Pseudo‐multi impulse for simulating critical response of elastic–plastic high‐rise buildings under long‐duration, long‐period ground motion

A pseudo‐multi impulse (PMI) is proposed as an extension of the ordinary base‐input multi impulse substituting a long‐duration, long‐period ground motion which can often be simulated by a multi‐cycle sine wave (MSW). PMI is treated as a multitude of impulsive lateral forces and hardly excites the higher‐mode responses of elastic multi‐degree‐of‐freedom (MDOF) models because the undamped fundamental participation vector is adopted as the influence coefficient vector. It is shown that the critical time interval of PMI can be obtained without any repetition. This enables a smart derivation of the critical response. The displacement transfer functions are derived for elastic MDOF models, where two kinds of the influence coefficient vectors are adopted: (1) one at every component (conventional one) and (2) the undamped fundamental‐mode participation vector. It is demonstrated that the critical PMI can efficiently and accurately evaluate the maximum responses under MSW and the critical input period of MSW for elastic–plastic MDOF models. Furthermore, PMI is extended to treat the critical case for the second eigenmode. Finally, the critical PMI is applied to high‐rise buildings for the investigation into the input energy and the cumulative plastic deformation ductility demand.