It is believed that earthquake has a bound on its magnitude. In other words, the earthquake energy radiated from the fault has a bound. The problem is to find the most unfavorable ground motion for a building or a group of buildings.A significance of critical excitation is supported by its broad perspective. There are two classes of buildings in a city. One is the important buildings which play an important role during disastrous earthquakes. The other one is ordinary buildings. The former one should not have damage during earthquake and the latter one may be damaged partially especially for critical excitation larger than code-specified design earthquakes. The concept of critical excitation may enable structural designers to make ordinary buildings more seismic resistant.There are a variety of buildings in a city. Each building has its own natural period and its original structural properties. When an earthquake occurs, a variety of ground motions are induced in the city. The combination of the building natural period with the predominant period of the induced ground motion may lead to disastrous phenomena in the city. Many past earthquake observations demonstrated such phenomena.
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