Abstract
A critical excitation problem is formulated for a long-span moment-resisting frame subjected to a multi-component base input. The horizontal and vertical ground motions are characterized by a non-stationary model consisting of a given deterministic envelope function and a stochastic function, to be found, obeying a zero-mean Gaussian process. The critical excitation problem is such that, given the power spectra of the horizontal and vertical ground motions, find the worst cross spectrum of the horizontal and vertical inputs which maximizes the mean-squares of the sum of bending moments at the end of the beam under horizontal and vertical inputs. It is shown that the real part (co-spectrum) and the imaginary part (quad-spectrum) of the worst cross spectrum can be obtained by an algorithm including the order interchange of the double maximization procedure for the time and cross-spectrum domains. Numerical examples indicate that the proposed algorithm can work very well. The physical meaning of the critical cross-correlation function is also discussed.
