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

The acceleration, velocity and displacement data of the earthquake can be downloaded from here: http://www.strongmotioncenter.org/vdc/scripts/download.plx?action=download&session=1407966735.66478

## 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.

This can be downloaded from here: http://resolver.caltech.edu/CaltechEERL:1971.EERL.1971.001

## Copyright

Copyright (c) 13-Sep-2015 by George Papazafeiropoulos