that are combinations of parameters, such as spectral acceleration at a particular period and duration, or the peak velocity and period of the near-fault rupture directivity pulse, to predict building response more optimally.

The most complete treatments abandon response-spectrum analysis, which is based on linear modal superposition, and use suites of ground-motion time histories to drive simulations of the fully nonlinear response, the most complete treatment for capturing the essence of building damage and failure. If ground motions within the specified probabilities are found by structural analysis to cause building drifts that exceed those required to meet the associated performance objective, the design of the building has to be modified (e.g., by increasing its stiffness, strength, or ductility capacity) until the performance objective is met. (Figure 3.26 shows the results of nonlinear dynamic analyses of a model of a five-story steel moment-resisting building frame.) Because the suites of observed strong-motion seismograms are limited, there is an increasing need for realistic simulations of wavefields at frequencies important for building performance (0.3 to 10 hertz). Current physics-based simulations of ground motions for relatively well-characterized regions, such as the Los Angeles metropolitan area, are now feasible only at the lower end of this frequency range (94).

Major efforts will be required to improve the accuracy of predictions of nonlinear structural behavior, to link the displacements to cost and injury statistics, and to simplify the procedures for routine practice. Progress toward the last objective will require new types of intensity measures more general than response spectral values (e.g., nonlinear functionals of the seismogram), judiciously derived as predictable aspects of the time histories and explicitly formulated for a simplified nonlinear analysis. This generalization of seismic hazard analysis to seismic performance assessment analysis holds great promise (95) and is well matched with the new capabilities of earthquake science in earthquake forecasting, source characterization, and ground-motion simulation. However, this research will demand a greater degree of collaboration between the scientific and engineering communities.

Warning and Rapid Response

John Milne anticipated the current enthusiasm for seismic warning systems when he wrote in 1899 (96):

An earthquake which traveled at the rate of four seconds to a mile might, if it were allowed to close a circuit which fired a gun at a station fifteen miles distant, give the inhabitants at that place a minute’s warning to leave their houses. The inhabitants of Australia and the western shores



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