Civil Engineering Reference
In-Depth Information
spectra by selecting the plot of the time history of the base fi xed node of a cantilever beam to which
the strong motion is applied. Spectra can thus be plotted in terms of acceleration, velocity and displace-
ment for various values of damping.
Problem 3.9
Use Seismo -Signal or USEE to plot the acceleration, velocity and displacement response spectra
for the 1999 Kocaeli (Turkey) earthquake (Station Ducze, horizontal component). Consider an
elastic system with 5% viscous damping and an inelastic system with ductility of 4. For the latter
system, assume two inelastic response models, namely linear elastic-perfectly plastic and linear
elastic strain hardening. Use four values for the post-yield hardening of 1%, 5%, 10% and 20%.
Comment on the results. For the inelastic spectra, use a viscous damping of 0.5%.
3.8.2 Generation of Ground - Motion Records
Statistically independent accelerograms can be simulated through SIMQKE- 1 (Gasparini and
Vanmarcke, 1976), which can be downloaded from the Internet at http://nisee.berkeley.edu/elibrary/
Software/SIMQKE1ZIP. The source code is written in standard Fortran and the executable fi le can
be obtained by using a standard compiler. This program generates earthquake strong motions whose
response spectra either match or are compatible with a set of specifi ed response spectra. Moreover,
SIMQKE-1 performs baseline correlation on the generated motions to ensure zero fi nal ground veloc-
ity. Response spectra are also calculated automatically. It is worth mentioning that the generation of
the spectrum-compatible motion is based on the relationship between the response spectrum values,
for a given damping, and the expected Fourier amplitudes of the earthquake motion. The latter is
synthesized by superimposing sine and cosine components and pseudo-random phase angles. The
stationary trace is then multiplied by a function representing the variation of ground- motion intensity
with time; this function is user- specifi ed. Furthermore, iterative adjustments of the spectral density
ordinates may be required to improve the matching between the computed and the smooth target
response spectra.
Ground-motion records can also be generated with the Simulink
®
of Matlab. This software has a user-
friendly graphical interface along with online help and some examples for the processing of records.
Problem 3.10
Consider the design (5% damping) spectrum relative to a site of construction located, for example,
in the western USA, expressed by equations (3.31.1) to (3.31.3). Use the software SIMQKE and
Matlab (Simulink
®
) to determine spectrum-compatible earthquake records for the design
spectrum.
S
T
a
1
1
0
(3.31.1)
≤<
TT ST
()
=
0 40
.
S
+
0 60
.
T
1
a
a
1
TTT ST S
1
≤<
()
=
(3.31.2)
2
a
a
2
S
T
a
2
TT
≥
ST
()
=
(3.31.3)
2
a
where
T
1
= 0.166 second and
T
2
= 0.830 second. The values of the spectral accelerations
S
a1
and
S
a2
are 1.207 g and 1.001 g, respectively.
