• Structural Engineering and Mechanics
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• v.67 no.4
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• pp.327-336
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• 2018

In this study, an efficient damage index is proposed to identify multiple damage cases in structural systems using the concepts of frequency response function (FRF) matrix and strain energy of a structure. The index is defined based on the change of strain energy of an element due to damage. For obtaining the strain energy stored in elements, the columnar coefficients of the FRF matrix is used. The new indicator is named here as frequency response function strain energy based index (FRFSEBI). In order to assess the performance of the proposed index for structural damage detection, some benchmark structures having a number of damage scenarios are considered. Numerical results demonstrate that the proposed index even with considering noise can accurately identify the actual location and approximate severity of the damage. In order to demonstrate the high efficiency of the proposed damage index, its performance is also compared with that of the flexibility strain energy based index (FSEBI) provided in the literature.

• Steel and Composite Structures
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• v.10 no.4
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• pp.331-348
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• 2010

Ample research effort has been oriented into developing damage indices with the aim of estimating in a reasonable manner the consequences, in terms of structural damage and deterioration, of severe plastic cycling. Although several studies have been devoted to calibrate damage indices for steel and reinforced concrete members; currently, there is a challenge to study and calibrate the use of such indices for the practical evaluation of complex structures. The aim of this paper is to introduce an energy-based damage index for multi-degree-of-freedom steel buildings that accounts explicitly for the effects of cumulative plastic deformation demands. The model has been developed by complementing the results obtained from experimental testing of steel members with those derived from analytical studies regarding the distribution of plastic demands on several steel frames designed according to the Mexico City Building Code. It is concluded that the approach discussed herein is a promising tool for practical structural evaluation of framed structures subjected to large energy demands.

• Structural Engineering and Mechanics
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• v.10 no.1
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• pp.37-51
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• 2000

Identification of damage location based on modal measurement is an important problem in structural health monitoring. The damage index method that attempts to evaluate the changes in modal strain energy distribution has been found to be effective under certain circumstances. In this paper two damage index methods using bending strain energy and shear strain energy have been evaluated for numerous cases at different locations and degrees of damage. The objective is to evaluate the feasibility of the damage index method to localize the damage on large span concrete bridge. Finite element models were used as the test structures. Finally this method was used to predict the damage location in an actual structure, using the results of a modal survey from a large concrete bridge.

• Structural Engineering and Mechanics
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• v.46 no.1
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• pp.75-90
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• 2013

In order to identify damage of highway bridges rapidly, a method for damage identification using dynamic response of bridge induced by moving vehicle and static test data is proposed. To locate damage of the structure, displacement energy damage index defined from the energy of the displacement response time history is adopted as the indicator. The displacement response time histories of bridge structure are obtained from simulation of vehicle-bridge coupled vibration analysis. The vehicle model is considered as a four-degree-of-freedom system, and the vibration equations of the vehicle model are deduced based on the D'Alembert principle. Finite element method is used to discretize bridge and finite element model is set up. According to the condition of displacement and force compatibility between vehicle and bridge, the vibration equations of the vehicle and bridge models are coupled. A Newmark-${\beta}$ algorithm based professional procedure VBAP is developed in MATLAB, and used to analyze the vehicle-bridge system coupled vibration. After damage is located by employing the displacement energy damage index, the damage extent is estimated through the least-square-method based model updating using static test data. At last, taking one simply supported bridge as an illustrative example, some damage scenarios are identified using the proposed damage identification methodology. The results indicate that the proposed method is efficient for damage localization and damage extent estimation.

• Steel and Composite Structures
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• v.36 no.1
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• pp.31-45
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• 2020

The purpose of this study is to develop an effective iterative two-stage method (ITSM) for structural damage identification of offshore platform structures. In each iteration, a new damage index, Modal Energy-Based Damage Index (MEBI), is proposed to help effectively locate the potential damage elements in the first stage. Then, in the second stage, the beetle antenna search (BAS) algorithm is used to estimate the damage severity of these elements. Compared with the well-known particle swarm optimization (PSO) algorithm and genetic algorithm (GA), this algorithm has lower computational cost. A modal energy based objective function for the optimization process is proposed. Using numerical and experimental data, the efficiency and accuracy of the ITSM are studied. The effects of measurement noise and spatial incompleteness of mode shape are both considered. All the obtained results show that under these influences, the ITSM can accurately identify the true location and severity of damage. The results also show that the objective function based on modal energy is most suitable for the ITSM compared with that based on flexibility and weighted natural frequency-mode shape.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2006.04a
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• pp.167-174
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• 2006

In this paper, the applicability of strain data to a strain-energy-based damage evaluation methodology in detecting damage in a beam-like structure is demonstrated. For the purpose of this study, one of the premier damage evaluation methodology based on modal amplitudes, the damage index method, is expanded to accomodate strain data, and the numerical and experimental verifications are conducted using numerical and experimental data. To compare the relative performance of damage detection, the damage evaluation using acceleration data is also performed for the same damage scenarios. The experimental strain and acceleration data are extracted from laboratory static and dynamic tests. The numerical and experimental studies show that the strain data as well as acceleration data can be utilized in detecting damage.

