Critical Input and Response of Elastic–Plastic Structures Under Long-Duration Earthquake Ground Motions

The multiple impulse input is introduced as a substitute of the long-duration earthquake ground motion, mostly expressed in terms of harmonic waves, and a closed-form solution is derived of the elastic–plastic response of a single-degree-of-freedom structure under the “critical multiple impulse input.” Since only the free vibration appears under such multiple impulse input, the energy approach plays an important role in the derivation of the closed-form solution of a complicated elastic–plastic response. It is shown that the critical inelastic deformation and the corresponding critical input frequency can be captured depending on the input level by the substituted multiple impulse input in the form of original and modified input sequence. The validity and accuracy of the proposed theory are investigated through the comparison with the response analysis to the corresponding sinusoidal input as a representative of the long-duration earthquake ground motion.