MATLAB Examples

# Wood: Linear Elastic Response Spectrum of San Fernando earthquake (component DOWN)

## Earthquake information

• CORRECTED ACCELEROGRAM
• SAN FERNANDO EARTHQUAKE, FEBRUARY 9, 1971 - 0600 PST
• IG 110 71.032.0 EP
• STATION NO. 267 34 12 01N,118 10 25W, JET PROPULSION LAB., BASEMENT, PASADENA, CALIFORNIA
• COMPONENT DOWN
• EPICENTER 34 24 00N,118 23 42W
• INSTR PERIOD = 0.0460 SEC DAMPING = 0.612 SENSITIVITY = 1.90 CM/G
• NO. OF POINTS = 5548 DURATION = 97.587 SEC
• UNITS ARE SEC AND CM
• RMS ACCLN OF COMPLETE RECORD = 0.1093 G/10
• ACCELEROGRAM IS BAND-PASS FILTERED BETWEEN .110- .130 AND 25.00-27.00 HZ
• 4880 INSTRUMENT AND BASELINE CORRECTED DATA AT EQUALLY-SPACED INTERVALS OF .020 SEC.
• PEAK ACCELERATION = -126.34100 CMS/SEC/SEC AT 5.060 SEC
• PEAK VELOCITY = -5.94892 CMS/SEC AT 6.460 SEC
• PEAK DISPLACEMENT = 2.60064 CMS AT 8.920 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=1407974560.17328

## Initial definitions

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

Open file 1971SanFernandoJPLDOWN.dat.

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

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

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

Close file 1971SanFernandoJPLDOWN.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:4880*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(0.05),log10(15),1000)'; 

Set five 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; ksi5=0.20; 

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 five 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); [~,~,~,Sv5,~]=LERS(dt,xgtt,T,ksi5); 

## 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') semilogx(T,Sv1/0.0254,'-b','LineWidth',1.) hold on semilogx(T,Sv2/0.0254,'-r','LineWidth',1.) semilogx(T,Sv3/0.0254,'-g','LineWidth',1.) semilogx(T,Sv4/0.0254,'-m','LineWidth',1.) semilogx(T,Sv5/0.0254,'-k','LineWidth',1.) grid on xlabel('T_n','FontSize',13); ylabel('S_V','FontSize',13); title('Relative Velocity Spectra','FontSize',13) xlim([0.05,15]); legend('\xi=0','\xi=0.02','\xi=0.05','\xi=0.1','\xi=0.2','Location','NorthEast') 

Original figure of [1] (page 144).

## Reference

[1] Wood, J.H., 'Analysis of the Earthquake Response of a Nine-Story Steel Frame Building During the San Fernando Earthquake' Report, California Institute of Technology, Earthquake Engineering Research Laboratory, Center for Research on the Prevention of Natural Disasters, EERL 72-04, Pasadena, California, October 1972.

This can be downloaded from here: http://resolver.caltech.edu/CaltechEERL:1972.EERL-72-04

## Copyright

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