# Parametric Analysis of Outrigger Systems for High-Rise Buildings with Different Geometric Shapes
## 2 Simplified Approach for Outrigger Systems
### Results and Discussion
Beyond this threshold, the curves flatten, indicating comparable performance with increasing outrigger stiffness (approximately 5%). As previously noted, outrigger system efficacy in twisted models exhibits a strong inverse correlation with twist rate. Outrigger benefits diminish with increasing twist, and beyond a 3\({}^{\circ}\) twist, outrigger effectiveness is significantly reduced. Beyond a stiffness ratio of 3, relative differences range from 5% to 0%, depending on the outrigger's location. Figure 8: _Cont._  
Figure 7: Normalized bending moments for the analyzed structures. Based on the outcomes provided so far, two key interpretations can be drawn. First, a mid-height outrigger location provides a reasonable compromise between enhanced lateral stiffness and material consumption. In general, a two-outrigger system appears to be more effective than a single outrigger in reducing core bending moments and top displacements. However, this might be attributable to the adoption of uniform cross-sections for the equivalent outrigger beams across the model typologies, thus endowing two-outrigger configurations with inherently greater stiffness. As observed by [PERSON] et al. [60], optimal outrigger placement strongly depends on the design objective: top outriggers minimize wind-induced drift, bottom outriggers reduce overturning, and mid-height outriggers reduce bending moments. Consequently, outrigger placements at two-thirds and one-third of the building height are anticipated to maximize both displacement and core base bending moment reductions. However, for a single outrigger, the optimal location--where \"optimal\" denotes the configuration that minimizes material consumption while maximizing structural performance--can be reasonably identified at mid-height even for complex-shaped tall structures. Second, outrigger systems are more effective for regular and tilted configurations than for twisted geometries, with efficacy decreasing as geometric complexity increases. Specifically, outrigger systems demonstrate comparable lateral stiffness enhancement in regular and tilted configurations. [PERSON] [37; 38] attributes the superior performance of tilted structures to a triangulation effect within the core-column-outrigger system. The tilt induces a large, complex triangular geometry, which facilitates a more efficient load-transfer mechanism. Lateral forces acting on the tilted structure try to deform this triangle but are redirected along the core, columns, and outriggers, primarily as axial forces--compression and tension--rather than bending moments arising from non-tilted structures. Increased tilt angles further optimize this triangular geometry, improving lateral load resistance. On the other hand, outrigger systems exhibit a marked reduction in effectiveness within highly twisted tall buildings, resulting in only marginal improvements to lateral stiffness. This performance degradation stems from several factors. Primarily, the inherent geometry of twisted configurations causes complex load-transfer mechanisms, disrupting the efficient force redistribution observed in regular and tilted structures. Also, the triangulation effect, which facilitates efficient load transfer in tilted structures, is not replicable within twisted configurations. Secondly, the planar operational mechanism of outriggers proves conflicting with the rotational deformation modes of twisted buildings. Indeed, these structures are susceptible to significant torsional demands under lateral loading, demands that outriggers, primarily designed to enhance flexural stiffness, are ill equipped to counteract. Lastly, the twist introduces stiffness discontinuities along the building's vertical axis, impeding the uniform distribution of forces and thereby limiting outrigger effectiveness.