PSI - Issue 78

Maria Maglio et al. / Procedia Structural Integrity 78 (2026) 153–160 155 where is the relative displacement of the device along its axis and is the amplification factor; is the inter-storey displacement. Similarly, the axial force in the damper, , is related to the horizontal force exerted on the structural frame by eq. (2) indicating that the toggle mechanism not only amplifies displacements but also reduces the force transmitted to the damper by the same factor. = ∙ (2) Consequently, the amplification factor can be defined either as the ratio between the displacement of the damper and the inter-storey displacement, or, equivalently, as the ratio between the horizontal force acting on the structure and the axial force transmitted to the dissipative device: = / = / (3) For a given top displacement induced by the design seismic action, a higher amplification factor leads to a larger displacement of the dissipative device, thereby enhancing the energy dissipation capacity of the structure. Simultaneously, as the damper displacement increases, the force it must resist decreases proportionally. This makes toggle-brace systems particularly efficient and suitable for application in stiff structural configurations. The damper displacement can be derived from the kinematic relationships and the geometric configuration of the toggle-brace mechanism. 2.2. Scissor Toggle configuration The scissor configuration of toggle-brace dampers (Fig. 1) represents an advanced seismic energy dissipation system, specifically designed to improve damper performance in stiff structures or in buildings with limited architectural space. Developed by Constantinou and Sigaher (2003), this system evolves from the traditional toggle brace mechanism by introducing a pantograph-like layout that amplifies the relative displacement of the damper compared to the inter-storey drift. This amplification allows greater energy dissipation with shorter damper strokes and lower force demands, resulting in more compact, efficient, and cost-effective devices. Thanks to its vertically compact geometry, the scissor toggle configuration is particularly advantageous in buildings where space constraints or architectural preservation are critical. The displacement amplification not only enhances damping efficiency but also enables the use of smaller, lower-capacity devices, making the system suitable for both seismic and wind applications in rigid-frame structures.

Fig. 1. Scissor Toggle configuration with acting forces.

In addition to new constructions, the scissor configuration is highly suitable for seismic retrofitting of existing buildings. Its geometric adaptability allows installation in confined areas, such as stairwells or between structural bays, while maintaining high effectiveness even under small structural drifts, which are typical in reinforced concrete buildings. Its minimal architectural impact further contributes to its appeal, allowing seismic upgrades without compromising the building’s function or aesth etics. For this configuration, the amplification factor is expressed as: = Ψ/ (4) where Ψ and ϑ are geometric parameters defined by the layout of the scissor mechanism. The forces acting on the bracing members and the damper rod are illustrated in Fig. 2 . It is important to note that the frame operates as a mechanism, in which the force represents the horizontal component of the inertial force