## 8 Objective 3: Ductility According to Pushover Analysis  
It is accepted that nonlinear time history analysis is the most accurate and reliable analysis procedure as long as realistic modeling of the structure and the cyclic load deformation characteristics of its structural elements are provided. The latter characteristic cannot be considered in pushover analysis implying that the effect of the dissipation of energy on the seismic response is neglected. Despite this, nonlinear static procedures are broadly used to estimate seismic responses in terms of different parameter for low- and medium-rise buildings. In this section of the paper, the different types of ductility under consideration are calculated by using pushover analysis and compared to those of dynamic analysis. The pattern of loads is the classical one where a triangular distribution is used; gravity loads were also considered. In order to have a reasonable comparison, the maximum drifts considered in pushover analysis (about 5%) is quite similar to those observed in dynamic analysis for many strong motions for the case of maximum seismic intensity (\(S_{a}\) = 1.2 g and 0.8 g for the 3- and 10-level buildings). Similar to the case of dynamic analysis, as the lateral loads are gradually increased, the structural deformations are gradually increased too. As soon the first plastic hinge is developed in a particular member, in any member of a story, or in any member of the structure, the corresponding deformations \(\phi_{y}\), \(\Delta_{y}\) and \(D_{y,t}\) as indicated in Equations (1), (3), and (5), respectively, are recorded. Then, by considering the associated maximum deformations (\(\phi_{max}\), \(\Delta_{max}\) and \(D_{max,t}\)) the values of local, story and global ductility are calculated. The results for bending local ductility are shown in last column of Table 3 for the 3-level building. As for the case of dynamic results, the values are much larger for beams than for columns. It is observed that for beams, the values of \(\mu_{L\phi}\) of pushover analysis, which range from 13.01 to 16.64, can be much larger than the \(\mu_{L\phi}\) mean values of dynamic analysis (ranging from 7.81 to 11.86). There are several reasons for this: (a) as stated earlier, the maximum drift was approximately the same for both type of analyses, however, it was observed for many but not for all the strong motions in the case of dynamic analysis, for many of them the maximum drift were about 4% for the maximum seismic intensity, (b) for the case of pushover, the drifts were very close to 5% for all stories, but for dynamic analysis values of 3% and even smaller were observed for some stories, (c) the drift at which first yielding occurred for the stories were smaller for pushover than for of dynamic analysis. Results also indicate that for the case of columns, \(\mu_{L\phi}\) values may be larger or smaller than those of dynamic analysis; however, the values tend to increase and decrease with the story number for pushover and dynamic analysis, respectively, showing an opposite trend. The \(\mu_{L\phi}\) pushover results for the 10-level building are shown in last column of Table 4. The major observations made before for the 3-level building apply to this building: (a) the pushover values are larger for beams than for columns (in both cases tend to increase with the story number), (b) for the case of beams, the maximum pushover values are larger than the maximum dynamic mean values, and (c) for beams and columns, the values tend to increase and decrease with the story number for pushover and dynamic analysis, respectively. The additional observation that can be made is that for the case of beams, the maximum pushover or dynamic values are larger for the 10- than for the 3-level buildings. The \(\mu_{S}\) values for pushover analysis are given in last columns of Tables 6 and 7 for the 3- and 10-level models, respectively. It can be observed that, as for bending ductility demands of beams, \(\mu_{S}\) in general is larger for pushover than for dynamic analysis.