The dynamic response of piping system is significantly influenced by plastic deformation. As part of the work for elastic-plastic dynamic analysis of piping system, the present paper studied the elastic-plastic behavior of a pipe subjected to a steady axial force and a cyclic bending moment. A load regime diagram for the pipe is given, in which the dimensionless load plane n-m is divided into several regions with different elastic-plastic behaviors: pure elastic, shakedown, plastic fatigue, ratcheting and collapse. From the diagram, we can determine the behavior of piping under different combination of steady axial force and cyclic bending moment. An analysis of energy dissipation of corresponding regions in the load regime diagram is developed, and the formulation of plastically dissipated energy is derived for each region, through which we can obtain the energy absorbed by cyclic plastic bending of the piping. Some numerical examples of plastic energy dissipation computing are provided. Based on the present paper's work, an equivalent viscous damping that causes the same energy loss per cycle can be estimated and thus the influence of plastic deformation on piping dynamic response can be treated by introducing a plastic equivalent damping into the elastic dynamic analysis.
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