When piping systems are subjected to extreme seismic excitation, they undergo a plastic deformation that produces a large damping effect via energy dissipation. Based on our studies of the damping effect of the elasto-plastic response of piping, we have presented a simplified method for predicting the elasto-plastic response of piping in PVP conferences over the last several years. The method has taken the plastic deformation of in-plane bending elbows into consideration. The elasto-plastic response predicted by the method resulted in good agreement with piping model excitation tests. In this paper, we report an additional method to consider out-of-plane bending elbow and the mixed bending of in-plane and out-of-plane bending. The simulation results by this method and the comparisons with 3D piping model excitation tests are also reported.

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