CLOSED-FORM CRITICAL EARTHQUAKE RESPONSE OF ELASTIC-PLASTIC STRUCTURES WITH BILINEAR HYSTERESIS UNDER NEAR-FAULT GROUND MOTIONS

KOJIMA Kotaro, TAKEWAKI Izuru

doi:10.3130/aijs.81.1209

The near-fault ground motions have special characters and the effects of such near-fault ground motions on structural response have been investigated extensively so far. The fling-step (fault-parallel) and forward-directivity (fault normal) inputs have been characterized simply by two or three wavelets. For this class of ground motions, many sophisticated analyses have been conducted from various viewpoints. However, as far as a forced input is employed, both a free-vibration term and a forced-vibration term appear and the closed-form expression of the elastic-plastic response may be difficult. In order to overcome this difficulty, the double impulse input is used as a good substitute of the near-fault ground motion and the closed-form expression is derived of the bilinear elastic-plastic critical response of a structure under this double input.<br> For guaranteeing the equivalence of the double impulse and the corresponding one-cycle sinusoidal input as a substitute of a near-fault ground motion, the equivalence of the maximum Fourier amplitudes of both inputs is introduced together with the equivalence of input frequency. Because only the free-vibration appears after each impulse of such double impulse input, the energy balance formulation using the kinetic energy and the strain and dissipated energy leads to the derivation of the closed-form expression of a complicated bilinear elastic-plastic response. It is shown that the maximum inelastic deformation of a structure with a positive post-yield stiffness can occur after the second impulse different from the case for elastic-perfectly plastic models. Furthermore it is made clear that, as the positive post-yield stiffness becomes larger, the correspondence between the double impulse and the corresponding sinusoidal input becomes better.<br> The closed-form expression is also derived for the non-critical case. The introduction of the concept of critical excitation enabled this derivation of the closed-form expression of the maximum elastic-plastic response. The validity and accuracy of the proposed theory are investigated through the comparison with the response analysis to the corresponding one-cycle sinusoidal input and recorded ground motions (Imperial Valley 1979, Northridge 1994, Hyogoken-Nanbu 1995). It is demonstrated that the proposed method using the double impulse is applicable to actual recorded pulse-type ground motions within a reasonable accuracy.

CLOSED-FORM CRITICAL EARTHQUAKE RESPONSE OF ELASTIC-PLASTIC STRUCTURES WITH BILINEAR HYSTERESIS UNDER NEAR-FAULT GROUND MOTIONS

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