Page 83 - Pipelines and Risers

56 Chapter 3

phase, strain levels between 10% and 20% is usual and the material definition should
therefore at least be governing up to this level. In the present analyses, a Ramberg-Osgood
stress-strain relationship has been used. For this, two points on the stress-strain curve are
required along with the material Young’s modules. The two points can be anywhere along the
curve, and for the present model, specified minimum yield strength (SMYS) associated with a
strain of 0.5% and the specified minimum tensile strength (SMTS) corresponding to
approximately 20% strain has been used. The material yield limit has been defined as
approximately 80% of SMYS.

The advantage in using SMYS and SMTS instead of a stress-strain curve obtained from a
specific test is that the statistical uncertainty in the material stress-strain relation is accounted
for. It is thereby ensured that the stress-strain curve used in a finite element analysis in general
will be more conservative than that from a specific laboratory test.

To reduce computing time, symmetry of the problem has been used to reduce the finite
element model to one-quarter of a pipe section. The length of the model is two times the pipe
diameter, which in general will be sufficient to catch all bucklinglcollapse failure modes.

The general-purpose shell element used in the present model, account for finite membrane
strains and allows for changes in thickness, which makes it suitable for large-strain analysis.
The element definition allows for transverse shear deformation and uses thick shell theory
when the shell thickness increases and discrete Kirchoff thin shell theory as the thickness
decreases.

For a further discussion and verification of the used finite element model, see Bai et a1 (1993),
Mohareb et a1 (1994), Bruschi et a1 (1995) and Hauch & Bai (1998).
3.5.2 Analytical Solution Versus Finite Element Results

In the following, the above-presented equations are compared with results obtained from
finite element analyses. First are the capacity equations for pipes subjected to single loads
compared with finite element results for a D/t ratio from 10 to 60. Secondly the moment
capacity equation for combined longitudinal force, pressure and bending are compared against
finite element results.

3.5.3 Capacity of Pipes Subjected to Single Loads
As a verification of the finite element model, the strength capacities for single loads obtained
from finite element analyses are compared against the verified analytical expressions
described in the previous sections of this chapter. The strength capacity has been compared
for a large range of diameter over wall thickness to demonstrate the finite element model’s
capability to catch the right failure mode independently of the D/t ratio. For all the analyses,
the average diameter is 0.5088m, SMYS = 450 MPa and SMTS = 530 MPa. In Figure 3.7 the
bending moment capacity found from finite element analysis has been compared against the
bending moment capacity equation, Eq. (3.17). In Figure 3.8 the limit longitudinal force Eq.
(3.19), in Figure 3.9 the collapse pressure Eq. (3.15) and in Figure 3.10 the bursting pressure
Q. (3.18) are compared against finite element results. The good agreement between the finite