MATLAB Examples

# Hudson: San Fernando earthquake (02/09/71, Castaic old ridge route, component DWN)

## Earthquake information

• CORRECTED ACCELEROGRAM
• SAN FERNANDO EARTHQUAKE, FEBRUARY 9, 1971 - 0600 PST
• ID056 71.007.0 N
• STATION NO. 110 34 33 18N,118 39 24W, CASTAIC OLD RIDGE ROUTE, CALIFORNIA
• COMPONENT DOWN
• EPICENTER 34 24 00N,118 23 42W
• INSTR PERIOD = 0.0520 SEC DAMPING = 0.577
• NO. OF POINTS = 2954 DURATION = 61.842 SEC
• UNITS ARE SEC AND CM
• RMS ACCLN OF COMPLETE RECORD = 0.1736 G/10
• ACCELEROGRAM IS BAND-PASS FILTERED BETWEEN .050- .070 AND 25.00-27.00 HZ
• 3093 INSTRUMENT AND BASELINE CORRECTED DATA AT EQUALLY-SPACED INTERVALS OF .020 SEC.
• PEAK ACCELERATION = 153.31100 CMS/SEC/SEC AT 2.880 SEC
• PEAK VELOCITY = -6.40146 CMS/SEC AT 1.340 SEC
• PEAK DISPLACEMENT = 3.48894 CMS AT 1.020 SEC

## Initial definitions

The following initial definitions are made (in the order presented below):

Open file 1971SanFernandoCastaicDOWN.dat.

fid=fopen('1971SanFernandoCastaicDOWN.dat','r');

Read the text contained in the file 1971SanFernandoCastaicDOWN.dat.

text=textscan(fid,'%f %f %f %f %f %f %f %f');

Close file 1971SanFernandoCastaicDOWN.dat.

fclose(fid);

Set the time step of the input acceleration time history.

dt=0.02;

Set the time range of the input acceleration time history.

t=(dt:dt:3096*dt)';

Set the input acceleration time history (). Multiply by 0.01 to convert from cm/s^2 to m/s^2.

xgtt=[text{1,1},text{1,2},text{1,3},text{1,4},text{1,5},text{1,6},text{1,7},text{1,8}]';
xgtt=0.01*xgtt(:);

Set the eigenperiod range for which the response spectra will be calculated.

T=logspace(log10(0.01),1,1000)';

Set four distinct values for the critical damping ratio () of the response spectra to be calculated.

ksi1=0.00;
ksi2=0.02;
ksi3=0.05;
ksi4=0.10;

Set the minimum absolute value of the eigenvalues of the amplification matrix.

rinf=1;

Set the algorithm to be used for the integration.

AlgID='U0-V0-Opt';

Set the initial displacement of all SDOF oscillators analysed.

u0=0;

Set the initial velocity of all SDOF oscillators analysed.

ut0=0;

Plot the acceleration time history of the earthquake.

figure('Name','Acceleration time history','NumberTitle','off')
plot(t,xgtt,'LineWidth',1.)
grid on
xlabel('t(s)','FontSize',13);
ylabel('a_g(m/s^2)','FontSize',13);
title('Acceleration time history','FontSize',13)

## Processing

Calculation of the elastic relative velocity response spectra for the four values of the critical damping ratio.

[~,~,~,Sv1,~]=LERS(dt,xgtt,T,ksi1);
[~,~,~,Sv2,~]=LERS(dt,xgtt,T,ksi2);
[~,~,~,Sv3,~]=LERS(dt,xgtt,T,ksi3);
[~,~,~,Sv4,~]=LERS(dt,xgtt,T,ksi4);

## Validation

Plot relative velocity spectra. Divide the relative velocity by 0.0254 to convert m/s into inch/s.

figure('Name','Relative Velocity','NumberTitle','off')
plot(T,Sv1/0.0254,'-b','LineWidth',1.)
hold on
plot(T,Sv2/0.0254,'-r','LineWidth',1.)
plot(T,Sv3/0.0254,'-g','LineWidth',1.)
plot(T,Sv4/0.0254,'-k','LineWidth',1.)
grid on
xlabel('T_n','FontSize',13);
ylabel('S_V','FontSize',13);
title('Relative Velocity Spectra','FontSize',13)
legend('\xi=0','\xi=0.02','\xi=0.05','\xi=0.1','Location','NorthEast')

Original figure 4.c of [1] (page 194).

## Reference

[1] Hudson, D.E. (editor), 'Strong-motion instrumental data on the San Fernando earthquake of Feb. 9, 1971' Report, Earthquake Engineering Research Laboratory, Division of Engineering and Applied Science, California Institute of Technology & Seismological Field Survey, (formerly U. S. Coast & Geodetic Survey) National Oceanic and Atmospheric Administration, U. S. Department of Commerce, September 1971.