# Frontiers of Structural and Civil Engineering

 Front. Struct. Civ. Eng.    2020, Vol. 14 Issue (3) : 722-730     https://doi.org/10.1007/s11709-020-0624-5
 RESEARCH ARTICLE
Multiple damage detection in complex bridges based on strain energy extracted from single point measurement
1. Department of Structural Engineering, Road, Housing & Urban Development Research Center, Tehran 13145-1696, Iran
2. Department of Structural Engineering, Faculty of Civil and Environmental Engineering, Tarbiat Modares University, Tehran 14115-397, Iran
3. Department of Civil Engineering, Faculty of Engineering, University of Maragheh, Maragheh 55136-553, Iran
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 Abstract Strain Energy of the structure can be changed with the damage at the damage location. The accurate detection of the damage location using this index in a force system is dependent on the degree of accuracy in determining the structure deformation function before and after damage. The use of modal-based methods to identify damage in complex bridges is always associated with problems due to the need to consider the effects of higher modes and the adverse effect of operational conditions on the extraction of structural modal parameters. In this paper, the deformation of the structure was determined by the concept of influence line using the Betti-Maxwell theory. Then two damage detection indicators were developed based on strain energy variations. These indices were presented separately for bending and torsion changes. Finite element analysis of a five-span concrete curved bridge was done to validate the stated methods. Damage was simulated by decreasing stiffness at different sections of the deck. The response regarding displacement of a point on the deck was measured along each span by passing a moving load on the bridge at very low speeds. Indicators of the strain energy extracted from displacement influence line and the strain energy extracted from the rotational displacement influence line (SERIL) were calculated for the studied bridge. The results show that the proposed methods have well identified the location of the damage by significantly reducing the number of sensors required to record the response. Also, the location of symmetric damages is detected with high resolution using SERIL. Corresponding Author(s): Farhad DANESHJOO Just Accepted Date: 22 April 2020   Online First Date: 21 May 2020    Issue Date: 13 July 2020
 Cite this article: Alireza ARABHA NAJAFABADI,Farhad DANESHJOO,Hamid Reza AHMADI. Multiple damage detection in complex bridges based on strain energy extracted from single point measurement[J]. Front. Struct. Civ. Eng., 2020, 14(3): 722-730. URL: http://journal.hep.com.cn/fsce/EN/10.1007/s11709-020-0624-5 http://journal.hep.com.cn/fsce/EN/Y2020/V14/I3/722
 Fig.1  3D finite element model of the bridge. Fig.2  The geometric specification of the bridge’s central pier and deck. Tab.1  The equivalent stiffness of Intermediate piers and abutment Tab.2  Location and damage characteristics on the bridge deck Tab.3  The intensity of the simulated damage in accordance with the effective inertia of the deck Fig.3  The defined damage location and the deck response record points in the model. Fig.4  Detecting the damages in the bridge's deck using SEDIL index. Fig.5  Detecting the damages in the bridge’s deck using SERIL index.