• Journal of the Computational Structural Engineering Institute of Korea
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• v.13 no.2
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• pp.165-178
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• 2000

The simplified model for 3-dimensional analysis of vehicle-bridge interactions is presented in this study. By using the analysis model which includes the eccentricity of axle loads and the effect of the torsional forces acting on the bridge, the more accurate analysis results of the behavior of the bridge can be obtained. The equations of kinetic energy, potential energy and damping energy are expressed by degrees of freedom of the vehicle and the bridge. And then by applying Lagrange's equations of motion, the equations of motion of the vehicle and the bridge are obtained. By deriving the equations of forces acting on the bridge considering the vehicle-bridge vertical interactions and also by identifying the position of vehicle as time goes by, mass matrix, stiffness matrix, damping matrix and load vector of vehicle-bridge system are constructed in accordance with the position of vehicles. Then using Newmark's β-method(average acceleration), the equations of motion for the total vehicle bridge system are solved.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2010.04a
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• pp.31-34
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• 2010

본 논문에서는 교량의 자유진동 모드의 중첩원리를 이용하여 KTX-교량의 동적상호작용 해석법을 제시한다. 이를 위하여 모드중첩법에 기초한 3차원 교량-차량의 에너지 식으로부터 에너지원리를 적용하여 교량과 차량의 상호작용을 고려할 수 있는 운동방정식을 유도한다. 이때 운동방정식의 해는 Newmark-${\beta}$ 방법을 사용한다. 그리고 궤도의 불규칙성은 FRA의 6등급 분류규정을 고려하여 각 등급별로 고속철도의 열차속도에 따르는 응답을 분석한다. 실제 고속철도에 사용되는 PSC 박스형 교량을 상용프로그램(MIDAS)를 이용하여 모델링하고 그로부터 각 모드별 형상을 얻어내어 본 논문에서 개발한 열차-교량 상호작용 프로그램에 입력하여 상호작용 해석을 수행한다.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.16 no.2
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• pp.141-151
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• 2003

Railway bridges are subject to dynamic loads generated by the interaction between moving vehicles and the bridge structures. These dynamic loads result in response fluctuations in bridge members. To investigate the real dynamic behavior of the bridge, therefore, a number of analytical and experimental Investigations should be carried out. In this paper, a train/track/bridge interaction analysis program for evaluating the dynamic characteristics of bridges due to KTX operation in terms of structural safety, operational safety and passenger comfort is developed. To build a practical model of train/track/bridge, Hertzian spring for wheel/rail contact modeling and Winkler element for ballast are applied. This program also used torsional degree of freedom and constraint equation based on geometrical relationship in order to take into consideration three-dimensional eccentricity effect due to the operation on double track through quasi-three dimensional analysis. To verify the developed Program, comparison has been made between the measured results and those of simulation of the typical PSC box bridge(2@40m=80m) of the KHSR bridges.

• Journal of Korean Society of Steel Construction
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• v.20 no.1
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• pp.151-163
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• 2008

A formulation of three-dimensional model of articulated train-b ridge dynamic interaction has been made for the Korean eXpress Train (KTX). Semi-periodic profiles of rail irregularities consisting of elevation, alignment, cross and gauge irregularities have also been proposed using FRA maximum tolerable rail deviations. The effects of rail joints and sleeper step were also included. The resulting system matrices of train and bridge are very spare, and thus, are stored in one-dimensional arrays, yielding a time-efficient solution. A numerical algorithm for computing bridge-train response including an iterative scheme is also formulated. A program simulating train-bridge interaction and solving this problem using the new algorithm is implemented as new modules for the f inite element analysis software named XFINAS. Computed results using the new program are then checked by that of the validated 2-D bridge-train interaction model. This new 3D analysis provides more detailed train responses such as swaying, bouncing, rolling, pitching and yawing accelerations, which are useful inevaluating passenger riding comfort. Train operation safety and derailment could also be directly investigated by relative wheel displacements computed from this program.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.12 no.4
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• pp.629-638
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• 1999

본 연구에서는 고속철도에서 차량·교량 구조물의 상호작용을 가능한 정밀하게 취급할 수 있는 3차원 해석모형을 개발하였다. 경부고속철도 교량형식인 PSC 박스거더 교량을 40m 단순 와 25-40-25m 3경간 연속 에 대해 뼈대요소를 사용하여 3차원으로 모형 하였으며, 궤도의 불규칙성은 정상확률과정으로 가정하고, 지수 스펙트럼 밀도함수를 사용하여 궤도의 형상을 생성시켰다. 열차는 경부고속철도 차량 하중효과가 가장 큰 동력차 만을 대상으로 17 자유도 모형과 38 자유도 모형으로 분리하여 개발하였다. 다양한 조건에 대한 분석결과를 검토하면 여러 가지 상황에서 38 자유도 모형의 필수 성이 보여지고 있다. 특히 교량의 솟음 및 장기 처짐에 의한 궤도형상변화가 있는 경우에는 반드시 38 자유도 모형이 적용되어야 하는 것으로 분석되었다. 또한 제동하중이 작용할 때 쏠림 효과에 의한 영향이 큰 것으로 평가되어, 제동에 의한 교량의 동적 거동은 종변 위에 대한 자유 도를 고려할 수 있는 주행차량모형으로 해석되어야 함이 규명되었다.

