Worst-Case Analysis for Earthquake Energy Input Rate in SDOF and MDOF Structures: Fid-Bau Portal

Worst-Case Analysis for Earthquake Energy Input Rate in SDOF and MDOF Structures

Takewaki, Izuru

Possible realization of earthquake ground motion and its effects on structures are very uncertain even with the accumulated knowledge. It is therefore desirable to develop a robust structural design method taking into account these uncertainties. Under these circumstances worst excitation approaches have been proven to be promising. A new worst-case analysis method is developed here in which the mean value of the earthquake energy input rate is chosen as a measure of criticality. The concepts of statistical input energy and statistical input rate are new directions. The non-stationary ground motion is described as a uniformly modulated nonstationary random process. The power and the intensity of the input ground motion are bounded and the worst excitation is found under these restrictions. The key for solving the problem is the interchange of the order of the double maximization procedures with respect to time and to the power spectral density function. It is further shown that the formulation in single-degree-of-freedom models can be extended to multi-degree-of-freedom models with proportional damping. Examples for a specific envelope function of the non-stationary ground motion are presented in single and multi-degree-of-freedom models for demonstrating the validity of the method.