PSI - Issue 78

Riccardo Piazzon et al. / Procedia Structural Integrity 78 (2026) 230–236

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1. Introduction Earthquakes pose significant challenges to urban infrastructure, thus requiring advanced seismic design strategies for steel structures. Knee-braced frames (KBFs) have gained interest due to their ability to dissipate seismic energy through knee elements, safeguarding primary structural components such as beams and columns [1], [2]. Nomenclature A Cross-sectional area of dissipator (mm 2 ) F � Yield force of dissipator (N) K � Initial stiffness of dissipator (N/mm) E Young’s modulus of steel (MPa) h Story height (mm) b Span width (mm) Passive energy dissipation is a key aspect of structural control, where devices absorb portions of seismic input energy to reduce responses and protect members. Knee braces in KBFs function as such devices, dissipating energy through hysteretic behavior under displacement. These systems are popular in seismic design for their low maintenance and cost-effective implementation [3]. The addition of knee braces is known to lessen seismic responses in structures. For designing KBFs, selecting optimal brace locations plays a crucial role in minimizing responses and meeting performance goals. While distributing braces uniformly across stories might seem simple, it can be inefficient and suboptimal, as it increases stiffness in certain levels and may amplify demands in adjacent ones. Consequently, optimizing brace placement has become a research priority. Over recent decades, various methods have advanced optimal device placement. Early approaches, like heuristic integer programming [4] or maximizing fundamental mode damping [5], often yielded local optima tied to initial guesses. Sequential searches [6], parametric analyses [7], topological methods [8], simulated annealing [9], and gradient-based techniques [10, 11] have been explored, with some tested on multi-story frames [12, 13]. However, for discrete problems with fixed brace numbers, exhaustive enumeration of positions and orientations is impractical due to the vast search space. Genetic algorithms (GAs) are well-suited for such challenges, handling non-continuous objectives and discrete spaces effectively [14–16]. GA has been applied to damper layout and parameters [17, 18], including for high-rises under wind [19] and with performance indices [20]. Given the nonlinear characteristics of knee braces, structures with them require time-history analysis for accurate evaluation. The primary aim of this research is to determine the optimal knee brace topology (positions and orientations) that maximizes dissipated energy. We employ GA to address this, evaluating configurations under specific constraints and earthquake loading. While traditional optimization efforts have often focused on adjusting structural parameters, recent studies have shifted towards topological optimization to enhance seismic performance. Studies on passive energy dissipation devices such as viscous dampers have shown that the strategic placement of these elements can significantly increase energy dissipation and reduce structural response under seismic loading, a concept directly applicable to optimizing the presence and orientation of knee braces [4]. Similarly, research on steel plate shear walls has demonstrated that optimizing their placement improves stiffness and energy dissipation providing a parallel strategy for enhancing frame resilience [21]. Building on these insights, this study applies topological optimization to a 4-story, 3-span KBF, employing a genetic algorithm (GA) to determine the optimal configuration of exactly six knee braces, aiming to maximize hysteretic energy dissipation under the L’Aquila 2009 earthquake [22]. Recent experimental and numerical investigations have deepened the understanding of KBF behavior. Studies by Gusella et al. have explored the dissipative properties of steel components, analysing effects like pinching in braces and cyclic energy absorption through experimental validation [23], [24]. Meanwhile, Piazzon et al. developed a simplified numerical model to capture nonlinear response of a knee bracing system with a dissipative fuse, using