Critical Earthquake Response of Elastic–Plastic Structures Under Near-Fault Ground Motions (Part 2: Forward-Directivity Input)

The triple impulse input is used as a simplified version of the forward-directivity near-fault ground motion and a closed-form solution of the elastic–plastic response of a structure by this triple input is obtained. It is noteworthy that only the free-vibration appears under such triple impulse input. An almost critical excitation is defined and its response is derived. 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 maximum inelastic deformation can occur after the second impulse or the third impulse depending on the input level. The validity and accuracy of the proposed theory are discussed through the comparison with the response analysis result to the corresponding three wavelets of sinusoidal waves as a representative of the forward-directivity near-fault ground motion.