Abstract

A dynamic collapse criterion for elastic-plastic structures under near-fault ground motions is derived analytically by approximately transforming near-fault ground motions into double impulse and using an energy balance law. A negative post-yield stiffness is introduced to treat the P-delta effect in the single-degree-of-freedom (SDOF) model. The principal part of fling-step near-fault ground motions is modeled by a one-cycle sine wave and then a double impulse. The double impulse enables the efficient use of the energy approach in the derivation of compact expressions of complicated elastic-plastic responses of structures with the negative post-yield stiffness. In contrast to the previous work (Kojima and Takewaki 2016b) for the resonant critical case, a general collapse criterion is provided for the velocity amplitude and the frequency of the double impulse. It is significant that no iteration is needed in the derivation of the dynamic collapse criterion except the solution of transcendental equations. It is shown that discussions on several patterns of dynamic collapse behaviors introduced in the previous critical case are useful for deriving a boundary between the collapse and the non-collapse in the plane of the input velocity and the input frequency. The most important point to be remarked is that the critical state (Kojima and Takewaki 2016b) corresponding to the nonlinear resonance does not necessarily provide the minimum input velocity level with respect to arbitrary impulse timing. The validity of the proposed dynamic collapse criterion is examined by the numerical response analysis for structures under double impulses with collapse or non-collapse parameters.

Highlights

  • The dynamic collapse of structures is of permanent interest in the field of structural and earthquake engineering and applied mechanics

  • In contrast to the previous work (Kojima and Takewaki, 2016b) for the resonant critical case, a general collapse criterion is provided for the velocity amplitude and the frequency of the double impulse

  • It is significant that no iteration is needed in the derivation of the dynamic collapse criterion except the solution of transcendental equations

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Summary

INTRODUCTION

The dynamic collapse of structures is of permanent interest in the field of structural and earthquake engineering and applied mechanics. Since the second impulse acts after the structure goes into a plastic region and attains the maximum deformation (Point B), Equations (4), (12) require to satisfy the condition In this case, the displacement and velocity of the mass just before the action of the second impulse are described from Equations (14) and (15) as u∗ = u(t0 − (tOA + tAB)). The timing of the second impulse is indicated In this case, the second impulse acts after the structure goes into a plastic range and attains the maximum deformation, Point B. The response behaviors can be well-understood from these figures

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