# Parametric Analysis of Outrigger Systems for High-Rise Buildings with Different Geometric Shapes
## 2 Simplified Approach for Outrigger Systems
### Parametrization of the Core-Column-Outrigger System  
This section explores the effectiveness of outrigger systems in mitigating displacement and stress demands in complex-shaped tall buildings subjected to uniformly distributed lateral load. A parametric analysis was performed by varying the building geometric attributes, the outrigger-to-core relative stiffness, and the number and location of outriggers along the height. Given the large number of variables, simplified numerical models were preferred in lieu of computationally intensive, detailed models. The equivalent models were derived from the conceptualization of actual 3D models, as shown in Figure 2.  
A 50-story reference building was considered with a 40 \(\times\) 40 m square plan and a 4 m story height. The primary lateral load-resisting system comprises an RC MRF structure and a central square RC core with a 20 m side length and 1.2 m wall thickness. The core is made with C50/60 concrete. Six 1.5 \(\times\) 1.5 m RC perimeter columns are positioned along each building side. The structure incorporates a secondary interior system consisting of two-story-deep outriggers. Linear elastic material behavior was assumed for all structural elements. The inner core was idealized as a vertical cantilever Euler-Bernoulli beam fixed at the base to capture its primary flexural stiffness (Figure 2). This simplification is a common approach in the preliminary design and analysis of tall buildings, effectively representing the core's global behavior under lateral loading (e.g., ([PERSON] et al., 2018)). Outriggers were modeled as horizontal, perfectly rigid arms extending from the core to the perimeter columns. This idealization primarily represents their function in inducing axial forces within these columns to counteract overturning moments, thereby retaining the fundamental core-to-column load-transfer mechanism. Notwithstanding the inherent flexibility of actual outrigger members, their principal role as stiff connecting elements renders the rigid link assumption a justifiable simplification for the assessment of overall structural system behavior, particularly within the context of parametric studies where relative stiffness constitutes a key variable (e.g., ([PERSON] et al., 2018)). It is acknowledged that these idealizations inherently exclude second-order effects and localized phenomena such as differential axial shortening between the core and perimeter columns due to elastic deformation, as well as potential shear lag in the core and flexural deformations in the outriggers. However, the scope of this simplified model is specifically intended for a preliminary parametric investigation of the outrigger effectiveness across a range of complex geometric configurations, before more detailed analyses are warranted. Two equivalent columns represent the aggregate stiffness and load-carrying capacity of the perimeter columns. The cross-sectional properties of these equivalent columns were calibrated to ensure that the lateral stiffness of the simplified model approximated that of the detailed model. By focusing on essential structural elements and their interactions, in fact, the simplified model effectively provides valuable insights into the outrigger system's global behavior and its influence on displacement and stress demands under lateral loading. While more complicated models, incorporating outrigger flexibility and detailed column representation, could capture local effects, this simplified approach provides a pragmatic balance between accuracy and computational efficiency, making it well suited for the parametric investigation undertaken in this study. To avoid adding unnecessary complexity to the general problem, the core and equivalent columns were modeled with uniform cross-sections and material properties throughout their height. The simplified model was subjected to a uniformly distributed lateral load (q) of 150 kN/m applied along the full height of the core. For the tilted model, lateral forces were applied in the direction of tilt.