Use of Ritz method for damage detection of reinforced and post-tensioned concrete beams

Damage-induced changes in modal characteristics can be detected using experimental modal analysis. In this article, based on changes in natural frequency, mode shapes, and damping ratios, a methodology for detecting damage location and severity is presented. The damage was induced by application of point load at half span location on the reinforced and post-tensioned concrete beams. The load was gradually increased to obtain different crack patterns to be used in simulation of damage scenarios. Experimental modal analysis was performed on the undamaged and damaged beams. The natural frequency and mode shapes were used to determine the location of damage. The approach is developed at an element level with a conventional finite element (FE) model by Ritz method, which is called Ritz damage detection method (RDDM). The mathematical model for both damped and undamped damaged structures have been established through the eigenvalue equations. The singular value decomposition (SVD) technique is used for determination of damage or sound index. These indexes are sensitive to the change of dynamic characteristics due to damages. This approach is applied to five simply supported post-tensioned concrete beams. The numerical results show that the exact location and severity of damage for different simulated damage scenarios could be efficiency found by the present methodology.     

基于模态应变能的结构损伤识别研究

文中应用有限元分析软件ANSYS10.0建立一个平面刚架结构模型。通过有限元模态分析获得未损伤结构与损伤结构的固有频率和振型。应用单元模态应变能法对模型进行损伤定位。结果证明这种方法对于平面刚架的损伤识别是有效的。     

Effect of the model updating on the earthquake behavior of steel storage tanks

In this paper, effect of the finite element model updating on the earthquake behavior of steel storage tanks considering fluid-structure interaction is investigated. For this purpose, a cylindrical steel storage tank filled some liquid fuel oil located in Trabzon, Turkey is selected as an example. Initial finite element model of the storage tank is developed by ANSYS software and dynamic characteristics (natural frequencies, and mode shapes) are determined analytically. Ambient vibration tests are conducted on the storage tank under natural excitations to obtain dynamic characteristics (natural frequencies, mode shapes and damping ratios), experimentally. Peak Picking technique in the frequency domain is used to extract experimental dynamic characteristics. When the analytically and experimentally identified dynamic characteristics are compared to each other, some differences are found between both results. To minimize these differences, initial finite element model of the storage tank is updated according to experimental results using some uncertainties modeling parameters such as elasticity modulus. To investigate the effect of finite element model updating on the earthquake behavior of the storage tank, earthquake analyses are performed before and after model updating. In the earthquake analyses, YPT330 component of 1999 Kocaeli earthquake is selected and applied to the models in the horizontal directions. It is seen from the analyses that the displacements and the stresses after model updating are more effective than the displacements and the stresses before model updating.     

Experimental and analytical system identification of Eynel arch type steel highway bridge

This paper describes a full scale arch type steel highway bridges, its finite element modelling and Operational Modal Analysis. Eynel Highway Bridge which has arch type structural system with a total length of 336 m and located in the Ayvac?k county of Samsun, Turkey is selected as a case study. The bridge connects the villages which are separated with Suat U?urlu Dam Lake. The three dimensional finite element model is constructed using project drawings and an analytical modal analysis is then performed to generate natural frequencies and mode shapes in the three-orthogonal directions. The ambient vibration tests on the bridge deck under natural excitation such as traffic, human walking and wind loads are conducted using Operational Modal Analysis. Sensitive seismic accelerometers are used to collect signals obtained from the experimental tests. To obtain experimental dynamic characteristics, two output-only system identification methods are employed namely, Enhanced Frequency Domain Decomposition method in the frequency domain and Stochastic Subspace Identification method in time domain. The correlation between the finite element model and experimental results is studied. Good agreement is found between dynamic characteristics in the all measurement test setups performed on the bridge deck. It is demonstrated that the ambient vibration measurements using Enhanced Frequency Domain Decomposition and Stochastic Subspace Identification methods are enough to identify the most significant modes of steel highway bridges. It is seen that there are some differences between analytical and experimental natural frequencies and experimental natural frequencies are generally bigger than the others.     

