Critical Response of Multi-Story Damped Bilinear Hysteretic Shear Building Under Multi Impulse as Representative of Long-Period, Long-Duration Earthquake Ground Motions

The critical response is investigated for a multi-story damped bilinear hysteretic shear building model under a multi impulse as a representative of long-period, long-duration earthquake ground motions. The critical response for an elastic–plastic single-degree-of-freedom (SDOF) model under a multi impulse was derived in previous papers. However, it is difficult to derive the critical response for a multi-degree-of-freedom (MDOF) model under a multi impulse because the phase lag among masses induces a complicated situation. In place of deriving an explicit critical response, a criterion on the criticality of the multi impulse for the elastic–plastic MDOF model is derived and the properties of the critical responses are clarified. In the analysis, a new concept of “Multi Impulse Pushover (MIP)” is introduced and the progressive performance evaluation for the increasing input level is conducted. The analysis of energy response (input energy, dissipated energy, etc.) and the comparison with the response to the corresponding sinusoidal wave are made to enhance the reliability and practicality of the proposed method using the multi impulse as a substitute of sinusoidal waves, which are representatives of long-period, long-duration earthquake ground motions.