Improvement and Assessment of the Plastic Collapse Bending Moment Equations in Circumferentially Cracked Pipe

The plastic collapse bending moment in a pipe cross-section with a circumferential crack is defined in ASME B&PV Code Section XI, Appendix C using simplified equilibrium equations by approximating the pipe mean radius Rm and the neutral axis angle β. In previous papers it was demonstrated by the authors that, for externally cracked pipes, those simplified equilibrium equations are not conservative and hence improved equations were developed and proposed which account for the cracked pipe ligament mean radius Rmc. In this paper, it is demonstrated that the accuracy of the collapse bending moment equation can be refined by taking into account the neutral axis position Yna of the cracked pipe section. This leads to exact collapse bending moment equations without any approximation on the pipe mean radius Rm nor on the neutral axis angle β. In this framework, it is shown that, for externally cracked pipes, the Appendix C equations could lead to more than 20% less conservative collapse bending moment than with the exact equations. An extended finite element method analysis completes this study to assess the relevance of the model used to determine the plastic collapse bending moment.