• Journal of the Computational Structural Engineering Institute of Korea
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• v.18 no.3
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• pp.227-243
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• 2005

This paper presents a hybrid control system combining lead rubber bearings and hydraulic actuators for seismic response control of a cable stayed bridge. Because multiple control devices are operating, a hybrid control system could improve the control performances. However, the overall system robustness may be impacted negatively by additional active control devices. Therefore, a secondary on-off type controller according to the responses of lead rubber bearings is combined with LQG algorithm to improve the controller robustness. Numerical simulation results show that control performances of the hybrid system controlled by an on off type LQG algorithm are improved compared to those of the passive and active control systems and are similar to those of performance oriented hybrid system controlled by a LQG algorithm with the similar peak and normed control forces. Furthermore, it is verified that the hybrid system with an on-off type LQG controller is more robust for stiffness matrix perturbation than conventional hybrid control of system, and there are no signs of instability in the overall system. The proposed control system also maintains the control performance under not only the design earthquakes but also the other earthquakes. Therefore, the hybrid control system using on-off type LQG algorithm could be proposed as an improved control strategy for seismically excited cable-stayed bridges containing many uncertainties.

• Journal of Korean Society of Steel Construction
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• v.15 no.2
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• pp.175-185
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• 2003

The extended tangent stiffness matrices and force-deformation relations of the elastic catenary element were initially derived through the addition of the unstrained length of cables to unknown nodal displacements. A beam-column element was then introduced to model the deck and pylon of cable-stayed bridges. The conventional geometric nonlinear analysis, initial force method, and TCUD method were summarized, with an effective method combining two methods presented to determine the initial shapes of cable-stayed bridges with dead loads. In this combined method, TCUD method was applied to eliminate vertical and horizontal displacements at cable-supported points of decks and on top of pylons, respectively. The initial force method was also adopted to eliminate horizontal and vertical displacements of decks and pylons, Finally, the accuracy and validity of the proposed combined method were demonstrated through numerical examples.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.26 no.5A
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• pp.849-859
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• 2006

This paper presents an extensive robust analysis of a ${\mu}$-controller in the hybrid system for various uncertainties using the benchmark cable-stayed bridge. The overall system robustness may be deteriorated by introducing active devices and the active controller may cause instability due to small margins. Therefore, a ${\mu}$-synthesis method that simultaneously guarantees the performance and stability of the closed-loop system (robust performance) with uncertainties is used for active devices to enhance the robustness in company with the inherent reliability of passive devices. The robustness of the ${\mu}$-synthesis method is investigated with respect to the additional mass on the deck, structural stiffness matrix perturbation, time delay of actuator, and combinations thereof. Numerical simulation results show that the proposed control system has the good robustness without loss of control performances with respect to various uncertainties under earthquakes considered in this study. Furthermore, the control system robustness is more affected by the perturbation of structural stiffness matrix than others considered in this study. Therefore, the hybrid system controlled by a ${\mu}$-synthesis method could be proposed as an improved control strategy for a seismically excited cable-stayed bridge containing many uncertainties.

• Journal of the Earthquake Engineering Society of Korea
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• v.1 no.2
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• pp.1-15
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• 1997

This paper presents substructural identification methods for the assessment of local damages in complex and large structural systems. For this purpose, an auto-regressive and moving average with stochastic input (ARMAX) model is derived for a substructure to process the measurement data impaired by noises. Using the substructural methods, the number of unknown parameters for each identification can be significantly reduced, hence the convergence and accuracy of estimation can be improved. Secondly, the damage index is defined as the ratio of the current stiffness to the baseline value at each element for the damage assessment. The indirect estimation method was performed using the estimated results from the identification of the system matrices from the substructural identification. To demonstrate the proposed techniques, several simulation and experimental example analyses are carried out for structural models of a 2-span truss structure, a 3-span continuous beam model and 3-story building model. The results indicate that the present substructural identification method and damage estimation methods are effective and efficient for local damage estimation of complex structures.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.29 no.1A
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• pp.31-43
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• 2009

In this study, the numerical method is presented, which can consider the various train types and can solve the equations of motion for a vehicle-bridge interaction analysis by non-iteration procedure through formulating the coupled equations of motion. The coupled equations of motion for the vehicle-bridge interaction are solved by the Newmark ${\beta}$ of a direct integration method, and by composing the effective stiffness matrix and the effective force vector according to a analysis step, those can be solved with the same manner of the solving procedure of equilibrium equations in static analysis. Also, the effective stiffness matrix is reconstructed by the Skyline method for increasing the analysis effectiveness. The Cholesky's matrix decomposition scheme is applied to the analysis procedure for minimizing the numerical errors that can be generated in directly calculating the inverse matrix. The equations of motion for the conventional trains are derived, and the numerical models of the conventional trains are idealized by a set of linear springs and dashpots with 16 degrees of freedom. The bridge models are simplified by the 3 dimensional space frame element which is based on the Euler-Bernoulli theory. The rail irregularities of vertical and lateral directions are generated by the PSD functions of the Federal Railroad Administration (FRA). The results of the vehicle-bridge interaction analysis are verified by the experimental results for the railway plate girder bridges of a span length with 12 m, 18 m, and the experimental and analytical data are applied to the low pass filtering scheme, and the basis frequency of the filtering is a 2 times of the 1st fundamental frequency of a bridge bending.

