The structural behaviour of bends loaded by combinations of bending moment and internal or external pressure is determined using the principle of virtual work. A new analytical model to describe the strains, stresses and deformations in both the elastic and elastoplastic region has been developed. The new model will enable further research on the analysis of the stressstrain variations that occur in the low cycle fatigue range of bends loaded by combinations of bending moment and internal or external pressure. Both elastic and elastoplastic geometrical non-linear results are presented.
Bending moments on bends in pipelines, may cause severe ovalization, strains and stresses. Compared with straight pipelines, bends show a reduced bending stiffness, much greater ovalization and a complex pattern of strains and stresses in both longitudinal and in circumferential direction. The operational fluctuations in internal pressure in an ovalized bend will give variations in bending moment, curvature and ovalization. The resulting variations in stresses and strains may lead to alternating yielding and eventually lead to failure due to low-cycle fatigue. Present analytical models can describe accurately the strains and stresses in the elastic region, but after yielding has occurred, these models give less accurate results, in particular for the plastic strains. For static loading, this is not a problem, but for cyclic loading a more accurate knowledge of the occurring strain variations is necessary to evaluate the danger (limit state) of low cycle fatigue. There are several situations where low cycle fatigue has been or will be considered as a limit state. Examples are bends in buried pipelines that experience differential settlements causing high bending moments, offshore pipelines where risers are subjected to severe bending moments due to temperature differences and finally also pipelines in district heating.
