1734 Elastic Response Spectra

If a single degree-of-freedom (SDOF) mass is subjected to a time history of ground (i.e., base) motion similar to that shown in Figure 17.7, the mass or elastic structural response can be readily calculated as a function of time, generating a structural response time history, as shown in Figure 17.8 for several oscillators with differing natural periods. The response time history can be calculated by direct integration of Equation 17.1 in the time domain, or by solution of the Duhamel integral (Clough and Penzien 1975). However, this is time consuming, and the elastic response is more typically calculated

El Centro,

El Centro,

FIGURE 17.8 Computation of deformation (or displacement) response spectrum (Chopra, A.K. 1981).

in the frequency domain

1 f1

where ^(t) is the elastic structural displacement response time history, — is the frequency,

0 0

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