### 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.