PSI - Issue 78

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

156

balanced by the damping system. By analyzing the equilibrium in the undeformed configuration, the force in each diagonal member is given by: = /2 (5) where is the axial force in the brace and is the axial force in the damper. 3. Parametric analysis of Scissor Toggle Damper configurations To evaluate the performance of various scissor toggle damper configurations, a numerical study was conducted on a single-story, single-bay steel frame equipped with a dissipative bracing system. The objective was to identify the optimal geometry by varying the inclination angles of the diagonal members, parameters that directly influence the amplification factor. The structural frame is composed of S355 steel members, with IPE 300 profiles used for the beam and HE 320B profiles for the columns. The finite element model was developed using SAP2000 (2000). Boundary conditions include fixed supports at the base, while all internal connections are modeled as pinned joints. Diaphragm constraints are applied at the beam ends to enforce uniform lateral displacements at the external nodes. The Scissor Toggle Damper has been introduced into the model using a nonlinear link element to simulate its dissipative behaviour. Specifically, the damper is modeled by creating a link element through the “Define Link Properties” command in the modeling s oftware. The energy dissipation device is represented by a Multilinear Plastic link, defined using a user-specified force – deformation relationship to capture the nonlinear hysteretic behaviour of the damper. Directional properties are assigned accordingly: in this case, the 1 direction is activated, as it represents the primary axis along which the damper dissipates energy. A custom multilinear force-deformation relationship is defined in the 1 direction based on eq. (6), where the displacement is computed as: 1 =( ∙ )/( ) (6) where is the design axial force in the damper, is the effective length of the damper link, is the Young’s modulus of the damper material, and is the cross-sectional area of the damper. The forces values defined in the link model correspond to the design force . A horizontal load of 10 is applied at the top of the frame to perform a pushover analysis. For scissor toggle configurations, the amplification factor decreases as the angle increases, due to its proportionally to . Conversely, increases with decreasing values of the internal diagonal angle . However, a minimum threshold for must be respected, not only for geometric compatibility and device installation, but also to avoid behaviour converging toward that of a conventional diagonal brace, which is not the intended mechanism. Notably, the axial force in the diagonals is the same across all configurations and remains closely linked to the internal inclination angle.

Table 1. Different configurations for Scissor Toggle Damper

( ° ) ( ° ) (-)

Diagonal rod profile dxs (mm)

Configuration

C1 C2 C3

9.00 9.00

51.00 30.00 30.00

3.97 5.47 3.23

D273x5.6 D219.1x5 D219.1x5

15.00

Three scissor toggle configurations were analyzed to assess how performance varies with the connection location of the diagonal members, either to the beam or directly to the beam-column joint. The first configuration (C1), proposed by Constantinou et al. (2003), features a connection to the beam. Two additional configurations (C2 and C3) connect the diagonals directly to the beam-column joint but differ in the value of ϑ , selected within the range recommended in the literature ( 9° < < 15°) . Table 1 summarizes the angles and amplification factors assigned to each configuration and the section profile of the assigned diagonals. To capture the bidirectional nature of seismic excitation, two loading scenarios were considered: one in which the toggle mechanism is loaded at its connection point to the frame (“rx - Configuration”), and another where the force acts in the opposite direction (“sx Configuration”). These configurations are illustrated in Fig. 2.