MATLAB Examples

Wood: Linear Elastic Response Spectrum of San Fernando earthquake (component S82E)

Contents

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 S82E
  • EPICENTER 34 24 00N,118 23 42W
  • INSTR PERIOD = 0.0460 SEC DAMPING = 0.572 SENSITIVITY = 1.90 CM/G
  • NO. OF POINTS = 5285 DURATION = 97.570 SEC
  • UNITS ARE SEC AND CM
  • RMS ACCLN OF COMPLETE RECORD = 0.1556 G/10
  • ACCELEROGRAM IS BAND-PASS FILTERED BETWEEN .110- .130 AND 25.00-27.00 HZ
  • 4879 INSTRUMENT AND BASELINE CORRECTED DATA AT EQUALLY-SPACED INTERVALS OF .020 SEC.
  • PEAK ACCELERATION = 207.92500 CMS/SEC/SEC AT 5.100 SEC
  • PEAK VELOCITY = 13.88702 CMS/SEC AT 5.180 SEC
  • PEAK DISPLACEMENT = -4.87016 CMS AT 7.680 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 1971SanFernandoJPLS82E.dat.

fid=fopen('1971SanFernandoJPLS82E.dat','r');

Read the text contained in the file 1971SanFernandoJPLS82E.dat.

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

Close file 1971SanFernandoJPLS82E.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 ($$\mathrm{\alpha_g}$). 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 ($$\mathrm{\xi_1}=0,\mathrm{\xi_2}=0.02,\mathrm{\xi_3}=0.05,\mathrm{\xi_4}=0.1,\mathrm{\xi_5}=0.2$) 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 143).

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