## 6 One vs. More than One Element per Member
### Global and Local Parameters, 2 Intermediate Nodes  
The same parameters analyzed earlier, namely lateral drifts, shears, axial loads, and flexural moments, are now calculated for the representation \(3E\) of the models and contrasted to those of the representation \(1E\). Ratios of the responses of representation \(1E\) to those of representation \(3E\) of the models were developed. However, since no considerable differences were observed with respect to those of Sections 6.1 and 6.2 (where \(1E\) and \(2E\) were compared), only a few comparative ratios for the case of local response parameters are presented. Equations (10) and (11) are used to make the comparison for axial loads and flexural moments, respectively. \(A_{3}\) and \(B_{3}\) in these equations represent the axial loads and flexural moments, respectively, in the members when three elements per beam (representation \(3E\)) are used in the models. The other terms were defined earlier. \[R_{A2}=\frac{A_{1}}{A_{3}} \tag{10}\]  
Figure 13: Mean values of \(R_{B1}\), \(NS\): (**a**,**c**,**e**), exterior beams of Models 1-2-3, respectively; (**b**,**d**,**f**), interior beams of Models 1-2-3, respectively. \[R_{B2}=\frac{B_{1}}{B_{3}} \tag{11}\]  
The \(R_{A2}\) averages for exterior columns of Models 1 and 2 are presented in Figure 14a,b, respectively. Most of the major observations made before for the \(1E\) and \(2E\) comparison (Figure 11a,c) apply to this case. However, it is observed that, for the 3-story model, the level of overestimation of axial loads when no intermediate nodes are used resulting from the comparison \(1E\)-\(3E\) is a little greater than that of the comparison \(1E\)-\(2E\) (68% vs. 56%). For Model 2, on the other hand, the level of overestimation is essentially the same (about 40%) for the two comparison cases. The average values of \(R_{B2}\) for exterior columns can be seen in Figure 14c,d. Results indicate that the levels of overestimation, or underestimation, of these flexural moments obtained from the comparison of the \(1E\) and \(3E\) structural representations, essentially remain the same as those of the \(1E\) and \(2E\) representations. The \(R_{B2}\) averages of beams are can be seen in Figure 15. By comparing the results with those of Figure 14a through Figure 14d (\(1E\) vs. \(3E\)) it is concluded that, as for the case of flexural moments at columns, the level of underestimation in flexural moments of beam obtained from the comparison \(1E\)-\(2E\) is quite similar to that of the comparison \(1E\)-\(3E\). The responses of the models with four elements (three intermediate nodes) per beam were also calculated for some cases, but the results are not shown. It is worth mentioning, however, that the results are essentially identical to those of the representation \(3E\). The abovementioned results indicate that there is a certain degree of overestimation or underestimation of the seismic response when intermediate nodes are not used in the beams. Such underestimations or overestimations turned out to be practically the same when the results of not considering intermediate nodes were compared with those of one, two, or three intermediate nodes. Hence, there is no necessity of using more than three elements to represent the beams since practically convergence is reached for this number of elements. The accuracy is good even for the two-element case. Figure 14: Mean values of \(R_{A2}\) and \(R_{B2}\), exterior columns, \(NS\): (**a,b**) \(R_{A2}\) Models 1 and 2, respectively; (**c,d**) \(R_{B2}\) Models 1 and 2, respectively. From the earlier discussion it is concluded that if just one element per beam is used, the magnitude of inter-story shears can be overestimated by up to 33% and 21% for individual strong motions and on an average basis, respectively. The lateral drifts, however, are essentially the same for the models with none or with intermediate nodes.