7/17/2019 codigomatlab RESPONSE SPECTRUM

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%% Elastic Response Spectra% This is a function to generate elastic response specra including Displacement% Spectrum, Pseudo Acceleration Spectrum and Pseudo Velocity Spectrum which% are needed in "Response Spectrum Analysis" of Structures. In this function% to solve "Equation of Motions" for different periods, Newmark Linear Method% has been used.

%% @ Mostafa Tazarv, Carleton University, May 2011

%% SPEC Function Help:

% INPUTS:% dt: Time Interval (Sampling Time) of Record% Ag: Ground Motion Acceleration in g% zet: Damping Ratio in percent (%); e.g. 5% g: Gravitational Constant; e.g. 9.81 m/s/s% endp: End Period of Spectra; e.g. 4 sec

% OUTPUTS:% T: Period of Structures (sec)% Spa: Elastic Pseudo Acceleration Spectrum% Spv: Elastic Pseudo Velocity Spectrum% Sd: Elastic Displacement Spectrum

function [T,Spa,Spv,Sd]=SPEC(dt,Ag,zet,g,endp)u=zeros(length(Ag),1);v=zeros(length(Ag),1);ac=zeros(length(Ag),1);Ag(end+1)=0;T(1,1)=0.00;for j=1:round(endp/dt) % equation of motion(Newmark linear method) omega(j,1)=2*pi/T(j); % Natural Frequency m=1;

k=(omega(j))^2*m; c=2*m*omega(j)*zet/100; K=k+3*c/dt+6*m/(dt)^2;

a=6*m/dt+3*c; b=3*m+dt*c/2;for i=1:length(u)-1

u(1,1)=0; %initial conditions v(1,1)=0; ac(1,1)=0;

df=-(Ag(i+1)-Ag(i))+a*v(i,1)+b*ac(i,1); % delta Force du=df/K; dv=3*du/dt-3*v(i,1)-dt*ac(i,1)/2; dac=6*(du-dt*v(i,1))/(dt)^2-3*ac(i,1); u(i+1,1)=u(i,1)+du; v(i+1,1)=v(i,1)+dv; ac(i+1,1)=ac(i,1)+dac;

end Sd(j,1)=max(abs((u(:,1)))); %Sv(j,1)=max(abs(v)); %Sa(j,1)=max(abs(ac))/g; Spv(j,1)=Sd(j)*omega(j); Spa(j,1)=Sd(j)*(omega(j))^2/g; T(j+1,1)=T(j)+dt;endAg(end)=[];T(end)=[];

7/17/2019 codigomatlab RESPONSE SPECTRUM

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Sd(2,1)=0; Spv(1:2,1)=0;Spa(1:2,1)=max(abs(Ag))/g;

figure('Name','Spectral Displacement','NumberTitle','off')plot(T,Sd,'LineWidth',2.)grid onxlabel('Period (sec)','FontSize',13);ylabel('Sd (mm)','FontSize',13);title('Displacement Spectrum','FontSize',13)

figure('Name','Pseudo Acceleration Spectrum','NumberTitle','off')plot(T,Spa,'LineWidth',2.)grid onxlabel('Period (sec)','FontSize',13);ylabel('Spa (g)','FontSize',13);title('Pseudo Acceleration Spectrum','FontSize',13)