Parameter Design for Viscous Dampers to Near-fault Cable-stayed Bridge Based on Equivalent Damping Ratio

Abstract

In order to investigate the simplified design method for damper installed on cable-stayed bridge in near-fault zones, this paper proposed two-particle model for cable-stayed bridge and established the differential equations of motion. Parameter design formula for linear viscous damper is derived based on the concept of equivalent damping ratio, parameter design formula for nonlinear viscous damper is also deducted by equivalent linearization method. In the end, a single tower cable-stayed bridge is cited to verify accuracy of the formulations. Introduction After the Loma Prieta earthquake, Northridge earthquake, Izmit earthquake, Kobe earthquake and Chi-Chi earthquake, many disaster investigations showed that destruction of buildings in near-fault areas are more severe than the areas far away from fault [1] to , researches found the presence of strong seismic pulse in near-fault earthquake recordings, and that large velocity pulse can cause significant seismic response to structure several times higher than that of ordinary earthquake, which is the main reason for collapse or damage of bridge in near-fault areas. With the planning and construction of the transportation network, cable-stayed bridges are inevitably to be built in the vicinity of the fault. Cable-stayed bridge are mostly adopted the floating system, which has long natural period with the advantages of seismic energy dissipation. On the other hand, there is no restraint device between tower and girder in floating system, therefore the girder is floating with a large seismic displacement in longitudinal direction, resulting in expansion joints damages, girder collision and falling off. While, viscous damper is used widely as a displacement-limit device, it has the effect of energy dissipation, increasing the capacity of seismic and wind resistance for bridge, and controlling the displacement of girder. The mechanical model of hydraulic viscous dampers can be expressed by Equation 1: sgn( ) F C α n n = ⋅ ⋅ (1) Where F is the damper force, C is the damping coefficient determined by experiment, α is the damping exponent, whose value is generally in the range of 0.2~1.0 in engineering, v is relative velocity of the damper, sgn is the sign function. Determining reasonable damper parameters needs repeat calculation by finite element analysis, which is clearly unrealistic in the preliminary design stage of bridge engineering. Due to the lack of parameter design and research on cable-stayed bridge with viscous damper, this paper proposed a design formulation for viscous damper based on the concept of equivalent damping ratio, and an example is made to validate this method. Formulation derivation Firstly the concept of equivalent damping ratio is introduced. If the supplemental vicious damper on structure is considerd as additional damping, then the equivalent damping ratio is consist of the structural inherent damping ratio and the additional damping ratio (Equation 2), ξ , 0 ξ , d ξ represent the system equivalent damping ratio, structural inherent damping ratio and additional damping ratio (related to viscous dampers), respectively. Most domestic and international studies suggest that International Conference on Materials, Environmental and Biological Engineering (MEBE 2015) © 2015. The authors Published by Atlantis Press 612 structural damping ratio is basically fixed in elastic state, for example, 5% for concrete arch bridge, 3% for cable-stayed bridge and 2% for suspension bridge . For cable-stayed bridge with supplemental viscous damper, structural damping ratio is 3%, then additional damping ratio can be obtained according to the target equivalent damping ratio of the system, thus the design formula for parameters of viscous damper can be solved. 0 d = ξ ξ ξ + (2) Parameter design formulation for linear viscous damper. When cable-stayed bridge is installed with viscous dampers, the structure presents significant feature of two-particle system because of the interaction between the girder and the tower (Fig.1). In order to establish a relationship between damper parameters and target equivalent damping ratio of the system, a simplified two degree of freedom model for cable-stayed bridge is proposed. By using the equivalent modal method, many scholars have studied the simplification of bridge tower, the tower of cable-stayed bridge can be simplified to a single degree of freedom model with no distributional mass but concentrate mass at the top, the girder is regarded as another independent particle. According to the calculation diagram of cable-stayed bridge, the differential equations of motion of two-particle system in longitudinal direction is written as follows: