## 1 Introduction  
The seismic behavior of a building under the action of a strong motion represents a very complicated phenomenon, particularly when the building is deformed into the inelastic range. In spite of this most of building codes around the world permit the use of simple elastic procedures to determine the seismic demands on steel buildings either for small or large deformations. Due to their relatively simplicity in their application, simplified methods like the Static Equivalent Lateral Force (SELF) procedure, are broadly used. For example, The International Building Code (IBC) [1]. The National Building Code of Canada (NBCC) [2], The Mexico Federal District Code (MFDC) [3], and The Eurocode 8 (EC) [4], permit the use of the mentioned procedure for regular buildings with relatively short periods (low- and medium-rise). FEMA-273 and ATC-40 also permit to use nonlinear static procedure or pushover analysis. In the procedure, static analysis of the buildings under the action of equivalent lateral forces, which are related to the properties of the structure and the seismicity of the region, provides the design forces; then a serviceability revision is performed. Thus, it can be said that conventional seismic design considered in many seismic codes is essentially force-based with a final check on displacements. In the above mentioned procedure, the ductility parameter (\(\mu\)) plays an important role in the determination of the design seismic forces of building structural systems, it represents the capacity of a structure to dissipate energy, allowing for a reduction of the elastic strength demands; the larger the ductility, the smaller the design seismic forces. It is particularly important for steel structures since there are many sources of ductility and of energy dissipation. However, there is not unanimity on the profession on how to define it; it is argued that this parameter is constantly used in the profession in an indirect way to estimate the building seismic design forces, but there is no engineering definition of it in our specifications or unanimity on the profession on how to define it [5; 6]. In fact, the magnitude of the reduction of the elastic design seismic forces directly depends on the force reduction factor (\(R\)), which significant depends on an associated parameter called ductility reduction factor (\(R_{\mu}\)) [7; 8]. The estimation of these parameters represents one of the most controversial issues in the SELF procedure. In IBC the reduction factor is called'response modification factor' (\(R\)); it is stated that it depends on many parameters including the ductility capacity and inelastic performance of structural material. In NBCC the reduction parameter is called 'force modification factor' (\(R_{d}\)), where it is explicitly stated that it depends on the ductility capacity and materials as well as on the structural overstrength. In MFDC this parameter is called'seismic reduction factor' (\(Q^{\prime}\)) which depends on the structural material, the structural system and detailing. In EC the factor is called'seismic reduction factor' (\(q^{\prime}\)) and depends on an overstrength factor and on factors which in turn depends on structural materials and the structural system. It is implicitly assumed in these codes that ductility represents the capacity of the structure to dissipate energy. It is concluded that, it is essential to establish a measure of ductility. In this regard, the various types of ductility involved in a building must be considered [9]; local ductility must be differentiated from story or from global ductility. For the case of steel buildings, local ductility may be associated to the rotational capacity of a member under bending or to the longitudinal deformation capacity of a member under tension. Story ductility is essentially associated to the relative story displacements while global ductility is normally expressed in terms of story ductility or in terms of the absolute displacements of the roof.