### Free software for earthquake engineering and structural dynamic

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

GamaModel is an OCTAVE code for the calculation of the seismic response of a non-linear SDOF defined by the gamma-model and the elasto-plastic model.

The gamma-model is an improved elasto-plastic model in which the reloading curves of large yield excursion cross the elastic portion of the envelope at a relative height of 1-gamma. Otherwise the reloading curves take for target the point corresponding to the actual peak displacement. Even if the gamma-model does not consider the degradation of the unloading stiffness, the model provides a good simulation of reinforced concrete structures. The name of the model derives from the shape of the created force displacement relationships for the first cycles which look like the greek symbol gamma. GamaModel also includes the too simple elasto-plastic model.

#### To run GamaModel.m:

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

#### Informations and recommendations

- The hysteretic model was proposed in my PhD thesis.

- The following parameters are used in GamaModel.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

soft: parameter defining the model used (soft=0 for elasto-plastic and soft=1 for gamma-model)

Gama: parameter defining the cross point between reloading curve and the elastic portion of the envelope for large yield excursion

Mfz: discretisation frequency, Mfz=1/(time interval)

nb: number of points to be considered

- By using Gama=0 with the gamma-model, the whole reloading curves take the point corresponding to yield displacement for target.

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