## 10 Conclusions  
A numerical investigation regarding ductility evaluation of steel buildings with moment resisting steel frames is conducted in this paper. Some steel model buildings and some strong motions used in the SAC steel project are used in the study. Bending local (\(\mu_{L\phi}\)) and tension local (\(\mu_{L\delta}\)) ductilities, story ductility (\(\mu_{S}\)) as well as global ductility are studied; the most appropriate definition of global ductility is identified. Global ductility is calculated as the mean values of story ductilities (\(\mu_{GS}\)) and as the ratio of the maximum inelastic top displacement to the top displacement when yielding occurs for the first time (\(\mu_{GI}\)). The ductility values calculated according to dynamic analysis are compared to those of pushover analyses. Results of the study indicate that the ductility values significantly may vary with the strong motion, the ductility definition, the structural element, the story number, the type of analysis, and the structural model. The main conclusions are:  
1. For beams and columns and the maximum seismic intensity, the mean values of \(\mu_{L\phi}\) tend to decrease with the story number; however, as expected, the beam values are much larger than those of columns (10.22 and 14.69 against 4.8 and 6.51). The \(\mu_{L\delta}\) values are only significant for exterior columns and much smaller than that of \(\mu_{L\phi}\) for beams. Even though tensional ductility \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Definition**} & \multirow{2}{*}{**Model**} & \multicolumn{4}{c}{**Dynamic Analysis**} & \multirow{2}{*}{**Pushover**} \\ \cline{3-6}  & & & **EO** & & **NS** & \\ \cline{3-6}  & & **MV** & **CV** & **MV** & **CV** & \\ \hline \multirow{2}{*}{\(\mu_{GS}\)} & 3-LEVEL & 0.41 & 0.45 & 0.34 & 0.27 & 0.50 \\  & 10-LEVEL & 0.35 & 0.33 & 0.32 & 0.19 & 0.36 \\ \hline \multirow{2}{*}{\(\mu_{GI}\)} & 3-LEVEL & 0.79 & NA & 0.59 & NA & 0.55 \\  & 10-LEVEL & 2.87 & NA & 2.59 & NA & 0.56 \\ \hline \hline \end{tabular}  
NA = not applicable.  
\end{table} 
Table 10: Statistics of the \(R_{LG}\) ratio. demands are considered as an important issue in some research reports, and steel structural members may have a high ductility capacity in tension, these type of ductility is less relevant for the structural system under consideration. 2. The \(\mu_{S}\) values for the maximum seismic intensity range from 3.84 to 4.28 and from 2.49 to 5.19 for the low- and medium-rise models, respectively. The values of \(\mu_{GS}\) for dynamic analysis associated to the maximum seismic intensity (ductility capacity) are larger for the low- than for the medium-rise building (3.95 and 3.89 against 3.82 and 3.31). Unreasonable large values are obtained for \(\mu_{GI}\), values of 36.34 and 38.78 were obtained for the 10-level buildings. The implication of this is that the ductility definition based on the building top displacement, even though used in the profession, is not appropriate for the case of dynamic analysis, particularly for high buildings where significant structural contributions of the higher modes are expected. 3. As for the case of dynamic results, the ductility values obtained from pushover analysis are much larger for beams than for columns. For beams, the values of \(\mu_{L\phi}\), \(\mu_{S}\) and \(\mu_{GS}\) obtained from pushover can be much larger than the corresponding values obtained from dynamic analysis. 4. The ratio (\(R_{LG}\)) of global to local ductility (\(\mu_{L\phi}\)) is also calculated. Considering that: (a) \(\mu_{GI}\) for dynamic analysis results in unreasonable large values, (b) pushover analysis does not take into account for dissipation of energy, (c) SCWB concept was followed in the building design, and (d) the local axial ductility is not important in framed steel building structures, the \(R_{LG}\) ratio of dynamic analysis associated to bending local ductility is assumed to be the most appropriated definition. A value of 1/3 is proposed for this ratio.