Proposal to modify a subsea pipeline standard
The pipe cross section plastic hinge, created by the bending moment and axial force, consists of the tensile and compressive zones of stress. These zones are separated by the neutral axis. The angle (β) defines the neutral axis location. This angle is measured from the extreme fiber of the tensile zone. Based on the above assumption, the axial force and the bending moment in the pipe ring cross section (medium radius of r and thickness of t) will be calculated from the static condition of equilibrium using equations 3 or 4, accordingly.
The size of the angle, that describes the location of the border between tensile and compressive areas, and the value of the plastic moment were found by integration as shown in 3 and 4. The results are presented in equation 5. In these equations, N and M are relative values (dimensionless parameters), the ratio of the axial force and the moment to the plastic axial force and to the plastic moment resistances, accordingly to equation 6. Note that the plastic resistances (Sp and Mp values) in equation 6 match those in DNV.
Equation 5, which describes the relationship between the bending moment, the axial force in pipe wall, and the overpressure at limit state of pipe section, represents the combined load criteria. The accompanying graph illustrates the relationships described by equation 5. This graph plots the maximum relative bending moment (M ) versus the relative axial force in pipe wall (N) for different values of the relative hoop stress (σh), denoted in the graph as S_h.
As this graphs shows, the allowable bending moment is dependent on the value of the axial force as well as on the sign of the force. The internal pressure increasing also reduces the allowable moment. Dotted lines represent the DNV combined criteria per 5.23. The solution agrees with the DNV solution only when the pressure equals zero. In all other cases, the result is very different, especially when the axial force is compressive.
Application to design
Equation 5 encompasses the theoretical solution of the combined loading criteria for pipe members subjected to bending moment, axial force, and internal overpressure. For application in design, the equations were rewritten in the form of equation 7 to consider the design factors. Since DNV is based on LRFD consideration, relative parameters of loads and resistances used in equation 7 should be calculated in accordance with equations 8 - 10. The symbols and their definitions in these equations are identical to those in DNV.
Thus, the proposed methodology is based on classical theory of Von Mises and Tresca on combined stresses as well as the DNV philosophy of design loads factors, design resistances, and criteria of limit state design to allow for the safely design of offshore pipelines, especially HP/HT pipelines.
Alexander Aynbinder
WorleyParsons, Houston
References:
1. Offshore Standard DNV-OS-F101 “Submarine Pipeline System”, p.166, 2003
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Volume 68 Issue 9
September 2008
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