To investigate the strength checking methods for a semi-cylindrical header–nozzle intersection under combined piping loads, the simplified strength checking formulae for two piping load combinations, which are typical in engineering practice, are suggested based on the combined limit piping load interactions of the header. Furthermore, three methods for determining the allowable piping load parameters of the proposed formulae, namely the plastic work curvature (PWC) method of inelastic analysis route for design by analysis (DBA), the twice elastic slope (TES) method of inelastic analysis route for DBA, and the elastic finite element analysis (FEA) method of elastic analysis route for DBA, are presented and compared. Based on the theoretical analyses and the parametric comparison study results of the three methods, it can be concluded that the PWC method, which can take the hardening material effect on the plastic load results into account well and use the engineers' experience independent plastic work as the global indicator of gross collapse, is the most reliable one among the three methods, while the elastic FEA method is of great value for engineers to estimate the allowable piping loads quickly and conveniently.

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