• Structural Engineering and Mechanics
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• v.88 no.1
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• pp.53-65
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• 2023

With the gradual implementation of long-span suspension bridges into high-speed railway operations, the main beam's bending stiffness contribution to the live load response permanently grows. Since another critical control parameter of railway suspension bridges is the beam-end rotation angle, it should not be ignored by treating the main beam deflection as the only deformation response. To this end, the current study refines the existing method of the main cable shape and simply supported beam bending moment analogy. The bending stiffness of the main beam is considered, and the main beam's analytical expressions of deflection and rotation angle in the whole span are obtained using the cable-beam deformation coordination relationship. Taking a railway suspension bridge as an example, the effectiveness and accuracy of the proposed analytical method are verified by the finite element method (FEM). Comparison of the results by FEM and the analytical method ignoring the main beam stiffness revealed that the bending stiffness of the main beam strongly contributed to the live load response. Under the same live load, as the main beam stiffness increases, the overall deformation of the structure decreases, and the reduction is particularly noticeable at locations with original larger deformations. When the main beam stiffness is increased to a certain extent, the stiffening effect is no longer pronounced.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2011.04a
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• pp.477-480
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• 2011

장경간 케이블 교량은 과도한 변위 발생 등의 이유로 엄격한 안전성 및 사용성이 요구되는 철도교량에서는 제한적으로 적용되고 있다. 즉, 철도교량으로서 요구되는 주행안전성과 승차감을 만족하기 위해서는 면밀한 분석이 필요하다. 본 연구에서는 교량/열차 상호작용 해석을 수행하여 열차에서의 응답을 통해 교량 상을 주행하는 열차의 주행안전성 및 승차감을 직접적으로 평가하고자 하였다. 즉, 중앙경간 300m의 현수교를 주행하는 KTX 열차에 대하여 열차 내부의 가속도와 윤중감소율을 구해 평가하는 방법을 취하였다. 또한, 이동 열차하중과 지진하중이 동시에 작용할 경우를 고려한 교량/열차/지진 상호작용해석을 수행하여 지진 시의 응답을 평가하였다.

• Wind and Structures
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• v.12 no.6
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• pp.479-504
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• 2009

Structural health monitoring (SHM) systems have been recently embraced in long span cable-supported bridges, in which buffeting-induced stress monitoring is one of the tasks to ensure the safety of the bridge under strong winds. In line with this task, this paper presents a SHM-oriented finite element model (FEM) for the Tsing Ma suspension bridge in Hong Kong so that stresses/strains in important bridge components can be directly computed and compared with measured ones. A numerical procedure for buffeting induced stress analysis of the bridge based on the established FEM is then presented. Significant improvements of the present procedure are that the effects of the spatial distribution of both buffeting forces and self-excited forces on the bridge deck structure are taken into account and the local structural behaviour linked to strain/stress, which is prone to cause local damage, are estimated directly. The field measurement data including wind, acceleration and stress recorded by the wind and structural health monitoring system (WASHMS) installed on the bridge during Typhoon York are analyzed and compared with the numerical results. The results show that the proposed procedure has advantages over the typical equivalent beam finite element models.

• Wind and Structures
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• v.4 no.6
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• pp.505-518
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• 2001

Shantou Bay Bridge is the first long-span suspension bridge in China. Because of its location near the Shantou Seaport and its exposure to high typhoon winds, wind-resistant studies are necessary to be made. In this paper, critical flutter wind speeds and buffeting responses of this bridge at its operation and main construction stages are investigated. The Buffeting Response Spectrum method is first briefly presented. Then the sectional model test is carried out to directly obtain the critical flutter wind speed and to identify the flutter derivatives, which are adopted for the later analysis of the buffeting responses using the Buffeting Response Spectrum method. Finally the aeroelastic full bridge model is tested to further investigate the dynamic effects of the bridge. The results from the tests and the computations indicate that the flutter and buffeting behaviors of the Shantou Bay Bridge are satisfied.

• Structural Engineering and Mechanics
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• v.19 no.3
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• pp.261-279
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• 2005

The hot spot stress approach is usually adopted in the fatigue design and analysis of tubular welded joints. To apply the hot spot stress approach for fatigue evaluation of long span suspension bridges, the FEM is used to determine the hot spot stress of critical fatigue location. Using the local finite element models of the Tsing Ma Bridge, typical joints are developed and the stress concentration factors are determined. As a case for study, the calculated stress concentration factor is combined with the nominal representative stress block cycle to obtain the representative hot spot stress range cycle block under traffic loading from online health monitoring system. A comparison is made between the nominal stress approach and the hot spot stress approach for fatigue life evaluation of the Tsing Ma Bridge. The comparison result shows that the nominal stress approach cannot consider the most critical stress of the fatigue damage location and the hot spot stress approach is more appropriate for fatigue evaluation.

• Wind and Structures
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• v.24 no.5
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• pp.447-464
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• 2017

The flutter instability is one of the most important themes need to be carefully investigated in the design of long-span bridges. This study takes the central-slotted ideal thin flat plate as an object, and examines the characteristics of unsteady surface pressures of stationary and vibrating cross sections based on computational fluid dynamics (CFD) simulations. The flutter derivatives are extracted from the surface pressure distribution and the critical flutter wind speed of a long span suspension bridge is then calculated. The influences of angle of attack and the slot ratio on the flutter performance of central-slotted plate are investigated. The results show that the critical flutter wind speed reduces with increase in angle of attack. At lower angles of attack where the plate shows the characteristics of a streamlined cross-section, the existence of central slot can improve the critical flutter wind speed. On the other hand, at larger angles of attack, where the plate becomes a bluff body, the existence of central slot further reduces the flutter performance.

