresses. It is desirable to minimize the horizontal tension used so as to reduce the strain on the tensioning device and prevent possible slippage. In the effort to minimize tension, the possibility of yielding in the suspended portion arises due to the greater curvatures that result under low or no horizontal tensions.