On Multiaxial Strain Characteristics of Piping Systems Subjected to Earthquake Loads

The JSME Code Case N-CC-008 provides design rules for piping seismic design by inelastic response time history analysis and strain-based fatigue criteria. Since the strain time histories obtained from the analysis are multi-axial and random, the Code Case uses the Rainflow method for cycle counting in its procedure of evaluating the ranges of equivalent strain and the fatigue usage factor. The Rainflow method is used for identifying pairs of peaks/valleys of the representative strain and their occurrence times. Then, with the other components of strain and stress at these times, the range of equivalent strain is calculated sequentially. On the other hand, ASME Boiler and Pressure Vessel Code Section VIII, Division 2 reads “The Rainflow cycle counting method is recommended but not applicable for non-proportional loading.” The authors, then, analyzed the behavior of multi-axial strain from the inelastic response analyses of some dynamic tests of piping systems to test if the piping strains due to seismic excitations are proportional or non-proportional, or somewhere in between. The IS method, which was proposed by Itoh et.al for quantifying the degree of non-proportionality of multi-axial fatigue cycles, was used for the analysis. The analysis results showed that the multi-axial strain in piping systems induced by seismic excitation is almost proportional. Based on this result, the authors concluded that the Rainflow cycle counting method is well applicable for the piping seismic fatigue evaluation. In addition to these numerical analyses with the IS method, some discussions are also made in this paper from the viewpoint of the relation between vibration mode and strain components (compatibility condition between deformation and strain) to support the conclusion that the piping strain by seismic loads is proportional.