# Parametric Analysis of Outrigger Systems for High-Rise Buildings with Different Geometric Shapes
## 1 Introduction  
The rapid population growth since the early 20 th century and increasing urban density, driven by rural-to-urban migration, have been primary catalysts for vertical urban expansion [1]. This demographic trend, alongside advancements in high-performance materials, construction technologies, and digital resources, has accelerated the global proliferation of high-rise buildings [2, 3, 4]. Historically, early skyscrapers prioritized efficient land utilization, maximizing usable floor space and minimizing structural weight for cost andmaterial efficiency. Nowadays, these structures often serve as symbols of economic power and prestige, driving a competitive pursuit of the tallest and most iconic designs [3; 5]. Contemporary architecture, indeed, increasingly features complex-shaped tall buildings, which embody a synthesis of aesthetic, aerodynamic, and structural principles. However, as building tallness increases, a \"premium for height\" must be paid due to amplified horizontal wind forces. Consequently, a paradigm shift from traditional structural systems to more efficient alternatives is required to withstand increased lateral demands. The critical demand for enhanced strength, stiffness, and stability has motivated innovative research on next-generation structural systems, exploring geometric unit cells for both facade grids [6; 7; 8; 9] and spatial configurations [10]. Exhibiting high structural efficiency coupled with geometric versatility for non-orthogonal architectures, grid-like or tessellated typologies (such as Dia-grid, Penta-grid, Hexa-grid, Octa-grid, and Voronoi-grid) represent viable alternatives for lateral load-resisting systems of tall buildings with complex geometries. More recently, research efforts are increasingly directed towards the evaluation of optimal structural topologies aiming to identify designs that maximize performance-to-weight ratios. In this context, structural optimization methodologies constitute an effective tool for enhancing the design of tall buildings and identifying structurally efficient and innovative configurations, as demonstrated by application in multi-story frame structures [11; 12]. A comprehensive review of prevalent structural solutions for tall buildings was conducted by [PERSON] and [PERSON] [13]. Their survey underscored the potential of core-outrigger systems for tall, super-tall, and mega-tall buildings. Generally speaking, lateral forces (whether from wind or seismic loading) induce both shear and bending stresses that structural systems must resist [14]. Primary lateral load-resisting systems, such as moment-resisting frames (MRFs) and core shear walls, are commonly utilized; however, they often lack sufficient lateral stiffness in high-rise buildings [15]. This has motivated the integration of supplementary secondary interior load-resisting systems, of which outrigger systems are a prominent example. Outriggers are stiff, deep structural members--typically configured as auxiliary beams or trusses--that rigidly connect the high-rise building's inner core to its perimeter columns. Under lateral loading, the outrigger system acts as a stiff horizontal cantilever, effectively restraining the core rotation by redistributing a portion of its overturning moment as additional axial forces in the perimeter columns. The mobilization of these members promotes the core's stability [4]. The resulting tension-compression couple (with tension in the upwind and compression in the downwind columns) generates a resisting moment that counteracts core deformation. As observed by [PERSON] [16], this mechanism increases the overall flexural stiffness while maintaining the building's shear capacity largely unchanged. The enhanced rigidity yields reduced lateral displacement and bending moment demands, stabilizes the core's base overturning moments, and improves occupant comfort.