A Study on Dynamic Behaviour of Cable-Stayed Bridge by Vehicle Load

차량하중에 의한 사장교의 동적거동에 관한 연구

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.

본 연구는 사장교의 차량하중에 의한 동적거동을 파악하고자 수치해석상 비교적 간단한 일본의 풍리(豊里)(Toyosato)대교(大橋)의 자료를 근거로하여 수치해석 대상모델을 구조형식별로, 여러가지 설계변수-즉, (1) 경간비, (2) 중앙경간장과 주탑높이와의 비, (3) 거어더의 강성, (4) 주탑의 강성, (5) 케이블의 강성-을 변화시켜 수치해석을 수행하여 동적거동을 파악하고, 그 결과를 가지고 설계변수의 영향 및 충격계수의 변화에 대하여 비교 분석하였다. 이때 변위 및 단면력의 영향선을 구하기 위한 해석은 전달행렬법을 이용하였으며, 동적해석에 있어서는 평면구조계의 집중질량계로 모델을 가정하여 차량과 교량의 운동방정식을 유도한 후 모드중첩법을 사용하여 각 질점에 대한 변위 및 단면력의 동적시간이력을 구하였다.