Free software for earthquake engineering and structural dynamic

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

Qmodel is an OCTAVE code for the calculation of the seismic response of a non-linear SDOF defined by the well-known Q hysteretic model.
The Q-model is a simplified (set symmetric) Takeda model in which the absolute value of peak displacement is considered for both directions in order to define the degradation of unloading stiffness and the reloading curves.


To run Qmodel.m:

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

Informations and recommendations

  • The hysteretic model was proposed by Saiidi and Sozen. More informations may be found in their publication:

    Saiidi M., Sozen M. A.: Simple Nonlinear Seismic Analysis of R/C Structures.
    ASCE, Journal of the Structural Division, Vol. 107, No. ST5, May 1981.


  • The following parameters are used in Qmodel.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)
    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 Qmodel runs with the Central Difference Algorithmus, the numerical stability is ensured only for initial natural frequencies below Mfz/pi.