Damping reduction factors and code-based design equation for structures using semi-active viscous dampers

This study uses a semi-active viscous damper with three different control laws to reshape the structural hysteresis loop and mitigate structural response, referred to as 1–4, 1–3 and 2–4 devices, respectively. The 1–4 control law provides damping in all four quadrants of the force-displacement graph (it behaves like a standard viscous damper), the 1–3 control law provides resisting forces only in the first and third quadrants, and the 2–4 control law provides damping in the second and fourth quadrants. This paper first outlines the linear single degree of freedom structural performance when the three types of semi-active viscous dampers are applied. The results show that simultaneous reduction in both displacement and base-shear demand is only available with the semi-active 2–4 device. To enable guidelines for adding a 2–4 device into the design procedure, damping reduction factors (RFξs) are developed, as they play an important role and provide a means of linking devices to design procedures. Three methods are presented to obtain RFξ and equivalent viscous damping of a structure with a 2–4 semi-active viscous damper. In the first method, the relationship between RFξ and the damping of a semi-active structure can be obtained by calculating the area under the force-deformation diagram. The second and third method modified the Eurocode8 formula of RFξ and smoothed results from analysis, respectively. Finally, a simple method is proposed to incorporate the design or retrofit of structures with simple, robust and reliable 2–4 semi-active viscous dampers using standard design approaches.