This paper carries out the shakedown and limit analysis of 45-degree piping elbows subjected to steady internal pressure and cyclic in-plane closing, opening and reverse bending moments by means of the recently proposed stress compensation method (SCM). Different geometries of the piping elbows and various combinations of these applied loads are investigated to create various shakedown limit and plastic limit load interaction curves. The plastic limit loads for single internal pressure and single bending moment calculated with the SCM are compared to those calculated with the twice-elastic-slope method. Full step-by-step elastic-plastic incremental finite element analyses are utilized to verify the structural cyclic responses on both sides of the curves obtained and further to confirm the correct shakedown limit loads and boundaries. It is shown that the SCM calculates the shakedown limit load accurately and possess more than 40 times the computational efficiency of the step-by-step elastic-plastic incremental method. The effects of the ratios of bending radius to mean radius and mean radius to wall thickness of the piping elbow as well as loading conditions on shakedown limit and plastic limit load interaction curves are presented. The results presented in this work provide a comprehensive understanding of long term response behaviors of the piping elbow under the combined cyclic loading and offer some essential points to be concerned for the design and integrity assessment of piping systems.

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