MATLAB Examples

Clough & Penzien: Elcentro earthquake (California, May 18, 1940, NS component)

Contents

Initial definitions

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

Open file elcentro.dat.

fid=fopen('elcentro.dat','r');

Read the text contained in the accelerogram elcentro.dat.

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

Close file elcentro.dat.

fclose(fid);

Set the time step of the input acceleration time history.

time=text{1,1};
dt=time(2)-time(1);

Set the input acceleration time history ($$\mathrm{\alpha_g}$).

xgtt=text{1,2};

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

Tspectra=logspace(log10(0.1),log10(3),1000)';

Set four distinct values for the critical damping ratio ($$\mathrm{\xi_1}=0,\mathrm{\xi_2}=0.02,\mathrm{\xi_3}=0.2,\mathrm{\xi_3}=0.4$) of the response spectra to be calculated.

ksi1=0;
ksi2=0.02;
ksi3=0.2;
ksi4=0.4;

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;

Processing

Extraction of elastic response spectra and pseudospectra for the three values of the critical damping ratio

[~,PSv1,~,~,~]=LERS(dt,xgtt,Tspectra,ksi1);
[~,PSv2,~,~,~]=LERS(dt,xgtt,Tspectra,ksi2);
[~,PSv3,~,~,~]=LERS(dt,xgtt,Tspectra,ksi3);
[~,PSv4,~,~,~]=LERS(dt,xgtt,Tspectra,ksi4);

Validation

Verification of FIGURE 25-2 of Clough & Penzien (Dynamics of Structures).

Plot the four pseudo-velocity response spectra.

figure('Name','FIGURE 25-2','NumberTitle','off')
plot(Tspectra,30*PSv1,'-b','LineWidth',1.)
hold on
plot(Tspectra,30*PSv2,'-r','LineWidth',1.)
plot(Tspectra,30*PSv3,'-g','LineWidth',1.)
plot(Tspectra,30*PSv4,'-m','LineWidth',1.)
hold off
grid on
xlabel('T_n','FontSize',13);
ylabel('PS_V','FontSize',13);
title('FIGURE 25-2 of Clough & Penzien','FontSize',13)
xlim([0,3]);
legend('\xi=0','\xi=0.02','\xi=0.2','\xi=0.4')

Original FIGURE 25-2 of Clough & Penzien (Dynamics of Structures)

Copyright

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