轻钢-混凝土组合梁的试验研究及非线性有限元分析

针对轻钢-混凝土组合梁这种新的结构形式,本文进行了六个试件的试验研究,分析了构件的破坏形式、荷载-位移曲线、荷载-应变曲线、钢材和混凝土的应变分布及板宽度方向应变分布等。通过试验研究,初步了解了轻钢-混凝土组合梁的特点和各种截面的粘结性能。采用组合梁单元模型,对轻钢-混凝土组合梁进行了非线性有限元分析,理论计算结果与试验结果吻合较好。     

Response surface‐based finite‐element model updating of a historic masonry minaret for operational modal analysis

This study aimed to use the response surface (RS) method for finite element (FE) model updating, using operational modal analysis (OMA). The RS method was utilized to achieve better agreement between the numerical and field‐measured structure response. The OMA technique for the field study was utilized to obtain modal parameters of the selected historic masonry minaret. The natural frequencies and mode shapes were experimentally determined by the enhanced frequency domain decomposition (EFDD) method. The optimum results between the experimental and numerical analyses were found by using the optimization method. The central composite design was used to construct the design of experiments, and the genetic aggregation approach was performed to generate the RS models. After obtaining the RS models, an attempt was made to converge the natural frequency values corresponding to the five‐mode shapes with the frequency values identified by the experimental analysis. ANSYS software was used to perform 3D finite element (FE) modeling of the historic masonry minaret and to numerically identify the natural frequencies and mode shapes of the minaret. The results of the experimental, initial, and updated FE model were compared with each other. Significant differences can be seen when comparing the experimental and analytical results with the initial conditions.     

Vibration response of an elastically point-supported plate with attached masses

Experimentally determined natural frequencies and modes shapes are presented for an elastically point-supported isotropic plate with attached masses under impulsive loading. These results are compared to frequencies and to modes shapes determined from the Rayleigh–Ritz method and a finite element analysis using COMSOL. Accelerometers mounted at three locations on the plate, provide input for ME’Scope Modal Analysis Software to identify frequency peaks and modes shapes. Orthogonal polynomials, which meet free–free plate boundary conditions, are selected as the basis functions used in the Rayleigh–Ritz method. A Mindlin plate theory, adjusted for negligible transverse shear effects, is used in COMSOL. Frequencies and mode shapes for four plate configurations are presented, compared using each method, and indicate good agreement between the numerical, analytical and experimental results.     

Experimental and analytical system identification of Eynel arch type steel highway bridge

This paper describes a full scale arch type steel highway bridges, its finite element modelling and Operational Modal Analysis. Eynel Highway Bridge which has arch type structural system with a total length of 336 m and located in the Ayvacık county of Samsun, Turkey is selected as a case study. The bridge connects the villages which are separated with Suat Uğurlu Dam Lake. The three dimensional finite element model is constructed using project drawings and an analytical modal analysis is then performed to generate natural frequencies and mode shapes in the three-orthogonal directions. The ambient vibration tests on the bridge deck under natural excitation such as traffic, human walking and wind loads are conducted using Operational Modal Analysis. Sensitive seismic accelerometers are used to collect signals obtained from the experimental tests. To obtain experimental dynamic characteristics, two output-only system identification methods are employed namely, Enhanced Frequency Domain Decomposition method in the frequency domain and Stochastic Subspace Identification method in time domain. The correlation between the finite element model and experimental results is studied. Good agreement is found between dynamic characteristics in the all measurement test setups performed on the bridge deck. It is demonstrated that the ambient vibration measurements using Enhanced Frequency Domain Decomposition and Stochastic Subspace Identification methods are enough to identify the most significant modes of steel highway bridges. It is seen that there are some differences between analytical and experimental natural frequencies and experimental natural frequencies are generally bigger than the others.     

