Seismic Analysis of Bridges with nonlinear FVDs using effective damping

2 1 Introduction Fluid viscous dampers (FVDs) are passive energy dissipation devices that can reduce the dynamic response of a structure when subjected to seismic forces, and have been used in the last years in civil engineering structures, such as for damping of the longitudinal vibration of bridges under seismic actions. With the use of FVDs it is possible to add high damping values to structures, with values of the effective damping ratio �� up to 20-30 %, avoiding the need to develop plastic hinges to dissipate energy [3]. Using FVDs on a bridge it is possible to reduce its longitudinal displacement due to seismic actions, and therefore the maximum forces in the bridge’s structural members that depend on it. When compared to other passive energy dissipation devices, such as hysteretic dampers, friction dampers or viscoelastic dampers, FVDs have the advantage of not adding stiffness to the structures to which they are applied and not having any residual deformation after the seismic event [3]. Figure 1.1 shows a set of compression-only nonlinear FVDs in a bridge’s abutment, parallel to its longitudinal axis. Figure 1.1 – Set of OTP 400/600 compression- only nonlinear FVDs in Rion-Antirion bridge [4] The force-velocity relation in these devices may be described by expression (1.1): �� �� (�� ) = �� �� × sgn(�� ) × |�� | �� (1.1) where �� �� and α depend on the characteristics of the FVD, and �� is the relative velocity of the FVD’s ends. For seismic actions, which last for a few seconds, but require a big amount of energy dissipation, nonlinear FVDs having α<1 have a good performance because they can dissipate big amounts of energy, being therefore used in bridges to dampen the longitudinal vibrations due to seismic actions [4]. In bridge’s with FVDs the elastic force is out of phase with these devices damping forces on the deck’s ends near the abutments, which means that in such type of bridge there is always a force restraining the deck’s movement in the longitudinal direction during an earthquake [5]. The FVDs in the bridge’s abutments considered in this work are assumed to be placed in the horizontal, parallel to the deck’s longitudinal axis, as shown in figure 1.2. Figure 1.2 – Lateral view of a bridge with FVDs on its abutments, adapted from [6]