Page 217 - Pipelines and Risers

190 Chapter I2

(12.4)

The relationship between curvature and strain for the pipe is:
& =' (12.5)
R

The vertical component Tv is equal to the weight of the suspended part of the pipeline:
Tv = ws s (12.6)

Where s is the length of the suspended part of the pipeline and can be expressed as:

(12.7)

The angle between the pipeline and the x-y plane is:

tan0 =- TV (12.8)
Th

Th can be expressed through 6, w,, and z by setting T, into the expression for tane.

(12.9)

The departure angle and the height above seabed at stingertip are known for a specific lay-
vessel and stinger radius, while the location of the inflection point is unknown. At deep water
is it reasonable to say that the departure angle from stinger tip and the angle in the inflection
point are approximately the same. The inflection point in Figure 12.1 is the same as point a in
Figure 12.8. The horizontal tension can therefore be estimated using Eq. (12.9). Since the
inflection point and its location are unknown the tension can be estimated through using the
departure angle and height above seabed at the stinger tip. The predicated tension is
overestimated because 6 is smaller and z is greater at the stinger tip than in the inflection
point. The tension is also overestimated because the flexural rigidity of the pipeline are
neglected. The calculated curvature and strain in the sagbend will be conservative because the
flexural rigidity of the pipeline are neglected.

To get an accurate model the flexural rigidity of the pipeline has to be included in the
analyses. This is done in the finite element model. The finite element method deals with the
large deflection effects at a global level by stiffness and load updates, i.e. re-calculating
stiffness and loads at the deflected shape and iterate until convergence.