• Smart Structures and Systems
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• v.15 no.1
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• pp.227-244
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• 2015

This study develops a two stage procedure to identify the structural damage based on the optimized artificial neural networks. Initially, the modal strain energy index (MSEI) is established to extract the damaged elements and to reduce the computational time. Then the genetic algorithm (GA) and artificial neural networks (ANNs) are combined to detect the damage severity. The input of the network is modal strain energy index and the output is the flexural stiffness of the beam elements. The principal component analysis (PCA) is utilized to reduce the input variants of the neural network. By using the genetic algorithm to optimize the parameters, the ANNs can significantly improve the accuracy and convergence of the damage identification. The influence of noise on damage identification results is also studied. The simulation and experiment on beam structures shows that the adaptive parameter selection neural network can identify the damage location and severity of beam structures with high accuracy.

• Smart Structures and Systems
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• v.25 no.1
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• pp.1-22
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• 2020

The modal strain energy method is one of the efficient methods for detecting damage in the structures. Due to existing some limitations in real-world structures, sensors can only be located on a limited number of degrees of freedom (DOFs) of a structure. Therefore, the mode shape values in all DOFs of structures cannot be measured. In this paper, a modified modal strain energy based index (MMSEBI) is introduced to locate damaged elements of structures when a limited number of sensors are used. The proposed MMSEBI is based on the reconstruction of mode shapes using Improved Reduction System (IRS) method. Therefore, in the first step by employing IRS method, mode shapes in slave degrees of freedom are estimated by those of master degrees of freedom. In the second step, the proposed MMSEBI is used to located damage elements. In order to evaluate the efficiency of the proposed method, two numerical examples are considered under different damage patterns considering the measurement noise. Moreover, the universal threshold based on statistical hypothesis testing principles is applied to damage index values. The results show the effectiveness of the proposed MMSEBI for the structural damage localization when comparing with the available damage index named MESBI. The results demonstrate that the presented method can be used as a practical strategy for structural damage identification, especially when a limited number of sensors are installed on the structure. Finally, the combination of MMSEBI and IRS method can provide a reliable tool to identify the location of damage accurately.

• Earthquakes and Structures
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• v.8 no.3
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• pp.485-509
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• 2015

This paper presents the experimental results obtained by applying frequency-domain structural health monitoring techniques to assess the damage suffered on a special type of damper called Web Plastifying Damper (WPD). The WPD is a hysteretic type energy dissipator recently developed for the passive control of structures subjected to earthquakes. It consists of several I-section steel segments connected in parallel. The energy is dissipated through plastic deformations of the web of the I-sections, which constitute the dissipative parts of the damper. WPDs were subjected to successive histories of dynamically-imposed cyclic deformations of increasing magnitude with the shaking table of the University of Granada. To assess the damage to the web of the I-section steel segments after each history of loading, a new damage index called Area Index of Damage (AID) was obtained from simple vibration tests. The vibration signals were acquired by means of piezoelectric sensors attached on the I-sections, and non-parametric statistical methods were applied to calculate AID in terms of changes in frequency response functions. The damage index AID was correlated with another energy-based damage index -ID- which past research has proven to accurately characterize the level of mechanical damage. The ID is rooted in the decomposition of the load-displacement curve experienced by the damper into the so-called skeleton and Bauschinger parts. ID predicts the level of damage and the proximity to failure of the damper accurately, but it requires costly instrumentation. The experiments reported in this paper demonstrate a good correlation between AID and ID in a realistic seismic loading scenario consisting of dynamically applied arbitrary cyclic loads. Based on this correlation, it is possible to estimate ID indirectly from the AID, which calls for much simpler and less expensive instrumentation.

• Computers and Concrete
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• v.8 no.3
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• pp.311-325
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• 2011

Nowadays, many engineers believe that hybrid structures with reinforced concrete central core walls and perimeter steel frames offer an economical method to develop the strength and stiffness required for seismic design. As a result, a variety of such structures have recently been applied in actual construction. However, the performance-based seismic design of such structures has not been investigated systematically. In the performance-based seismic design, quantifying the seismic damage of complete structures by damage indices is one of the fundamental issues. Four damage states and the final softening index at each state for high-rise hybrid structures are suggested firstly in this paper. Based on nonlinear dynamic analysis, the relation of the maximum inter-story drift, the main structural characteristics, and the final softening index is obtained. At the same time, the relation between the maximum inter-story drift and the maximum roof displacement over the height is also acquired. A double-variable index accounting for maximum deformation and cumulative energy is put forward based on the pushover analysis. Finally, a case study is conducted on a high-rise hybrid structure model tested on shaking table before to verify the suggested quantities of damage indices.