Closed-Form Dynamic Stability Criterion for Elastic–Plastic Structures under Near-Fault Ground Motions

A dynamic stability criterion for elastic–plastic structures under near-fault ground motions is derived in closed form. A negative post-yield stiffness is treated in order to consider the P-delta effect. The double impulse is used as a substitute of the fling-step near-fault ground motion. Since only the free vibration appears under such double impulse, the energy approach plays a critical role in the derivation of the closed-form solution of a complicated elastic–plastic response of structures with the P-delta effect. It is remarkable that no iteration is needed in the derivation of the closed-form dynamic stability criterion on the critical elastic–plastic response. It is shown via the closed-form expression that several patterns of unstable behaviors exist depending on the ratio of the input level of the double impulse to the structural strength and on the ratio of the negative post-yield stiffness to the initial elastic stiffness. The validity of the proposed dynamic stability criterion is investigated by the numerical response analysis for structures under double impulses with stable or unstable parameters. Furthermore, the reliability of the proposed theory is tested through the comparison with the response analysis to the corresponding onecycle sinusoidal input as a representative of the fling-step near-fault ground motion. The applicability of the proposed theory to actual recorded pulse-type ground motions is also discussed.