Abstract
A set of multiple impulses is introduced as a substitute of many-cycle harmonic waves which represent the long-duration earthquake ground motion. A closed-form expression is derived of the elastic-plastic response of a single-degree-of-freedom (SDOF) structure with bilinear hysteresis under the ‘critical multiple impulse input’. As in the case of elastic-perfectly plastic models, an advantageous feature can be used such that only the free-vibration exists under the multiple ground motion impulse and the energy balance approach plays a key role in the derivation of the closed-form expression of a complicated elastic-plastic response. It is demonstrated that the critical inelastic maximum deformation and the corresponding critical impulse timing can be obtained depending on the input level. The validity and accuracy of the proposed theory are confirmed through the comparison with the response analysis to the corresponding sine wave as a representative of the long-duration earthquake ground motion.
Highlights
The classification of earthquake ground motions has often been conducted (Abrahamson et al, 1998)
It is investigated whether the response under the multi impulse with the critical time interval obtained in Section “Closed-Form Expression of Elastic–Plastic Steady-state Response under Critical Multi Impulse” converges to the steady state in which each impulse acts at the zero restoring-force point in Section “Convergence of Impulse Timing.”
While the resonant equivalent frequency of the elastic–plastic system for a specific input level has to be computed by changing the excitation frequency in a parametric manner in the conventional method dealing directly with the sinusoidal wave (Iwan, 1961), the steady-state elastic–plastic response under the critical multi impulse can be obtained in closed form and the critical time interval of the multi impulse can be obtained in closed form for the increasing input level in this proposed method
Summary
The classification of earthquake ground motions has often been conducted (Abrahamson et al, 1998). It can be observed that the response converges to a state in which each impulse acts at the zero restoring force irrespective of the input velocity level and the maximum deformation and the plastic deformation amplitude after convergence correspond to the closed-form expressions obtained in Sections “Case 1: Impulse in Unloading Process” and restoring force-deformation
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