• Journal of Korean Society of Steel Construction
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• v.16 no.3 s.70
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• pp.355-363
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• 2004

In order to obtain the effective length factor of beam-column members of plane frames, this paper extensively used an alignment chart approach, based on the nomograph given in LRFD-AISC specification commentaries. However, it should be noted that various simplifications and assumptions were introduced in constructing the alignment chart. To overcome the practical limitations of the alignment chart, this paper proposes a simple but accurate procedure that determined the effective buckling length for stability design of main members of cable-supported bridges. This method requires the full system buckling analysis. The numerical examples showing the suitability of the present scheme are discussed and some conclusions are drawn.

• Journal of Korean Society of Steel Construction
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• v.10 no.1 s.34
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• pp.47-61
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• 1998

The behavior of horizontally curved I-girder bridges is complex because the flexural and torsional behavior of curved girders are coupled due to their initial curvature. Also, the behavior is affected by cross beams. To investigate the behavior of horizontally curved I-girder bridges, it is necessary to consider curved girders with cross beams. In order to perform free vibration analyses of horizontally curved I-girder bridges, a finite element formulation is presented here and a finite element analysis program is developed. The formulation that is presented here consists of curved and straight beam elements, including the warping degree of freedom. Based on the theory of thin-walled curved beams, the shape functions of the curved beam elements are derived from homogeneous solutions of the static equilibrium equations. Third-order hermits polynomials are used to form the shape functions of the straight beam elements. In the finite element analysis program, global stiffness and mass matrix are composed, based on the Cartesian coordinate system. The Gupta method is used to efficiently solve the eigenvalue problem. Comparing the results of several examples here with those of previous studies, the formulation presented is verified. The validity of the program developed is shown by comparing results with those analyzed by the shell element.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.14 no.6
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• pp.1299-1308
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• 1994

This paper is considered on the dynamic behavior and the dynamic impact coefficient on the cable-stayed bridge under the vehicle load. The method of static analysis, that is, the transfer matrix method is used to get influence values about displacements, section forces of girder and cable forces. Gotten influence values were used as basic data to analyse dynamic behavior. This paper used the transfer matrix method because it is relatively simpler than the finite element method, and calculating speed of computer is very fast and the precision of computation is high. In the process of dynamic analysis, the uncoupled equation of motion is derived from simultaneous equation of the motion of cable-stayed bridge and vehicle travelling by using mode shape, which was borne from system of undamped free vibration. The solution of the uncoupled equation of motion, that is, time history of response of deflections, velocity and acceleration on reference coordinate system, is found by Newmark-${\beta}$ method, a kind of direct integral method. After the time history of dynamic response was gotten, and it was transfered to the time history of dynamic response of cable-stayed bridge by linear transformation of coordinates. As a result of this numerical analysis, effect of dynamic behavior for cable-stayed bridge under the vehicle load has varied depending on parameter of design, that is, the ratio of span, the ratio of main span length, tower height, the flexural rigidity of longitudinal girder, the flexural rigidity of tower, and the cable stiffness, investigated. Very good agreements with the existing solution in the literature are shown for the uncracked plate as well as the cracked plate.

• Journal of the Earthquake Engineering Society of Korea
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• v.5 no.3
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• pp.1-8
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• 2001

Seismic design forces for bridge components may be determined by modifying elastic member forces of design earthquakes using appropriate response modification factors according to the national design code of bridges Modeling technique of pile foundation system is one of the important parameters which greatly affects the results in the process of the elastic seismic analysis of a bridge system with pile foundation. In this paper, a approximate and simplified modeling technique of a pile foundation system for the practical purposes is presented. The modeling technique is based on the stiffnesses of pile foundation during earthquake. The horizontal stiffnesses are determined from the resistance-deflection curves derived from the results of dynamic field tests using cyclic loads and the vertical stiffness includes the effects of the end bearing capacities and side friction of piles as well as the pile compliances under the expected vertical load level. The applicability of the proposed technique has been validated through the some example bridge analyses.