# Parametric Analysis of Outrigger Systems for High-Rise Buildings with Different Geometric Shapes
## 3 Refined Modeling for Outrigger Systems
### Results and Discussion
The initial story displacements remain largely the same, while a substantial reduction occurs from mid-height, where the outrigger system is installed. IDR values follow the same trend. Such findings are consistent with the relevant literature (e.g., [43; 46; 66]). In line with [PERSON]'s [33] observations, curvature reversals occur proximate to outrigger truss levels (24 th-26 th floors) in straight, tilted, and twisted configurations. The outrigger system demonstrates consistent efficacy across minor geometric variations. A substantial reduction is also observed in the core base bending moments upon outrigger system implementation. Lastly, a comparative analysis of refined and simplified models, with and without outriggers, evaluates the approximation method's accuracy and highlights similarities and differences. The comparison is performed in terms of relevant engineering parameters, including lateral top displacement and core base bending moment. To quantify the performance enhancement provided by outriggers, an outrigger efficiency ratio is defined as the percentage reduction in each EDP achieved by the outrigger implementation. Results for both refined and simplified models, organized by building typology, are summarized in Table 10. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**W\({}_{2}\)**} & \multicolumn{4}{c}{**W\({}_{2,0}\)**} \\ \hline \multirow{2}{*}{**Mode**} & **Period** & **Sum UX** & **Sum UY** & **Period** & **Sum UX** & **Sum UY** \\  & **(s)** & **(\%)** & **(\%)** & **(\%)** & **(s)** & **(\%)** & **(\%)** \\ \hline
1 & 4.70 & 63\% & 4\% & 3.70 & 60\% & 10\% \\
2 & 4.66 & 67\% & 67\% & 3.67 & 71\% & 71\% \\
3 & 2.38 & 67\% & 68\% & 2.23 & 71\% & 72\% \\
4 & 1.38 & 82\% & 68\% & 1.33 & 84\% & 72\% \\
5 & 1.33 & 83\% & 83\% & 1.29 & 84\% & 84\% \\
6 & 1.03 & 83\% & 83\% & 1.03 & 84\% & 84\% \\
7 & 1.03 & 83\% & 83\% & 1.03 & 84\% & 84\% \\
8 & 1.01 & 83\% & 83\% & 1.00 & 84\% & 84\% \\
9 & 0.99 & 83\% & 83\% & 0.97 & 84\% & 84\% \\
10 & 0.96 & 83\% & 83\% & 0.96 & 84\% & 84\% \\
11 & 0.91 & 83\% & 83\% & 0.91 & 84\% & 84\% \\
12 & 0.89 & 83\% & 83\% & 0.89 & 84\% & 84\% \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Modal periods and cumulative participation mass ratios for refined twisted model (2\({}^{\circ}\)) with and without outrigger. The comparative analysis confirms the trends and percentage performance improvements observed in Section 2. However, refined models consistently exhibit higher efficiency ratios, although differences remain within 5%, likely due to a more detailed modeling of the outrigger system and its connections to the MRF. This refinement, in fact, allows for a more accurate capture of the intricate structural interaction between the braced outrigger system and the belt-truss assembly, as well as load-transfer mechanisms and component stiffness contributions. Conversely, simplified models, designed for broad parametric studies, inherently approximate these complex interactions since only the contribution of outriggers was modeled for practical reasons. A pronounced improvement is generally observed in lateral displacement compared to the reduction in the core base bending moment, a result consistent with observations made on simplified models. Notably, the refined twisted model (W) shows a significant overall improvement. This can be associated with a more accurate representation of the belt-truss effect, which contributes significantly to the torsional stiffness of the structure, \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model** & **Approach** & \(\Delta\mathbf{d_{roof}}\) & \(\Delta\mathbf{M_{b}}\) \\ \hline R & Simplified & 40.2\% & 27.9\% \\  & Refined & 40.4\% & 28.2\% \\ T\({}_{4}\) & Simplified & 29.8\% & 24.9\% \\  & Refined & 31.7\% & 20.4\% \\ W\({}_{2}\) & Simplified & 40.2\% & 30.6\% \\  & Refined & 44.3\% & 25.0\% \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Comparative analysis of outrigger efficiency ratios for simplified and refined models.