Abstract

Expected value of time-history response can be formulated by assuming the phase differences spectrum in Fourier transform of earthquake waves as a normal probability curve. The effect of damping on the response spectrum can be obtained based on the formula. The ratio of maximum displacement to previous peak displacement during nonlinear response can also be calculated theoretically, which may be used for estimation. Both theoretical values were compared with those calculated from the responses to earthquake motions, from which a fair correlation was observed, especially in relation to the duration of earthquake motions.

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