## 6 Objective 1: Local Ductility, Dynamic Analysis  
The local ductility parameter associated to bending, as defined by Equation (1), is calculated for all the structural members of both models for several intensities of the 20 strong motions as well as for the \(NS\) and \(EW\) directions. First, the models are subjected to the simultaneous action of the horizontal seismic component oriented in the \(EW\) direction, the vertical seismic component and the gravity loads. Then, the models are subjected to a similar set of loads, but the other horizontal component (\(NS\) direction) is considered instead. It is important to mention that even though, as stated earlier, the strong column-weak beam concept was considered in building design calculations, column hinging occurred in many cases. For a given story, the \(\mu_{L\phi}\) values are averaged, first over all the beams, and then over all the columns. The resulting averages for the beams of the 3-level building and the \(EW\) horizontal component, for seismic intensities \(S_{a}\) = 0.4 g, 0.8 g and 1.2 g, are presented in Figure 3a-c, respectively, while those associated to columns are given in Figure 3d-f, for the same strong motion intensities. The corresponding results for the 10-level building are presented in Figure 4, but in this case for seismic intensities of 0.2 g, 0.6 g and 0.8 g. In these figures, the symbol \"\(ST\)\" stands for the story level. It is worth to mention that moderate yielding occurs for seismic intensities of 0.4 g and 0.2 g for the 3- and 10-level structural models, respectively; the corresponding seismic intensities for significant deformations are 1.2 g and 0.8 g, for the 3- and 10-level models, respectively. In fact, even though it is not shown in the paper, the drifts for these significant levels of deformation were about 5% for some of the strong motions; the corresponding pattern of plastic hinges were very close to define a collapse mechanism. For this reason, the mentioned levels of maximum deformation are assumed to be associated the structural capacity of the models. Results of the figures indicate that, for beams, the maximum values of \(\mu_{L\phi}\) (bending local ductility capacity) are about 15 and 20 for the 3- and 10-level buildings, respectively. There are some numerical and experimental [9; 64; 65] evidence that the bending local ductility capacity can reach values larger than 20; however, it is for monotonic loading and individual members. It is also observed that, for a given value of \(S_{a}\), the magnitude of \(\mu_{L\phi}\) significantly varies from one seismic motion to another even though the seismic demands normalized according to \(S_{a}\) for each seismic motion was the same. For example, for the case of beams of Story 3 of the 3-level building and \(S_{a}=1.2\) g, values as small as 4 and as larger as 15 are observed for the twentieth and twelfth strong motions, respectively. Such broad variation reflects the influence of the strong motion frequencies and the contribution of several vibration modes to the structural response. Results also indicate that the \(\mu_{L\phi}\) values increase as the seismic intensity increases and that the values are much larger for beams than for columns, as expected. Plots similar to those given in of Figures 3 and 4 were also developed for the \(NS\) direction. In total 20 and 16 plots were developed for the 3- and 10-level buildings, respectively, but only the fundamental statistics in terms of the mean values (MV) and coefficients of variation (CV) are given for all cases; the results are presented in Tables 3 and 4. It can be observed from the tables that for the beams of the 3-level building, the maximum bending ductility demands occur, in general, for the second story. For the case of columns, as observed from individual graphs, the mean values are much smaller than those of beams; in fact for the two lowest intensities (\(S_{a}\) = 0.4 g and 0.6 g) they are essentially equal to unity for the two upper stories implying no yielding.