| Abstract: | This note is an extension of earlier works that presented probability distribution functions for amplitudes of the peaks (the highest, the second highest … the m-th highest) in response of deterministic single degree-of-freedom (SDOF) and multi degree-of-freedom (MDOF) structures to ground motion, with deterministic Fourier spectrum and duration. It shows how these probability distribution functions can be evaluated if the Fourier spectrum and duration of the excitation are random variables specified via distribution functions. Two cases are considered: (l) when the structural model is deterministic, and (2) when the modal frequencies are random variables. The procedure presented here approximates the transfer function of the structural response by Dirac delta functions at the modal frequencies, and is applicable to multi-storey buildings with small modal damping, and with natural frequencies that are not too close. The resulting probability distribution functions are needed in seismic hazard calculations of peak response amplitudes of SDOF and MDOF structures that will not be exceeded with given confidence during the service time of the structure from any earthquake at all known faults within certain distance from the structure. |
