Civil Engineering Reference
In-Depth Information
It is important to note the fundamental difference between elastic and inelastic spectra on the one
hand and design spectra on the other (Figure 3.1). Elastic and inelastic spectra, presented in Section
3.4.2 , are 'computed' quantities that are mathematically based and reproducible by parties other than
those who derived them. Design spectra, on the other hand, include features that are decided upon by
code committees or other interested parties, and are therefore not necessarily reproducible by others.
For example, a design spectrum may include features that prevent unconservative estimates of design
actions, or protect against the adverse effects of errors in calculating periods of vibration. Therefore,
design spectra, expressed in terms of acceleration response versus period, should not be used to derive
displacement spectra, since they carry features that may violate basic theoretical principles.
Since the peak ground acceleration, velocity and displacement from various earthquake records
generally differ, the computed response cannot be averaged on an absolute basis. Therefore, various
procedures are used to normalize response spectra before averaging is carried out. The general proce-
dure for generating statistically based averaged spectra is summarized as follows:
(i) Select a set of ground motions on the basis of their magnitude, distance and site conditions.
(ii) Generate response spectra in terms of acceleration, velocity and displacement, as appropriate
for the seismic structural design.
(iii) Average the response spectra derived in Step (ii). Curves are generally fi t to match computed
mean spectra.
(iv) Evaluate the design response spectrum with desired probability of being exceeded on the basis
of the relationships derived in the previous steps.
Site - specifi c design spectra can also be generated by employing ground- motion models (attenuation
relationships) of response spectral ordinates as discussed in Section 3.3, or by advanced numerical
modelling of the energy release and travel path associated with the ground motion, as illustrated in
Section 3.5.3 . Site - specifi c design spectra can also be provided as uniform hazard spectra as discussed
above where the probability of each ordinate being exceeded is uniform. The curves, evaluated statisti-
cally, correspond to all magnitude-distance pairs contributing to the distribution of the spectral values,
for all periods and damping levels considered.
From a structural engineering viewpoint, a design or smoothed spectrum is a description of seismic
design forces or displacements for a structure having a certain fundamental period of vibration and
structural damping. The fi rst earthquake design spectrum was developed by Housner (1959 ). Thereafter,
Newmark and Hall (1969) recommended simplifi ed linear forms to represent earthquake design spectra.
Design spectra can be either elastic or inelastic. The latter are employed to evaluate design forces and
displacements for structural systems responding inelastically under earthquake loading. Inelastic design
spectra can be obtained either directly (e.g. Mahin and Bertero, 1981; Vidic
et al.
, 1994 ; Fajfar, 1995 )
or by scaling elastic spectra through force reduction factors presented in Section 3.4.4 . Scaled elastic
spectra are provided in seismic design codes of practice. Such spectra are generally average acceleration
response spectra that have been smoothed using control periods, which are either 2 or 3 depending on
the code. The basic curves employ 5% damping; however, simplifi ed expressions exist to obtain spectra
for different damping values, e.g. equation (4.39) of Chapter 4. Moreover, the standard design response
spectra are based on fi xed spectral shapes, which vary as a function of the soil site conditions, e.g. rock,
stiff and soft soils. Earthquake magnitude and source distance are also used, e.g. in the USA, to char-
acterize the design spectra.
Design spectra are provided in the codes as normalized spectral curves; thus, the design spectra for
a given site are computed by multiplying the spectral shapes by zone factors obtained from contour
maps. Effective peak accelerations are sometimes used to scale the normalized spectra. Indeed, the
fi xed spectral shape is usually presented as normalized to 1.0-g ground acceleration, which is
the response acceleration at zero period. Spectra may be presented in several formats, such as
spectral ordinates (acceleration, velocity and displacements) versus period, tripartite plots and spectral
