## 4 Evaluation of the Model  
This paper presents two moment-resisting frame models (Figure 5) with distinct features for evaluating the proposed model. Detailed information regarding these models is provided below. The eigenvalue analyses of detailed finite element models are employed to calculate the dynamic characteristics of the structures, which are subsequently compared to those obtained using the approximate method proposed in this study. Furthermore, the buildings' lateral deformation responses and inter-story drift ratio demands are determined using detailed finite element analysis under the response spectrum analysis. The simplified method compares these results to the lateral deformation demands obtained. The buildings' two-dimensional linear finite element models were constructed utilizing the SAP2000 structural analysis software. The results obtained through the eigenvalue finite element analysis are assumed to be the \"exact\" results in this study. _Example 1_ consisted of a three-span, five-story moment-resisting frame model. The beam-column rigidity ratio was 0.6 (\(\rho\) = 0.6), and the spans and story heights were equal, measuring 4 m and 3 m, respectively. The floor weights in the frame were uniformly distributed, with each floor weighing 800 kN. The first-mode period of vibration was 0.90 s. Dynamic analysis was performed using the UBC97 response spectrum. The lateral deformation responses and the maximum inter-story drift ratio estimations for the fundamental mode were compared between the proposed approach and the analysis; the results are shown in Figure 6.  
In Example 1, the maximum inter-story drift ratio obtained through the proposed method (\(\alpha(\rho,\text{N})\) = 6.1, \(\theta\) = 1/5) exhibited a difference of 4.24% compared to the results obtained from the finite element model. This maximum value was observed at the corresponding height location in the SAP2000 model. When the same example was solved using [PERSON]'s approach (\(\alpha\) = 12.5, \(\theta\) = 0), the difference amounted to 10.51%. It can be observed that the proposed approach here yields an improvement of approximately 6% in this sample-building model. As evident from the results, when the correct \(\alpha\) definition was employed, the proposed method captured the structural responses more accurately along the building height. _Example 2_ considered a moment-resisting frame model with five spans and nine stories. The beam-to-column stiffness ratio was 0.9 (\(\rho\) = 0.9). The spans and story heights were equal in length and are 3.8 m and 3 m, respectively. The weights in the frame were equal at each story and 1200 kN. The first-mode period of vibration was 1.53 s. Dynamic analysis was performed using the UBC97 Response Spectrum. The lateral deformation responses and  
Figure 5: Frame views of Example Model 1 and Example Model 2.  
the maximum inter-story drift ratio estimations for the fundamental mode were compared between the proposed approach and the analysis; results are shown in Figure 7.  
For Example 2, the maximum inter-story drift ratio obtained through the proposed method (\(\alpha(\rho,\) N\()=10.44,\)\(\theta=1/9\)) exhibited a difference of 3.84% compared to the results obtained from the finite element model. This maximum value was nearly observed at the  
Figure 6: Shape function (**left** column) and inter-story drift shape function (**right** column) for Example 1. Figure 7: Shape function (**left** column) and inter-story drift shape function (**right** column) for Example 2.  
corresponding height location, aligning with the results from the SAP2000 model. When applying [PERSON]'s approach (\(\alpha\) = 12.5, \(\theta\) = 0) to the identical example, a discrepancy of 6.94% was observed. The proposed approach demonstrated a performance enhancement of approximately 3.1% in the analyzed sample building model. This result indicates a significant influence of the \(\theta\) dependent on N in Example 1, which had fewer floors.