Assessment of semi-rigid connections in steel structures by modal testing

In conventional design and analysis, the common assumption is that connections of steel frames are fully rigid or frictionless pinned. However, today, the accepted notion is that the connections of members of a steel structure exhibit semi-rigid characteristics. Semi-rigid connections as well as damage cause changes in the dynamic characteristics of the structures. This study presents an investigation into the determination of the quality of the semi-rigid connections when considering changes in dynamic characteristics of steel structures. The investigations involve three scaled models: columns with box cross-sections, columns with rectangular cross-sections, and a 2D frame. The investigation algorithm first calculates natural frequencies and mode shapes from theoretical modal analyses by assuming the supports and joint connections are fully rigid. Secondly, experimental measurements on the models are performed to obtain natural frequencies, mode shapes and modal damping ratios. Thirdly, to reduce differences between theoretical and experimental results, linear elastic rotational springs are used on supports and joint connections of the analytical model. Finally, the connection percentages of both support and beam-to-column connections are determined using an approach improved depending on the rotational spring stiffness.     

Earthquake analysis of reinorced concrete minarets using ambient vibration test results

This paper describes a Turkish style reinforced concrete minaret, its finite element model, modal testing, finite element model updating and earthquake behaviour, before and after model updating. The minaret of a mosque located in Trabzon, Turkey is selected as an application. A three‐dimensional (3D) model of the minaret and its modal analysis is performed to obtain analytical frequencies and mode shapes using ANSYS finite element program. The ambient vibration tests are conducted on the minaret under natural excitations such as wind effects and human movement. The output‐only modal parameter identification is carried out by Enhanced Frequency Domain Decomposition and Stochastic Subspace Identification methods in Operational Modal Analysis software and in doing so, dynamic characteristics (natural frequencies, mode shapes and damping ratios) are determined. A 3D finite element model of the minaret is updated to minimize the differences between analytical and experimental modal properties by changing some uncertain modelling parameters such as material properties and boundary conditions. The earthquake behaviour of the minaret is investigated using 1992 Erzincan earthquake before and after finite element model updating. Maximum differences in the natural frequencies are reduced from 21% to 8%, and good agreement is found between analytical and experimental natural frequencies. In addition to this, it is realized that finite element model updating is effective on the earthquake behaviour of the minaret. Copyright © 2008 John Wiley & Sons, Ltd.     

下承式钢桁架桥动力特性有限元分析

采用有限元分析软件MIDAS/CIVIL 2010对南昌某下承式钢桁架桥进行离散,建立空间有限元分析模型,并对其进行动力特性分析,得到振型及自振频率等数值,寻求桥梁整体结构的变形规律,并了解结构的实际受力情况和变化规律,是今后的优化设计,谐响应分析,瞬态分析及谱分析等动力学分析的重要起点。     

Finite element studies on profiled steel composite beams

This article is concerned with finite element studies on profiled steel composite beams to investigate their elastic and ultimate load behaviour. Finite element code LUSAS is used to carry out the non-linear analyses to determine the load carrying capacity of the beams. Results from the experimental studies reported by other researchers are first used to assess the accuracy of the finite element modelling. Analyses are carried out thereafter to study different shapes, arrangements and number of steel sheeting ribs. Effects of the parameters such as concrete compressive strength f _c, yield stress f _yp of the profiled steel sheeting, and thickness of the steel sheeting on the ultimate load capacity of the profiled steel composite beams are examined. The results are presented in the form of load-deflection plots and ultimate load values. It is concluded that the ultimate load capacity of the profiled steel composite beams can be predicted with an acceptable accuracy by the proposed finite element modelling. Results show that the load carrying capacity of the beams are influenced by shapes, arrangements and number of ribs. It is also found that compressive strength f _c of the concrete, and yield stress f _yp and thickness of profiled steel sheeting have significant influences on the performance of these beams.     

Vibration-based operational modal analysis of the Mikron historic arch bridge after restoration

This research presents finite element modelling, vibration-based operational modal analysis, and finite element model updating of a restored historic arch bridge. Mikron historic bridge, constructed on F?rt?na River in Rize, Turkey, is the subject of this case study. The General Directorate for Highways of Turkey repaired the bridge's main structural elements, arches, sidewalls, and filler material in 1998. To construct a 3D finite element model of the bridge, ANSYS finite element software estimated the analytical dynamic characteristics. Induced ambient vibrations such as human walking and wind excited the model bridge to allow measurement of the bridge's responses. Enhanced frequency domain decomposition in frequency domain and stochastic subspace identification in time domain methodologies extracted experimental dynamic characteristics. A comparison of the analytical and experimental results showed significant agreement between mode shapes, but some differences in natural frequencies appeared. Consequently, updating the finite element model of the bridge by changing boundary conditions minimised the differences between analytical and experimental natural frequencies. After the finite element model updating process, the differences between natural frequencies declined from 7% to 2%.     

