Assignment-2: Acceleration Response
Spectrum Prediction
1. Introduction
This report aims to develop predictive equations for acceleration response spectra using
ground motion data from 10 earthquakes in Japan. The primary parameters considered are
earthquake magnitude (M), epicentral distance (R), and spectral accelerations (A) at four
periods (T1 = 0.2s, T2 = 0.5s, T3 = 1.0s, T4 = 1.5s).
2. Methodology
The spectral acceleration values were calculated using a Fortran-based program. These
values were used to perform multiple linear regression to fit the empirical model:
logA = k1*M + k2*logR + k3
Separate equations were derived for each of the four time periods. Spectral data was then
plotted and a design response spectrum was determined by enveloping the maximum
acceleration values at each period.
3. Earthquake Data
The table below summarizes the magnitude, distance, and response spectra for each
earthquake.
EQ #
Magnitude
(M)
Distance (R
km)
A(T1)
A(T2)
A(T3), A(T4)
4. Regression Equations
Using the log-transformed acceleration data, the regression model was fitted for each
period. The coefficients (k1, k2, k3) were derived using Python's scikit-learn
LinearRegression.
T=T1 : logA = k_11*M + k_12*logR + k_13
T=T2 : logA = k_21*M + k_22*logR + k_23
T=T3 : logA = k_31*M + k_32*logR + k_33
T=T4 : logA = k_41*M + k_42*logR + k_43
5. Response Spectra Plots
Below are plots of the acceleration response spectra for all 10 earthquakes and the derived
design spectrum.
[Insert Plot Here]
6. Design Response Spectrum
The design response spectrum was developed by taking the maximum spectral acceleration
at each period across all earthquakes. This provides a conservative estimate for structural
design purposes.
7. Conclusion
This study demonstrates the relationship between earthquake magnitude, epicentral
distance, and spectral acceleration. By generating empirical prediction equations and
plotting response spectra, a reliable design spectrum was established which can be used for
seismic design in engineering applications.