# Parametric Analysis of Outrigger Systems for High-Rise Buildings with Different Geometric Shapes
## 1 Introduction
Belttrusses are often employed to optimize axial force distribution across perimeter columns, reduce corner deflections at outrigger locations, and mitigate differential axial deformations (i.e., shortening and elongation) within the columns [17; 18]. Essentially, the belt-truss ties the perimeter columns together, while the outrigger engages them with the central core. To ensure adequate flexural and shear stiffness, outriggers and belt-trusses are typically erected to a depth of one or two stories using steel, concrete, or composite materials. Unless explicitly defined otherwise, the combined outrigger and belt-truss system will be referred to as the \"outrigger system\" for the remainder of this paper. Figure 1 provides a schematic representation of a multi-level outrigger system integrated within an MRF structure with a central core. Key components labeled on the right-hand side include the following: core shear walls (primary vertical load-bearing elements), horizontal outrigger arms extending from the core at multiple levels and rigidly connected to outer perimeter columns, and a belt-truss connecting perimeter columns at outrigger levels. Core-outrigger systems offer practical advantages in high-rise construction, including flexible exterior column spacing and simplified perimeter beam-column connections, enabling the construction of exceptionally tall structures, potentially exceeding 150 stories [15]. A primary design consideration, however, is the reduced floor area at the outrigger level, which often dictates their placement on mechanical floors. Yet, the number and placement of outriggers are critical design constraints that significantly influence the structural response to lateral load [19; 20]. Extensive research has focused on the optimization of these parameters for enhanced performance. Studies have generally found optimal single-outrigger positions around mid-height [21; 22; 23; 24], while multi-outrigger systems suggest placements at approximately one-third and two-thirds of the building height [23; 25] or equidistant from the base [26]. The parametric analysis by [PERSON] and [PERSON] [27] further confirmed these trends, noting the superior drift and moment minimization achieved with a single mid-height outrigger and providing specific optimal placements for up to three outriggers. [PERSON] and [PERSON] [28] also found that tapering core and column sections necessitates an upward shift in the optimal outrigger position due to increased stiffness demands at the upper levels. Subsequent research has explored the influence of additional factors (such as lateral loading, column stiffness, span length, outrigger flexural stiffness, and building height) on the optimal number of outriggers. These studies indicate diminishing returns beyond four outriggers [29] and suggest two to three for effective drift control [30]. Furthermore, [PERSON] and [PERSON] [31]'s investigation on steel outriggers highlighted the dependence of single- and double-outrigger effectiveness on their vertical position and the adverse impact of increasing height-to-width ratios on lateral stiffness in composite buildings. Recognizing the complexity of outrigger system configurations, recent research emphasizes the need for optimized topology and size design for efficient structures. Key findings reveal that increasing the number of outriggers generally reduces top drift, inter-story drift, and core base moment, albeit with decreasing efficiency for each additional level [32; 33; 34; 35]. Figure 1: Schematic of multi-level outrigger and belt-truss system. In this context, the comprehensive review by [PERSON] et al. [36] provides guidelines on the optimum design of outrigger systems, illustrating the impact of design variables on the structural response. Despite extensive research having explored outrigger systems in tall buildings, primarily focusing on parameters influencing efficacy and optimal vertical placement, studies addressing complex geometries remain limited.