Spectrum analysis is used when the dynamic action causes seismic movement at the base of the foundation. In this case, the decoupled motion equation for each mode is expressed as:
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where
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This equation can also be resolved using the response spectra. In this case, only the maximum response of the structure is obtained. If a maximum acceleration of
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is assumed for the previous equation, it is evident that the maximum response acceleration of the system would amount to
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As a consequence, the maximum displacement is:
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Using this answer, we can calculate the maximum displacements in all of the nodes for mode j:
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where
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Different formulas for finding the value of
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As for the stresses, reactions, and in general any response R which is to be determined, we get analogously:
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