Free software for earthquake engineering and structural dynamic

(the software may be free downloaded and used at own risk)

Takeda is an OCTAVE code for the calculation of the seismic response of a non-linear SDOF defined by the well-known Takeda hysteretic model.


To run Takeda.m:

  • Run Octave
  • Type Takeda and Return
  • Answer the questions to define the non-linear SDOF

Informations and recommendations

  • The hysteretic model was first proposed by Takeda et al. and afterwards extended by different authors. More informations may be found in the following publications:

    Takeda T., Sozen M. A., Nielsen N. N.: Reinforced Concrete Response to Simulated Earthquakes.
    ASCE, Journal of the Structural Division, Vol. 96, No. ST12, December 1970.

    Allahabadi R., Powel G.: Drain-2DX User Guide. Report No. UCB/EERC-88/06.
    College of Engineering, University of California, Berkeley 1988.


  • The following parameters are used in Takeda.m:

    Fileacc: name of the file containing the ground accelerations
    Scale: percentage of the earthquake to be used for the calculation
    f: initial natural frequency of the SDOF
    hard: post yield stiffness in % of the initial stiffness
    z: damping ratio in %
    Frict: friction ratio in o/oo
    Ulin: elastic displacement (elastic behaviour of the SDOF), if unknown set a large value for its determination
    R: strength reduction factor, the yield displacement corresponds to Ulin/R
    Alpha: parameter defining the degradation of unloading stiffness (actual stiff.=initial stiff.*(peak displ./yield displ.)^-alpha)
    Beta: parameter defining the reloading curve (beta=1 target peak displacement and beta=0 target yield displacement)
    Mfz: discretisation frequency, Mfz=1/(time interval)
    nb: number of points to be considered


  • Check always the calculated relative displacement reaction force relationships carefully because, in some special cases, the implemented rules of the hysteretic model may lead to unrealistic structural seismic response.


  • Since Takeda runs with the Central Difference Algorithmus, the numerical stability is ensured only for initial natural frequencies below Mfz/pi.