MATLAB Examples

Chopra (2012): Constant ductility response spectrum for 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 file 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_old=text{1,2}; dt_new=0.005; tend=time(end); [xgtt_new,~] = THInterp(xgtt_old,time,dt_new,tend);

xgtt_new=text{1,2};
dt_new=0.02;

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

Tspectra=(0.1:0.1:3)';

Set the value of the critical damping ratio of the response spectra to be calculated ($$\mathrm{\xi_1}=0.05$).

ksi=0.05;

Take the maximum ground acceleration.

maxxgtt=max(abs(xgtt_new));

Set three values of the ductility of the response spectra to be calculated ($$\mathrm{\mu_1}=1,\mathrm{\mu_1}=1.5,\mathrm{\mu_1}=2$).

mu=[1,1.5,2];

Number of normalized strength-ductility pairs for interpolation

n=5;

Processing

Extraction of the elastoplastic response spectra for the three values of the constant ductility.

[Sd1,Sv1,Sa1]=CDRS(dt_new,xgtt_new,Tspectra,ksi,mu(1),n);
[Sd2,Sv2,Sa2]=CDRS(dt_new,xgtt_new,Tspectra,ksi,mu(2),n);
[Sd3,Sv3,Sa3]=CDRS(dt_new,xgtt_new,Tspectra,ksi,mu(3),n);

Validation

  • Verification of figure 7.5.2 of Chopra (Dynamics of Structures, 2012).

Plot constant ductility acceleration spectrum for $\mathrm{\mu}=1, 1.5, 2$ and $\mathrm{\xi}=0.05$.

figure('Name','Figure 7.5.2','NumberTitle','off')
plot(Tspectra,Sa1,'-b','LineWidth',1.)
hold on
plot(Tspectra,Sa2,'-r','LineWidth',1.)
plot(Tspectra,Sa3,'-g','LineWidth',1.)
hold off
grid on
xlabel('T_n','FontSize',13);
ylabel('S_a','FontSize',13);
title('Figure 7.5.2 of Chopra','FontSize',13)
xlim([0,3]);
legend('\mu=1','\mu=1.5','\mu=2')

Original figure 7.5.2 of Chopra (Dynamics of Structures, 2012).

Copyright

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