Forces In Cable-stayed Bridges Research Articles

A mixed approach for determination of initial cable forces in cable-stayed bridges and the parameters variability

The determination of initial cable forces in cable-stayed bridges is an important first step in design and analysis of the structure under external loads. Adjustments of stay forces are often required during construction in order to assure the requested behaviour of the bridge in terms of final geometrical configuration and internal force distribution. An accurate assessment of the stay tensioning system allows designers to obtain a good result at the end of construction, by considering the parameters involved as deterministic quantities, assuring the observance of the execution tolerances during works. Actual loads and their variations need instead a stochastic approach which can give useful indications about the effects of parameter variations. Particularly, the measurement on site of the actual values of stay elongations contains errors and the actual values of prestressing forces and working site loads are subjected to unknown variations. In this paper a procedure is implemented which takes into account the stochastic variation of stay elongations and the related uncertainties. The presented method does not require large computational efforts or computer memory. By approximating the probability density distribution of the variables involved by the Gaussian curve, a closed form expression of the imposed elongations given to stays and their variations during erection is provided. The main aim is to obtain an accurate prediction of the differences between the deterministic quantities found by the design analyses and the actual values of deck deformations and stresses in the erection of steel cable-stayed bridges.

Study on Cable Forces in Cable-Stayed Bridges Based on Forward Simulation Method

According to cable tension calculation of cable-stayed bridge on construction, and combining with the example of Xinzao Pearl River Grand Bridge, this work proposes forward-calculation method to analyze cable tension force on construction and establishes geometric calculation simulation model to compare measured cable tension with theoretical cable tension. This paper introduces some kinds of methods calculating cable tension force on construction. It importantly discusses the principle and method of forward-calculation and the practical application in the actual project. Spacial finite element model is established for analysis based on finite element software MIDAS and the application of forward-analysis iterative method is considered to analyze the cable tension on construction , then the method of determining cable force on construction is explored. Finally the result shows that the cable tension based on forward-calculation method is usually accurate, the measured value is approximately equal to the theoretical value and the error is in the extent permitted. The correctness and reliability of the frequency method is effectively confirmed and the cable tension calculation of the similar bridge on construction is compatibly applied.

Calibration of initial cable forces in cable-stayed bridge based on Kriging approach

Although optimization methods are useful in the preliminary design of cable-stayed bridges for sizing of components and getting optimal bridge configurations, further fine-tuning is invariably conducted in the detailed design thus affecting various sensitive properties such as the deck profile and cable forces. The zero-displacement method that adjusts the initial cable lengths repeatedly to achieve the design deck profile is both computationally intensive and prone to convergence difficulty. Therefore a calibration method is proposed based on a Kriging surrogate model built using the uniform design approach. Apart from establishing the relationship between the bridge deck geometry and the initial cable forces by statistical method, the Kriging model also obviates the need for a large number of repeated finite element analyses. A simple cable-stayed bridge is used to verify the feasibility and accuracy of the proposed method. In real-life cable-stayed bridges with many cables, a staged calibration is implemented so that the Kriging model is used to identify reasonable initial forces in the critical stay cables so that the zero-displacement method or similar can be used for further adjustments. Verification shows that this staged calibration can address not only the deck level tolerance but also the control of cable forces.

Estimation of Cable Tension Force Independent of Complex Boundary Conditions

The presence of unknown complex boundary conditions usually imposes difficulties in estimating the cable forces in cable-stayed bridges when using conventional model-based force identification methodologies. Therefore, there exists a need for new methodologies that can overcome these challenges while achieving acceptable force identification accuracy. This paper presents an innovative method to estimate the forces within stay cables with complex boundary conditions. The proposed approach transforms the cable force estimation problem from the common procedure of constructing and solving the equation of motion of the cable to a simpler problem of finding the zero-amplitude points of its mode shapes. Ultimately, the presented methodology yields accurate cable force estimations regardless of the complexity of the boundary conditions. An equivalent segmental model whose length is given by the distance between these points is used next to find an estimate of the cable tension force. A stay cable under axial force and constrained by end rotational springs is employed to analytically investigate the force identification accuracy of the proposed method. It is observed that with mode orders lower than 18, the proposed method achieves a maximum relative error less than 5% regardless of the end-restraint condition. Therefore, the proposed method has great potential for practical application because of its theoretical simplicity, accuracy, and feasibility.

