Pipe Bend Analysis
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Offshore Mechanical and Arctic Engineering, July 11-16, 1999
BENDING MOMENT CAPACITY OF PIPES
Søren Hauch and Yong Bai American Bureau of Shipping Offshore Technology Department Houston, Texas USA
ABSTRACT In most modern pipeline design, the required minimum wall thickness is determined based on a maximum allowable hoop stress under design pressure. This is an efficient way to come up with an initial wall thickness design, based on the assumption that pressure will be the governing load. However, a pipeline may be subjected to additional loads due to installation, seabed contours, impacts and high-pressure/high-temperature operating conditions for which the bending moment capacity is often the limiting parameter. If inplace analyses for the optimal route predict that the maximum allowable moment to a pipeline is going to be exceeded, it will be necessary to either increase the wall thickness or, more conventionally, to perform seabed intervention to reduce the bending of the pipe. In this paper the bending moment capacity for metallic pipes has been investigated with the intention of optimising the cost effectiveness in the seabed intervention design without compromising the safety of the pipe. The focus has been on the derivation of an analytical solution for the ultimate load carrying capacity of pipes subjected to combined pressure, longitudinal force and bending. The derived analytical solution has been thoroughly compared against results obtained by the finite element method. The result of the study is a set of equations for calculating the maximum allowable bending moment including proposed safety factors for different target safety levels. The maximum allowable moment is given as a function of initial out-of-roundness, true longitudinal force and internal/external overpressure. The equations can be used for materials with isotropic as well as an-isotropic stress/strain characteristics in the longitudinal and hoop direction. The analytical approach given herein may also be used for risers and piping if safety factors are calibrated in accordance with appropriate target safety levels.
Keywords: Local buckling, Collapse, Capacity, Bending, Pressure, Longitudinal force, Metallic pipelines and risers. NOMENCLATURE A D E F Fl f0 M MC Mp p pc pe pel pi pl pp py r SMTS SMYS t α
y γC ηR κ υ
Hauch & Bai
Area Average diameter Young’s modulus True longitudinal force Ultimate true longitudinal force Initial out-of-roundness Moment Bending moment capacity Ultimate (plastic) moment Pressure Characteristic collapse pressure External pressure Elastic collapse pressure Internal pressure Ultimate pressure Plastic collapse pressure Yield pressure Average pipe radius Specified Minimum Tensile Strength Specified Minimum Yield Strength Nominal wall thickness Strength anisotropy factor Distance to cross sectional mass centre Condition load factor Strength utilisation factor Curvature Poisson’s ratio
Offshore Mechanical and Arctic Engineering, July 11-16, 1999 σh σhl σl σll ψ
Hoop stress Limit hoop stress for pure pressure Longitudinal stress Limit longitudinal stress for pure longitudinal force Angle from bending plane to plastic neutral axis
INTRODUCTION Nowadays design of risers and offshore pipelines is often based on a Limit State design approach. In a Limit State design, all foreseeable failure scenarios are considered and the system is designed against the failure mode that is most critical to structural safety. A pipe must sustain installation loads and operational loads. In addition external loads such as those induced by waves, current, uneven seabed, trawl-board impact, pullover, expansion due to temperature changes etc need to be considered. Experience has shown that the main load effect on offshore pipes is bending combined with longitudinal force while subjected to external hydrostatic pressure during installation and internal pressure while in operation. A pipe subjected to increased bending may fail due to local buckling/collapse or fracture, but it is the local buckling/collapse Limit State that commonly dictates the design. The local buckling and collapse strength of metallic pipes has been the main subject for many studies in offshore and civil engineering and this paper should be seen as a supplement to the ongoing debate. See Murphey & Langner (1985), Winter et al (1985), Ellinas (1986), Mohareb et al (1994), Bai et al (1993, 1997) etc. BENDING MOMENT CAPACITY The pipe cross sectional bending moment is directly proportional to the pipe curvature, see Figure 1. The example illustrates an initial straight pipe with low D/t (