Page 154 - Dynamic Loading and Design of Structures

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(North America, Central America, and Southern Europe). The Pacoima Dam (California)
S16E and the Kalamata (Greece) N10W records are from earthquakes with similar magnitude
(6.6 and 6.2) and very close to the recording station (epicentral distances of 3 and 15 km). It is
seen that, although the magnitude of the accelerations is significantly larger for the Pacoima
record (see discussion of the topographic amplification effect in Section 4.2.4), the shape of
the two spectra is quite similar, with peaks occurring in the short period range. On the other
hand the Mexico City 1985 SCT transverse component, recorded during a magnitude 8.1
earthquake at a distance of 400 km, resulted in a significantly different spectral shape,
wherein the critical period range is between 1.7 and 2.8 sec; the effect of soil conditions (very
important in this case) is discussed in the next section. It is seen that the Mexico City record
with a PGA of only 0.17 g, will be more critical for high rise buildings with T>1.7 sec than
the Pacoima record with a PGA of 1.17 g.

Fourier spectra
Although most engineering applications involve the aforementioned response spectra, a better
understanding of the ground motion characteristics can be obtained from the Fourier
spectrum, defined as

(4.10)

where ü (i) is the ground acceleration time history and ωis the circular frequency of a
g
harmonic forcing function. It is then possible to express üg(t) through the superposition of a
full spectrum of harmonics (Clough and Penzien, 1993). Common applications involve the
Fourier amplitude spectrum, defined by

(4.11)

where t1 is the duration of the ground motion. Note that eqn (4.11) does not uniquely define a
ground motion (as eqn 4.10 does) since the phase angles between pairs of harmonics have
been lost in this definition.
Fourier spectra are commonly used to interpret phenomena associated with the transmission
of seismic energy from the source to distant locations. A useful application of these spectra in
the construction of simulated ground motions is briefly presented in Section 4.3.7.

Design spectra
For design purposes, it is clear that spectra smoother than those of Figures 4.9 and 4.10 are
required, since a future motion is very unlikely to be identical to a previously recorded one,
and also the exact periods of a structure are difficult to assess in practical situations (e.g. when
stiff cladding or partition elements are