doc CSReSp

Documentation of the CSReSp function.

helpFun('CSReSp')

 Constant Strength Response Spectra

 [SMU,SD,SV,SA,SEY,SED]=CSRESP(DT,XGTT,T,KSI,FYR,PYSF,DTTOL,...
     ALGID,RINF,MAXTOL,JMAX,DAK)

 Description
     The constant strength response spectra for a given time-history of
     constant time step, eigenperiod range, viscous damping ratio and
     yield strength ratio (yield shear to weight, V/W) are computed.

 Input parameters
     DT [double(1 x 1)] is the time step of the input acceleration time
         history XGTT.
     XGTT [double(1:numsteps x 1)] is the input acceleration time history.
         numsteps is the length of the input acceleration time history.
     T [double(1:numSDOFs x 1)] contains the values of eigenperiods for
         which the response spectra are requested. numSDOFs is the number
         of SDOF oscillators being analysed to produce the spectra.
     KSI [double(1 x 1)] is the fraction of critical viscous damping.
     FYR [double(1 x 1)] is the yield strength ratio (yield shear to
         weight, V/W) for which the response spectra are calculated.
     PYSF [double(1 x 1)] is the post-yield stiffness factor, i.e. the
         ratio of the postyield stiffness to the initial stiffness. PYSF=0
         is not recommended for simulation of an elastoplastic system. A
         small positive value is always suggested.
     DTTOL [double(1 x 1)] is the tolerance for resampling of the input
         acceleration time history. For a given eigenperiod T, resampling
         takes place if DT/T>dtTol.
     ALGID [char(1 x :inf)] is the algorithm to be used for the time
         integration. It can be one of the following strings for superior
         optimally designed algorithms:
             'generalized a-method': The generalized a-method (Chung &
             Hulbert, 1993)
             'HHT a-method': The Hilber-Hughes-Taylor method (Hilber,
             Hughes & Taylor, 1977)
             'WBZ': The Wood–Bossak–Zienkiewicz method (Wood, Bossak &
             Zienkiewicz, 1980)
             'U0-V0-Opt': Optimal numerical dissipation and dispersion
             zero order displacement zero order velocity algorithm
             'U0-V0-CA': Continuous acceleration (zero spurious root at
             the low frequency limit) zero order displacement zero order
             velocity algorithm
             'U0-V0-DA': Discontinuous acceleration (zero spurious root at
             the high frequency limit) zero order displacement zero order
             velocity algorithm
             'U0-V1-Opt': Optimal numerical dissipation and dispersion
             zero order displacement first order velocity algorithm
             'U0-V1-CA': Continuous acceleration (zero spurious root at
             the low frequency limit) zero order displacement first order
             velocity algorithm
             'U0-V1-DA': Discontinuous acceleration (zero spurious root at
             the high frequency limit) zero order displacement first order
             velocity algorithm
             'U1-V0-Opt': Optimal numerical dissipation and dispersion
             first order displacement zero order velocity algorithm
             'U1-V0-CA': Continuous acceleration (zero spurious root at
             the low frequency limit) first order displacement zero order
             velocity algorithm
             'U1-V0-DA': Discontinuous acceleration (zero spurious root at
             the high frequency limit) first order displacement zero order
             velocity algorithm
             'Newmark ACA': Newmark Average Constant Acceleration method
             'Newmark LA': Newmark Linear Acceleration method
             'Newmark BA': Newmark Backward Acceleration method
             'Fox-Goodwin': Fox-Goodwin formula
     RINF [double(1 x 1)] is the minimum absolute value of the eigenvalues
         of the amplification matrix. For the amplification matrix see
         eq.(61) in Zhou & Tamma (2004).
     MAXTOL [double(1 x 1)] is the maximum tolerance of convergence of the
         Full Newton Raphson method for numerical computation of
         acceleration.
     JMAX [double(1 x 1)] is the maximum number of iterations per
         increment. If JMAX=0 then iterations are not performed and the
         MAXTOL parameter is not taken into account.
     DAK [double(1 x 1)] is the infinitesimal acceleration for the
         calculation of the derivetive required for the convergence of the
         Newton-Raphson iteration.

 Output parameters
     SMU [double(1:numSDOFs x 1)] is the Spectral ductility.
     SD [double(1:numSDOFs x 1)] is the Spectral Displacement.
     SV [double(1:numSDOFs x 1)] is the Spectral Velocity.
     SA [double(1:numSDOFs x 1)] is the Spectral Acceleration.
     SEY [double(1:numSDOFs x 1)] is the Spectral yield energy.
     SED [double(1:numSDOFs x 1)] is the Spectral damping energy.

 Example
     dt=0.02;
     N=10;
     a=rand(N,1)-0.5;
     b=100*pi*rand(N,1);
     c=pi*(rand(N,1)-0.5);
     t=(0:dt:(100*dt))';
     xgtt=zeros(size(t));
     for i=1:N
         xgtt=xgtt+a(i)*sin(b(i)*t+c(i));
     end
     figure()
     plot(t,xgtt)
     T=(0.04:0.04:4)';
     ksi=0.05;
     fyR=0.1;
     pysf=0.1;
     dtTol=0.02;
     AlgID='U0-V0-Opt';
     rinf=1;
     maxtol=0.01;
     jmax=200;
     dak=eps;
     [Smu,Sd,Sv,Sa,Sey,Sed]=CSReSp(dt,xgtt,T,ksi,fyR,pysf,dtTol,...
       AlgID,rinf,maxtol,jmax,dak);
     figure()
     plot(T,Smu)
     figure()
     plot(T,Sd)
     figure()
     plot(T,Sv)
     figure()
     plot(T,Sa)
     figure()
     plot(T,Sey)
     figure()
     plot(T,Sed)

__________________________________________________________________________
 Copyright (c) 2018-2023
     George Papazafeiropoulos
     Major, Infrastructure Engineer, Hellenic Air Force
     Civil Engineer, M.Sc., Ph.D.
     Email: gpapazafeiropoulos@yahoo.gr
 _________________________________________________________________________

Published with MATLAB® R2022b