A new multiconstraint method for determining the optimal cable stresses in cable-stayed bridges.

Cable-stayed bridges are one of the most popular types of long-span bridges. The structural behaviour of cable-stayed bridges is sensitive to the load distribution between the girder, pylons, and cables. The determination of pretensioning cable stresses is critical in the cable-stayed bridge design procedure. By finding the optimum stresses in cables, the load and moment distribution of the bridge can be improved. In recent years, different research works have studied iterative and modern methods to find optimum stresses of cables. However, most of the proposed methods have limitations in optimising the structural performance of cable-stayed bridges. This paper presents a multiconstraint optimisation method to specify the optimum cable forces in cable-stayed bridges. The proposed optimisation method produces less bending moments and stresses in the bridge members and requires shorter simulation time than other proposed methods. The results of comparative study show that the proposed method is more successful in restricting the deck and pylon displacements and providing uniform deck moment distribution than unit load method (ULM). The final design of cable-stayed bridges can be optimised considerably through proposed multiconstraint optimisation method.

Application of Laser Vibrometer to the Measurement and Control of Cable Tensile Forces in Cable-Stayed Bridges

The tensile forces acting on the cable of long-span bridges are one of the most important factors since they reflect not only the structural stability of cables but also the overall quality of construction. Currently, indirect measurement using accelerometers attached to the surface of the cable is widely used to measure the natural frequency of cable. The frequency obtained from the accelerometer is converted to the tensile force of the cable. However, it sometimes requires many hazardous labors such as attaching the device on the surface of cable and wiring it with data logger, which could hinder the safety of workers during the erection of cables. In this study, a method using laser vibrometer is introduced to measure the tensile forces on cables at a distance. In addition, this study developed a unique postanalysis computer program that can calculate the tensile forces in real time. Compared with the values obtained from the accelerometers, the laser vibrometer system provided accurate and reliable matching.

사장교의 초기형상해석을 위한 개선된 초기부재력법 및 TCUD법의 비교연구

사장교 시스템의 초기형상해석이라 함은 주형의 수직 처짐과 휨모멘트, 주탑의 수평변위와 휨모멘트를 최소화하면서, 고정하중과 평형을 이룰 수 있는 케이블의 장력과 무응력길이를 결정하는 방법으로 이 때, 케이블이 정착되는 주형의 수평위치, 주탑의 수직위치가 목표형상에 부합할 필요가 있다. 본 연구에서는 고정하중을 받는 사장교의 초기형상을 효율적이고 합리적으로 결정하기 위하여 개선된 초기부재력법과 TCUD법의 비교연구 결과를 제시하고자 한다. 주형과 주탑의 케이블 정착부에서 힘의 평형조건을 이용하여 주형의 수직처짐과 주탑의 수평변위를 효과적으로 제어할 수 있는 절점평형법을 초기 부재력법에 적용하여 초기치에 민감한 기존 초기부재력법을 개선한다. 또한 개선된 TCUD법을 이용한 초기형상해석 수행결과와 비교함으로서 두 방법의 정확성을 입증하고자 한다. Initial shape analysis for cable-stayed bridges should be able to find optimizated initial cable forces and unstrained length that minimize deflection and bending moments of the deck and pylon. Comparison study of an improved initial force method and TCUD method for determination of initial cable forces in cable-stayed bridges is presented in this paper. For this purpose, an elastic catenary cable element and a nonlinear frame element are firstly described. And concepts and algorithm of two analysis methods are then presented. Finally to demonstrate the validity and the accuracy of two methods, numerical examples for initial state problems of cable-stayed bridges are given and compared based on these methods.