• Computational Structural Engineering
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• v.11 no.3
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• pp.253-262
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• 1998

본 연구에서는 경부고속철도의 주요 교량형식인 PSC 박스교량을 3차원 뼈대요소를 사용하여 모형화하였으며, 궤도불규칙성의 형상은 지수 스펙트럴 밀도함수를 사용하여 생성시켰다. 경부고속철도차량(K-TGV)중 동력차는 17자유도의 3차원 주행열차로 모형화하였고, 이러한 교량, 궤도불규칙성 및 차량 모형을 이용하여 교량과 차량의 상호작용을 해석할 수 있는 프로그램을 개발하였다. 동적해석을 위한 교량과 차량의 운동방정식은 Lagrange 방정식을 사용하여 유도하였으며, 운동방정식의 수치해석에는 Newmark-β법을 사용하였다. 개발된 프로그램을 이용하여 동력차의 주행에 의한 교량의 시간이력곡선을 구하였으며, 궤도불규칙성의 영향을 분석하였다. 또한 도상의 유무에 따른 교량동적거동의 특성과 함께 열하중의 편심의 영향도 분석하였다.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.26 no.6A
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• pp.989-999
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• 2006

In this paper, numerical analysis method to perform linear dynamic analysis of bridge considering the road surface roughness and bridge-vehicle interaction when vehicle is moving on bridge is presented. The vehicle and bridge are modeled as three-dimension where contact length of tire and pitching of tandem spring are considered and single truck with 2-axles and 3- axles, and tractor-trailer with 5-axles are modeled as 7-D.O.F., 8-D.O.F., and 14-D.O.F., respectively. Dynamic equations of vehicle are derived from the Lagrange's equation and solution of the equation is obtained by Newmark-${\beta}$ method. The surface roughness of bridge deck for this analysis is generated from power spectral density (PSD) function. Beam element for the main girder, shell element for concrete deck and rigid link between main girder and concrete deck are used. The equations of the motion of bridges are solved by mode-superposition procedures. The proposed procedure is validated by comparing the results with the experimental data by Whittemore and Fenves.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.18 no.4 s.70
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• pp.361-372
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• 2005

In the previous study(Kim 등, 2004), the finite element method was used for the vortical vibration analysis of suspension bridge with the effects of the shear deformation and the rotary inertia under moving load considering the bridge-vehicle interaction. The purpose of this study is to investigate the effect of an eccentric vehicle and shear deformation. So we firstly performs the eigenvalue analysis for the free vortical and the torsional vibration of suspension bridges using FEM analysis. Next the equations of motion considering interaction between suspension bridges and vehicles/trains are derived using the mode superposition method. And then dynamic analysis was performed using the Newmark method. Finally through the numerical examples, the dynamic responses of bridges are investigated according to the proposed procedure.

• Journal of Korean Society of Steel Construction
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• v.9 no.3 s.32
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• pp.309-321
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• 1997

The prediction of the dynamic response of a bridge resulting from passing vehicles across the span is a significant problem in bridge design. In this paper. the static and dynamic experiments are performed to understand the dynamic behavior of an actual two-span steel plate girder bridge. The road surface roughness of the roadway and bridge deck is directly measured by Intelligent Total Station. Numerical scheme to obtain the dynamic responses of the bridges in consideration of measuring road surface roughness and 3-D vehicle model is also presented. The bridge and vehicle are modeled as 3-D bridge and vehicle model, respectively. The main girder and concrete deck are modeled as beam and shell elements, respectively and rigid link is used for the structure between main girder and concrete deck. Bridge-vehicle interaction equations are derived and the impact factors of the responses for different vehicle speeds are calculated and compared with those predicted by several foreign specifications.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.15 no.4
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• pp.693-702
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• 2002

The aim of this study is to develop a 3-dimensional dynamic analysis model, capable of considering the interaction between vehicles and bridges more accurately. The dynamic analysis model is developed with the high-speed train (KTX) and a 2-span continuous prestressed concrete box girder bridge with a double track. The 20-car model is developed using the moving vehicle model for the regular trainset. Three-dimensional frame elements are used for the bridge model. Using the developed models, a dynamic behavior analysis program is coded. The analytical results are compared with the dynamic field test results and found to be valid to yield quite accurate dynamic responses. Based on the results of this study, the hybrid model, made up of the moving vehicle model for the heaviest power car and the moving force model for the other cars, is quite simple and effective without loosing the accuracy that much. Under the coincidence condition of two trains traveling with resonance velocity in the opposite directions, it is necessary to check not only the dynamic responses of the bridge with one-way traffic but those with two- way coincidence.