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PGA. As discussed in the previous section, this type of scaling, albeit convenient, is one of
the most unreliable ones. A more sophisticated procedure based on matching of spectra is
included in EC8 Part-2, Bridges (CEN, 1994c).
The 1997 UBC recommends the use of actual recorded accelerograms as input for time
history analysis; these should be selected from at least three different events, with due
consideration of magnitude, source distance and mechanisms, that should be consistent with
the design earthquake. In three-dimensional analysis, pairs of records are required (i.e. a
minimum of 3 pairs). Simulated time histories are allowed whenever three appropriate
recorded motions are not available (to make up the total number of records required for
design). For each pair of records the SRSS of the 5 per cent-damped site specific spectra is
first constructed. The accelerograms are then scaled in such a way that the average value of
the SRSS spectra does not fall below 1.4 times the 5 per cent-damped design spectrum, for the
period range 0.2T 1 to 1.5T 1. Note that in two-dimensional building models T3 (third mode
period) is close to 0.2T , while1.5T is a reasonable estimate of the post-yield period of the
1
1
structure. If only three time history analyses are performed the maximum response parameters
are used for design, while if seven (or more) analyses are carried out, the average response
parameters can be used. If the analysis is elastic, the response parameters can be scaled to the
design base shear level, as in modal analysis (see Section 4.3.6). If a non-linear time history
analysis is performed, the resulting response parameters (forces and displacements) can be
directly used.

4.3.8 Power spectrum analysis

Although treatment of the ground motion as a random process is a very reasonable approach
given the uncertainties involved in seismic wave propagation, the difficulties in calculating
the response of MDOF structures to a non-deterministic input (particularly when some
account for inelasticity must be made) make the application of stochastic dynamics to
practical seismic design almost prohibitive. In fact, among the leading codes, EC8 is the only
one including some provision for this type of analysis.
The basis of the procedure is the power spectrum (i.e. the power spectral density of the
acceleration time history that is considered as a random process). As explained in Section
10.2, if a stationary process x(t) has zero mean value and is gaussian, its power spectral
density S (ω) completely characterizes the process, since other properties can be calculated
x
from it, for instance the autocorrelation function is related to Sx(ω) through the Fourier
integral. It is often assumed for convenience that the ground motion does possess the previous
characteristics, which significantly simplifies the analysis. Models for stationary processes
can be found in the literature (e.g. Hu et al., 1996); one of the most commonly adopted for the
ground acceleration is the modified Kanai—Tajimi model proposed by Clough and Penzien,