## 5 Conclusions  
The behavior of added damping systems is largely dependent on the flexibility of elements connecting the damper with the main structure; these include brace extenders, damping units and other auxiliary elements such as gusset plates, bolts, pins, clevises, etc. The elements are connected in series, so the overall stiffness is dominated by the most flexible element in the set. Current engineering practice neglects the influence of the auxiliary elements and favors an estimate of the system stiffness based solely on the bracing element. This is partly motivated by the limited amount of available stiffness measurements performed on complete sets. In this work, previously published experimental data have been used to estimate that the actual stiffness of the set lies between 50% and 25% of the stiffness based purely on the bracing element. The implications of this result are studied through a numerical study on a 5-storey frame, equipped with different added damping systems, and subjected to different seismic intensity levels, in which the added damping system stiffness is consecutively scaled by 1, 0.5 and 0.25, and results for reduced and unreduced stiffness are compared. The sensitivity of the variables is defined according to their variation with damping stiffness as \"small\" (less than 10%), \"large\" (more than 30%) and \"moderate\" (in between). These results show that:  
Considering the average throughout all storeys:  
1. Relative energy input, damper shear and column axial force show a small sensitivity to the reduction in damping system stiffness. 2. Residual drift, absolute acceleration and plastic strain energy dissipated by frame elements show a large sensitivity to the reduction in damping system stiffness. Figure 15: Scatter plots of ratios for several variables versus the parameter \(k_{x}\)/\(k_{d}\), for Ground Motion Set ESB at intensity level C; (**a**) drift; (**b**) residual drift; (**c**) absolute acceleration; (**d**) energy dissipated by damper; (**e**) storey shear; (**f**) damper shear; (**g**) beam moment; (**h**) column moment. 3. For non-linear dampers and/or high damping ratios: storey shear, column moment, beam rotation and column rotation show a large sensitivity to reduction in damping system stiffness. 4. All other variables show a moderate sensitivity to reduction in damping system stiffness. Considering the height-wise distribution of results:
5. At the bottom part of the frame, only residual drift, plastic strain energy and column rotation are highly sensitive to reduction in damping system stiffness. 6. At the top part of the frame all variables are highly sensitive to variation in damping system stiffness, except energy input, column axial force and damper shear. The main goal of the inclusion of added viscous dampers is damage control; the study shows that three key variables related to damage (residual drift, absolute acceleration and plastic strain energy dissipated by main frame elements) are largely dependent on an accurate evaluation of the added damping system stiffness. Moreover, other relevant variables for damage control (drift, beam and column rotation, beam and column moment) also show a moderate to large dependency on this parameter. Thus, the main conclusion of this study is the need of experimental work to characterize the stiffness of added damping systems. In the absence of more accurate information at the design stage, it seems cautious to perform analyses with a reduced Maxwell stiffness based on a moderate fraction (0.25 to 0.50) of the brace extender stiffness. As most elements in the set are currently provided by the damping unit manufacturer, it would be convenient if tests were performed on damping systems (including all auxiliary elements whose stiffness cannot be reliably estimated) and the stiffness data published as part of the damper technical information.