E0-190-2008_(10)1D_Shear_Propagation(SHAKE)

Calculating the fourier transform of the acceleration

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Unformatted text preview: e strata). Calculating the Fourier transform of the acceleration time history wave, the wave can be expressed by the superposition type of each frequency components: (64) where, 2A(ωs) indicates the Fourier amplitude of the design basis acceleration ( Acceleration Fourier spectrum). The double integral of Eq.(64) by the time t gives the displacement time history: (65) where, (66) Using Eq.(61): (61) the displacement response time history at the j-th interface is given by: (67) And, the acceleration response time history is also given by: (68) Furthermore, the shear strain time history γj(t) in the j-th stratum is given by: (69) The calculations of Eq.(68) and Eq.(69) gives the response of acceleration and the shear strain. (68) The computations for Eq.(68) and Eq.(69) are performed using FFT. (5) Nonlinear Analysis One of the numerical procedures for nonlinear analysis is the equivalent linear analysis procedure, where the equivalent shear modulus Gej and the equivalent damping factor hej are determined in correspondence to the equivalent shear strain γe...
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This note was uploaded on 03/14/2014 for the course CE 5680 taught by Professor Drgrd during the Summer '14 term at Indian Institute of Technology, Chennai.

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