Finite element modelling of cold-formed steel beams under local buckling or combined local/distortional buckling

The finite element (FE) method is capable of solving the complex interactive buckling of cold-formed steel beams allowing for all important governing features such as geometrical imperfections, material nonlinearity, postbuckling, etc.; this is unlikely to be achieved by analytical methods. In this paper, two series of finite element models for buckling behaviour of laterally-restrained cold-formed steel Z-section beams have been developed with special reference to material and geometrical nonlinearities: one to allow for the possibility of combined local/distortional buckling and the other to allow for local buckling only. Four-point bending tests carried out by previous researchers have been used to verify the FE models. A simplified configuration of the test setup has been modelled in ABAQUS. In the local buckling FE models, distortional buckling has been restricted in the member using translational springs applied to the lip/flange corner of the beam. Predictions of load carrying capacity and deformed shapes exhibit excellent agreement with both the results from the more extensive models and laboratory tests. Further papers will exploit the developed FE models to investigate the different forms of buckling that occur in laterally-restrained cold-formed steel beams i.e. local, distortional and combined local/distortional.     

Nonlinear behaviour of unprotected composite slim floor steel beams exposed to different fire conditions

An efficient nonlinear 3D finite element model has been developed to investigate the structural performance of composite slim floor steel beams with deep profiled steel decking under fire conditions. The composite steel beams were unprotected simply supported with different cross-sectional dimensions, structural steel sections, load ratios during fire and were subjected to different fire scenarios. The nonlinear material properties of steel, composite slim concrete floor and reinforcement bars were incorporated in the model at ambient and elevated temperatures. The interface between the structural steel section and composite slim concrete floor was also considered, allowing the bond behaviour to be modelled and the different components to retain its profile during the deformation of the composite beam. Furthermore the thermal properties of the interface were included in the finite element analysis. The finite element model has been validated against published fire tests on unprotected composite slim floor steel beams. The time–temperature relationships, deformed shapes at failure, time–vertical displacement relationships, failure modes and fire resistances of the composite steel beams were evaluated by the finite element model. Comparisons between predicted behaviour and that recorded in fire tests have shown that the finite element model can accurately predict the behaviour of the composite steel beams under fire conditions. Furthermore, the variables that influence the fire resistance and behaviour of the unprotected composite slim floor steel beams, comprising different load ratios during fire, cross-section geometries, beam length and fire scenarios, were investigated in parametric studies. It is shown that the failure of the composite beams under fire conditions occurred for the standard fire curve, but did not occur for the natural fires. The use of high strength structural steel considerably limited the vertical displacements after fire exposure. It is also shown that presence of additional top reinforcement mesh is necessary for composite beams exposed to short hot natural fires. The fire resistances of the composite beams obtained from the finite element analyses were compared with the design values obtained from the Eurocode 4 for composite beams at elevated temperatures. It is shown that the EC4 predictions are generally conservative for the design of composite slim floor steel beams heated using different fire scenarios.     