• Wind and Structures
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• v.27 no.3
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• pp.149-161
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• 2018

A reliability analysis method is proposed in this paper based on the maximum entropy (MaxEnt) principle in which constraints are specified in terms of the fractional moments instead of integer moments. Then a multiplicative dimensional reduction method (M-DRM) is introduced to compute the fractional moments. The method is applicable for both explicit and implicit limit state functions of complex structures. After two examples illustrate the accuracy and efficiency of this method in comparison to the Monte Carlo simulation (MCS), the method is used to analyze the flutter reliability of suspension bridge. The results show that the empirical formula method in which the limit state function is explicitly represented as a function of variables is only a too conservative estimate for flutter reliability analysis but is not accurate adequately. So it is not suitable for reliability analysis of bridge flutter. The actual flutter reliability analysis should be conducted based on a finite element method in which limit state function is implicitly represented as a function of variables. The proposed M-DRM provide an alternate and efficient way to analyze a much more complicated flutter reliability of long span suspension bridge.

• Earthquakes and Structures
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• v.18 no.5
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• pp.625-635
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• 2020

Suspension bridges have the extended in plan configuration which makes them prone to dynamic events like earthquake. The longer span lead to more flexibility and slender of them. So, control systems seem to be essential in order to protect them against ground motion excitation. Tuned mass damper or in brief TMD is a passive control system that its efficiency is practically proven. Moreover, its parameters i.e. mass ratio, tuning frequency and damping ratio can be optimized in a manner providing the best performance. Meta-heuristic optimization algorithm is a powerful tool to gain this aim. In this study, TMD parameters are optimized in different-length suspension bridges in three distinct cases including 3, 4 and 5 TMDs by observer-teacher-learner based algorithm under a complete set of ground motions formed from both near-field and far-field instances. The Vincent Thomas, Tacoma Narrows and Golden Gate suspension bridges are selected for case studies as short, mean and long span ones, respectively. The results indicate that All cases of used TMDs result in response reduction and case 4TMD can be more suitable for bridges in near and far-field conditions.

• Structural Monitoring and Maintenance
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• v.2 no.1
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• pp.77-93
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• 2015

The idea of using measured dynamic characteristics for damage detection is attractive because it allows for a global evaluation of the structural health and condition. However, vibration-based damage detection for complex structures such as long-span cable-supported bridges still remains a challenge. As a suspension or cable-stayed bridge involves in general thousands of structural components, the conventional damage detection methods based on model updating and/or parameter identification might result in ill-conditioning and non-uniqueness in the solution of inverse problems. Alternatively, methods that utilize, to the utmost extent, information from forward problems and avoid direct solution to inverse problems would be more suitable for vibration-based damage detection of long-span cable-supported bridges. The auto-associative neural network (ANN) technique and the probabilistic neural network (PNN) technique, that both eschew inverse problems, have been proposed for identifying and locating damage in suspension and cable-stayed bridges. Without the help of a structural model, ANNs with appropriate configuration can be trained using only the measured modal frequencies from healthy structure under varying environmental conditions, and a new set of modal frequency data acquired from an unknown state of the structure is then fed into the trained ANNs for damage presence identification. With the help of a structural model, PNNs can be configured using the relative changes of modal frequencies before and after damage by assuming damage at different locations, and then the measured modal frequencies from the structure can be presented to locate the damage. However, such formulated ANNs and PNNs may still be incompetent to identify damage occurring at the deck members of a cable-supported bridge because of very low modal sensitivity to the damage. The present study endeavors to enhance the damage identification capability of ANNs and PNNs when being applied for identification of damage incurred at deck members. Effort is first made to construct combined modal parameters which are synthesized from measured modal frequencies and modal shape components to train ANNs for damage alarming. With the purpose of improving identification accuracy, effort is then made to configure PNNs for damage localization by adapting the smoothing parameter in the Bayesian classifier to different values for different pattern classes. The performance of the ANNs with their input being modal frequencies and the combined modal parameters respectively and the PNNs with constant and adaptive smoothing parameters respectively is evaluated through simulation studies of identifying damage inflicted on different deck members of the double-deck suspension Tsing Ma Bridge.

• Wind and Structures
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• v.10 no.1
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• pp.1-22
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• 2007

The suppression of aerodynamic response of long-span suspension bridges during erection and after completion by using single TMD and multi TMD is presented in this paper. An advanced finite-element-based aerodynamic model that can be used to analyze both flutter instability and buffeting response in the time domain is also proposed. The frequency-dependent flutter derivatives are transferred into a time-dependent rational function, through which the coupling effects of three-dimensional aerodynamic motions under gusty winds can be accurately considered. The modal damping of a structure-TMD system is analyzed by the state-space approach. The numerical examples are performed on the Akashi Kaikyo Bridge with a main span of 1990 m. The bridge is idealized by a three-dimensional finite-element model consisting of 681 nodes. The results show that when the wind velocity is low, about 20 m/s, the multi TMD type 1 (the vertical and horizontal TMD with 1% mass ratio in each direction together with the torsional TMD with ratio of 1% mass moment of inertia) can significantly reduce the buffeting response in vertical, horizontal and torsional directions by 8.6-13%. When the wind velocity increases to 40 m/s, the control efficiency of a multi TMD in reducing the torsional buffeting response increases greatly to 28%. However, its control efficiency in the vertical and horizontal directions reduces. The results also indicate that the critical wind velocity for flutter instability during erection is significantly lower than that of the completed bridge. By pylon-to-midspan configuration, the minimum critical wind velocity of 57.70 m/s occurs at stage of 85% deck completion.