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Behavior of imaginary rate-independent linear damping incorporated into a building structure subjected to strong ground motions is examined.It is well known that linear viscous damping and rate-independent linear damping yield almost identical response displacements and velocities during earthquakes.If the response central frequency is close to the fundamental frequency of the structure, the two linear damping elements yield almost identical damping forces;these two damping elements yield, however, substantially different damping forces, thereby resulting in substantially different floor response accelerations when the average response frequency and the fundamental frequency differ significantly.The benefit of rate-independent linear damping incorporated into a long-period structure is that it yields relatively low floor response accelerations even if the structure is subjected to a ground motion containing high-frequency components, whereas linear viscous damped structures might suffer high accelerations induced by high damping forces generated by high-frequency components of the ground motion.Generally, adding damping to a structure reduces response displacement at the expense of floor response accelerations.Implementation of rate-independent linear damping in a long-period structure is expected to be effective for controlling response displacements without increasing floor response accelerations when the structure is subjected to a ground motion containing high-frequency components.