Machine learning based novelty detection using modal analysis

Among many structural assessment methods, the change of modal characteristics is considered a well‐accepted damage detection method. However, the presence of environmental or operational variations may pollute the baseline and prevent a dependable assessment of the change. In recent years, the use of machine learning algorithms gained interest within structural health community, especially due to their ability and success in the elimination of ambient uncertainty. This paper proposes an end‐to‐end architecture to detect damage reliably by employing machine learning algorithms. The proposed approach streamlines (a) collection of structural response data, (b) modal analysis using system identification, (c) learning model, and (d) novelty detection. The proposed system aims to extract latent features of accessible modal parameters such as natural frequencies and mode shapes measured at undamaged target structure under temperature uncertainty and to reconstruct a new representation of these features that is similar to the original using well‐established machine learning methods for damage detection. The deviation between measured and reconstructed parameters, also known as novelty index, is the essential information for detecting critical changes in the system. The approach is evaluated by analyzing the structural response data obtained from finite element models and experimental structures. For the machine learning component of the approach, both principal component analysis (PCA) and autoencoder (AE) are examined. While mode shapes are known to be a well‐researched damage indicator in the literature, to our best knowledge, this research is the first time that unsupervised machine learning is applied using PCA and AE to utilize mode shapes in addition to natural frequencies for effective damage detection. The detection performance of this pipeline is compared to a similar approach where its learning model does not utilize mode shapes. The results demonstrate that the effectiveness of the damage detection under temperature variability improves significantly when mode shapes are used in the training of learning algorithm. Especially for small damages, the proposed algorithm performs better in discriminating system changes.     

锈蚀钢筋再生混凝土梁力学性能试验研究及ANSYS分析

通过对钢筋通电加速锈蚀的方法,对12根不同钢筋锈蚀率下粗骨料取代率为100%再生混凝土梁的三分点加载试验,分析相同强度条件下不同钢筋直径和锈蚀率的再生混凝土梁力学性能的影响。结果表明:当钢筋锈蚀率小于10%时,钢筋与再生混凝土的粘结强度足以保证两者能够共同工作,此时试验梁发生材料强度破坏模式;当钢筋锈蚀率超过了10%时,钢筋与再生混凝土的粘结强度不足以保证两者共同工作,此时试验梁发生粘结失效破坏模式。基于ANSYS有限元软件对不同钢筋锈蚀率的再生混凝土梁进行模拟分析,并对锈蚀钢筋再生混凝土梁跨中截面的荷载应力关系曲线进行验算,通过有限元结果与试验结果对比,验证了有限元分析模型的可靠性。     

钢板-超高性能混凝土梁有限元分析研究

为了研究钢板-超高性能混凝土(UHPC)组合梁的抗弯性能,在钢板-UHPC-T组合梁方案下,以钢板厚度、钢板强度等级、UHPC抗拉强度和UHPC极限拉应变为参数,利用ABAQUS软件进行了有限元分析。结果表明:钢板厚度和钢板强度等级的改变对组合梁抗弯承载力的提高作用较为明显;UHPC抗拉强度的提高可以适当提高开裂荷载;UHPC极限拉应变的增加可适当提高梁体的延性。     

Finite element modeling of block shear failure in coped steel beams

Block shear is a potential failure mode that is encountered in the connection regions of coped steel beams. Limited experimental studies completed so far have shown that the block shear failure in coped steel beams is a complex phenomenon, which is highly dependent on the number of bolt lines. In this paper, the use of the finite element method in predicting the block shear failure load was studied by making comparisons with experimental findings. The effects of numerical modeling details on load capacity predictions were investigated. In light of these investigations, a finite element analysis methodology has been developed and used to conduct a parametric study. Simplified load capacity prediction equations were developed based on the results of the parametric study and are presented herein.     

Ultimate load carrying capacity of optimally designed steel cellular beams

The objective of the current research is to present ultimate load carrying capacities and finite element analysis of optimally designed steel cellular beams under loading conditions. The tests have been carried out on twelve full-scale non-composite cellular beams. There are three different types of NPI_CB_240, NPI_CB_260 and NPI_CB_280 I-section beams, and four tests have been conducted for each specimen. These optimally designed beams which have beginning span lengths of 3000 mm are subjected to point load acting in the middle of upper flange. The design method for the beams is the harmony search method and the design constraints are implemented from BS 5950 provisions. The last part of the study focuses on performing a numerical study on steel cellular beams by utilizing finite element analysis. The finite element method has been used to simulate the experimental work by using finite element modeling to verify the test results and to investigate the nonlinear behavior of failure modes such as web-post buckling and Vierendeel bending of steel cellular beams.