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Research Papers

Identifying Cable Tension Loss and Deck Damage in a Cable-Stayed Bridge Using a Moving Vehicle

[+] Author and Article Information
Shih-Hsun Yin1

Department of Civil Engineering, National Taipei University of Technology, Taipei 10608, Taiwan, R.O.C.shihhsun@ntut.edu.tw

Chung-Yu Tang

Department of Civil Engineering, National Taipei University of Technology, Taipei 10608, Taiwan, R.O.C.

1

Corresponding author.

J. Vib. Acoust 133(2), 021007 (Mar 03, 2011) (11 pages) doi:10.1115/1.4002128 History: Received September 23, 2009; Revised May 30, 2010; Published March 03, 2011; Online March 03, 2011

This paper presents a computational study on a new method of detecting multiple simultaneous damages in a cable-stayed bridge by use of the analysis of the vertical dynamic response of a vehicle passing the bridge. First, the study uses a finite-element method to simulate the vehicle cable-stayed bridge system. Then, the vertical vibration interaction between the bridge and the vehicle is solved by a time-step integration scheme. In this research, we consider that two kinds of damage including cable tension loss and deck damage may occur simultaneously at different locations. The differences between the vertical displacement responses of a vehicle passing the damaged bridge and the healthy bridge are sampled and called the relative displacement response vector of the vehicle. The proper orthogonal decomposition (POD) is utilized to decompose the relative displacement response vector of the vehicle passing the bridge with unknown multiple damages into an optimal set of basis vectors formed from the ones of the vehicle moving over the known damaged bridges. The associated system parameters variation with the unknown multiple damages can be reconstructed further. Discussions are given concerning the feasibility and limitation of the proposed detection technique as well as directions for future research.

Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

The schematic plots of the transition from a single cable supporting deck to equivalent continuously distributed springs supporting deck

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Figure 2

A cable-deck element model

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Figure 3

A sprung mass representing a vehicle acts on a cable-deck element

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Figure 4

Flow chart for demonstrating the proposed damage detection method

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Figure 5

The structural model of the Kao Ping River Bridge in Taiwan

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Figure 6

The bridge is divided into 31 sections based on the cable-stayed layout

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Figure 7

The vertical displacement of the car-body of the vehicle varies with the location where the vehicle acts along the healthy bridge

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Figure 8

The relative vertical displacements of the car-body of the vehicle passing the damaged bridge where 0.25% reduction of spring stiffness (Ks2∼Ks14 and Km17∼Km30) and moment of inertia of deck (Is1∼Is15 and Im16∼Im31) takes place independently.

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Figure 9

The eigenvalues of the correlation matrix based on the relative vertical displacement vectors for all 58 sample damage cases (z¯1z¯2⋯z¯58)

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Figure 10

The eigenvalues of the correlation matrix based on the relative vertical displacement vectors for all 58 sample damage cases (z¯1z¯2⋯z¯58) and one more sample damage case z¯59 (e.g., 0.25% reduction in Km28–Km30 and Im28–Im30).

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Figure 11

The relative displacement of the car-body of the vehicle passing the damaged bridge with 0.1% loss of Km28–Km30 and Im28–Im30 for case A

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Figure 12

The relative displacement of the car-body of the vehicle passing the damaged bridge with 0.1% loss of Ks6–Ks8 and 0.2% loss of Im23–Im25 for case B

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Figure 13

The relative displacement of the car-body of the vehicle passing the damaged bridge with 0.2% loss of Is2, Is8, and Is14 and 0.1% loss of Km17, Km23, Km24, and Km30 for case C

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Figure 14

The relative displacement of the car-body of the vehicle passing the damaged bridge with 0.5% loss of Km28–Km30 and Im28–Im30 for case D

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Figure 15

The cable tension versus the equivalent continuously distributed spring stiffness for the eleventh cable in the bridge model shown in Fig. 5

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