Taking account of soil-structure interaction on seismic wave input

based on the theory of a two-step method

equivalent seismic wave input considering radiation damping effects is established. Firstly

the base response of single degree of freedom system is considered as the input of superstructure; and then damping ratio of the system is calculated by the state-space method considering soil-structure interaction

which is used to modify the damping coefficients of superstructure; thus the impact of soil-structure interaction is approximately calculated from the response of rigid foundation. Subsequently

a single degree of freedom system and a five-story frame structure are analyzed; numerical examples show that the calculation errors even exceed 100%; while directly taking seismic wave of free field and bedrock as the input of superstructure. However

the calculation errors of the two-step method are less than 10%; furthermore

the calculation errors will be less than 5% adopting the modified damping two-step method

which can satisfy the requirements of engineering.