Simplified design of nonlinear damper parameters and seismic responses for long-span cable-stayed bridges with nonlinear viscous dampers

doi:10.1007/s11709-024-1033-y

2024, Vol. 18

Issue (7) : 1103-1116 https://doi.org/10.1007/s11709-024-1033-y

Simplified design of nonlinear damper parameters and seismic responses for long-span cable-stayed bridges with nonlinear viscous dampers

Huihui LI^1,², Lifeng LI³(

), Rui HU³, Meng YE³

¹. College of Civil and Transportation Engineering, Shenzhen University, Shenzhen 518060, China
². Guangdong Provincial Key Laboratory of Durability for Marine Civil Engineering, Shenzhen University, Shenzhen 518060, China
³. College of Civil Engineering, Hunan University, Changsha 410082, China

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Abstract

Viscous dampers are widely used as passive energy dissipation devices for long-span cable-stayed bridges for mitigation of seismic load-induced vibrations. However, complicated finite element (FE) modeling, together with repetitive and computationally intensive nonlinear time-history analyses (NTHAs) are generally required in conventional design methods. To streamline the preliminary design process, this paper developed a simplified longitudinal double degree of freedom model (DDFM) for single and symmetric twin-tower cable-stayed bridges. Based on the proposed simplified longitudinal DDFM, the analytical equations for the relevant mass- and stiffness-related parameters and longitudinal natural frequencies of the structure were derived by using analytical and energy methods. Modeling of the relationship between the nonlinear viscous damper parameters and the equivalent damping ratio was achieved through the equivalent linearization method. Additionally, the analytical equations of longitudinal seismic responses for long-span cable-stayed bridges with nonlinear viscous dampers were derived. Based on the developed simplified DDFM and suggested analytical equations, this paper proposed a simplified calculation framework to achieve a simplified design method of nonlinear viscous damper parameters. Moreover, the effectiveness and applicability of the developed simplified longitudinal DDFM and the proposed calculation framework were further validated through numerical analysis of a practical cable-stayed bridge. Finally, the results indicated the following. 1) For the obtained fundamental period and longitudinal stiffness, the differences between results of the simplified longitudinal DDFM and numerical analysis were only 2.05% and 1.5%, respectively. 2) Relative calculation errors of the longitudinal girder-end displacement and bending moment of the bottom tower section of the bridge obtained from the simplified longitudinal DDFM were limited to less than 25%. 3) The equivalent damping ratio of nonlinear viscous dampers and the applied loading frequency had significant effects on the longitudinal seismic responses of the bridge. Findings of this study may provide beneficial information for a design office to make a simplified preliminary design scheme to determine the appropriate nonlinear damper parameters and longitudinal seismic responses for long-span cable-stayed bridges.

Keywords cable-stayed bridges viscous dampers simplified analytical model equivalent damping ratio seismic mitigation

Corresponding Author(s): Lifeng LI

Just Accepted Date: 13 June 2024 Online First Date: 09 July 2024 Issue Date: 06 August 2024

Cite this article:

Huihui LI,Lifeng LI,Rui HU, et al. Simplified design of nonlinear damper parameters and seismic responses for long-span cable-stayed bridges with nonlinear viscous dampers[J]. Front. Struct. Civ. Eng., 2024, 18(7): 1103-1116.

URL:

https://academic.hep.com.cn/fsce/EN/10.1007/s11709-024-1033-y
https://academic.hep.com.cn/fsce/EN/Y2024/V18/I7/1103

Fig.1 The simplified analytical models for single-tower cable-stayed bridges: (a) the whole bridge model; (b) the simplified longitudinal DDFM.

Fig.2 The simplified analytical models for symmetric twin-tower cable-stayed bridges: (a) the whole bridge model; (b) half bridge model; (c) the simplified longitudinal DDFM.

Fig.3 Deformation diagram of the half bridge model.

Fig.4 Computation diagram of the longitudinal stiffness of the tower.

Fig.5 Computation diagram of the simplified longitudinal DDFM considering the equivalent damping effect.

Fig.6 The proposed simplified calculation framework for long-span cable-stayed bridges.

Fig.7 Schematic diagram of the bridge: (a) bridge elevation; (b) cross-section of the girder; (c) elevation of the tower (unit: m).

Fig.8 FE model of the bridge: (a) FE model; (b) first order mode shape.

Tab.1 Results of the fundamental period and longitudinal stiffness of the girder obtained from the numerical results and the suggested simplified longitudinal DDFM

Fig.9 Deformation diagram of the half bridge model of the bridge.

Fig.10 Comparisons of the relative errors of displacements, bending moments, and damping forces with respect to the applied loading period under different equivalent damping ratios: (a) longitudinal girder-end displacements; (b) damping forces; (c) bending moments of the bottom tower section.

Fig.11 Comparisons of the displacements, bending moments, and damping forces with respect to the applied loading period under different equivalent damping ratios: (a) longitudinal girder-end displacements; (b) damping forces; (c) bending moments of the bottom tower section.

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