MATLAB Examples

# Chopra (2012): Constant ductility response spectrum for Elcentro earthquake (California, May 18, 1940, NS component)

## 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 (). 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 ().

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 ().

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 and .

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).