PSI - Issue 78

Maria Maglio et al. / Procedia Structural Integrity 78 (2026) 153–160

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1. Introduction Seismic protection is a critical aspect of structural engineering, aimed at improving the resilience of buildings during seismic events. Over the years, various techniques have been developed to mitigate structural damage and enhance safety. Among the most promising innovations are the FREEDAM (FREE from DAMage) connections, which enable damage-free seismic performance by allowing controlled frictional sliding at beam-to-column joints (Piluso et al., 2022). These systems offer high energy dissipation while reducing residual deformations and repair costs (Maglio et al., 2022). Recent studies have proposed probabilistic design approaches to further optimize their seismic performance in steel moment-resisting frames (Maglio et al., 2024). Comparative analyses have confirmed their superior behaviour over traditional moment connections in terms of both energy dissipation and damage control (Maglio et al., 2021). Recent advances in supplementary energy dissipation systems have emphasized the integration of bracing within structural frames to enhance stiffness and energy dissipation. Efficient performance requires sufficient bracing stiffness to transfer energy effectively to dissipative devices. While increased stiffness can reduce displacements, it may also raise accelerations and internal forces due to a shorter natural period. As noted by Swain et al. (2016), combining braces with appropriate energy dissipation devices helps mitigate both displacements and forces, making this approach especially suitable for retrofitting existing structures. However, optimal design demands a precise balance of stiffness and dissipation capacity to avoid inefficiencies or non-activation of devices, while also meeting cost-effectiveness criteria (Zhang et al., 2023). Since the 1980s, extensive research has focused on reducing seismic vulnerability through bracing systems, with diagonal and chevron configurations being the most studied and widely used. Their dominance is linked to both engineering practice and experimental focus. More recently, attention has shifted toward toggle-brace-damper (TBD) systems, which enhance dissipative efficiency by amplifying damper displacements, however their full operational characteristics have yet to be completely understood. Hanson and Soong (2001) examined displacement amplification devices to address the challenge of small displacements, which can render viscous dampers ineffective. Following this, several geometric configurations of TBD systems were patented. These include the “ scissor-jack ” design proposed by Taylor, and the “ upper toggle ” , “ lower toggle ” and “ reverse toggle ” configurations introduced by Constantinou et al. (2001). These configurations were validated through cyclic tests and shake table experiments on single-degree-of-freedom (SDOF) steel frames. Building on these developments, McNamara and Huang (2006) implemented Constantinou et al.'s patented TBD systems in a 39-story building in Boston. Their analysis revealed a critical insight: the stiffness of the knee braces significantly affects the efficiency of the damping system. Supporting this observation, Hwang et al. (2005) demonstrated the importance of modifying brace stiffness to improve TBD performance beyond what theoretical and laboratory analyses had previously shown. Meanwhile, Shao and Miyamoto (2002) used TBD systems to mitigate torsional irregularities in reinforced concrete shear wall structures. This introduction provides an overview of the current state of research and practice in seismic protection, with a specific focus on toggle-brace-damper systems. While significant progress has been made, many aspects remain to be fully explored, offering numerous opportunities for future research and innovation in this field. The objective of the present study is to explore the influence of the axial behaviour of braces in various scissor toggle configurations through a series of numerical analyses conducted in SAP2000. This toggle brace damper typology was selected due to its inherent ability to amplify the displacement imposed on the dissipative device, thereby enhancing energy dissipation efficiency compared to conventional bracing systems. 2. Theoretical aspects of Toggle-Brace Damper systems 2.1. Definition of the amplification factor Toggle-brace system is a novel configuration for energy dissipation devices, based on a toggle mechanism that amplifies the displacement experienced by the damper relative to the structural inter-storey displacement. This amplification is quantified by a parameter known as amplification factor , which depends on the geometry of the toggle linkage. While theoretically the amplification can be substantial, practical values typically range between 2.0 and 5.0. The relationship between the amplification factor and the inter-storey displacement can be expressed as follows: = ∙ (1)