Page 225 - Pipelines and Risers

198 Chapter 12

There is an interesting difference between the contribution of the two moment terms along the
centerline. From the solution of the elementary problem of a horizontal long beam tensioned
axially in the gravitational field, it follows that only at distances less than:

(12.24)

from the ends does the bending moment differ from a constant term. The rest behaves as a
catenary. For pipelay, this distance is normally small compared to the length of the free span.
Therefore, we can say that the boundary conditions only have a local influence in bending.
The twist is entirely different: A rotation of the pipe at the tensioner is immediately felt at the
touch-down point. Twist acts over long distances, as does the gravity force.

How does the residual strain in the overbend change the value of the potential energy? An
example will illustrate the point: Consider first that the suspended pipe is entirely in the
vertical plane. Assume two pipelay scenarios that only differ because one material remains
completely elastic, whereas the other experiences plastic strains in the overbend section on the
stinger. In the underbend section, the pipe with plastic strain hangs higher than the elastic one
because its natural (unloaded) shape has become convex. This means that the potential energy
is higher for the plastically deformed pipe than for the elastic one. Allowing for a 3D
deformation, the bent pipe can reduce its potential energy through twist. The elastic pipe is
already at its lowest potential energy and so it is stable.

It is reasonable to conclude from this argumentation that the reduction of potential energy is
the mechanism that underlies pipeline rotation during pipelaying. The theory of large
deflection of beams is found in classic texts, e.g. Landau or Love.

A non-linear 3D finite element program can solve the virtual work equation with very few
approximations. Three simple models will illustrate the main point of interest. All represent a
pipe of length 1218 m and with D/t=36. They are all fixed in one end and pinned in the other
where a sliding condition is specified. Both ends are at the same elevation and the body force
is equal to the submerged weight. In order to produce elastic strains below 0.035% an
appropriate horizontal force is applied in the pinned end to represent the lay tension.

A 3D load-case is created by means of a horizontal force corresponding to a sea current of 0.5
m/s that is applied normal to the plane of the equilibrium configuration. First the horizontal
force is applied, and then the submerged weight. Before the application of the horizontal
force, the pinned end is locked in all translational degrees of freedom at their current values.
The models are:

1. Straight pipe
2. Pre-curved "overbend" pipe, R=571 m,
3. Pre-curved "underbend pipe, R=571 m,

The displacement and rotation of a point in the middle of the span will be studied for each of
the models. The equilibrium configurations shown are similar to that of the underbend during