Multiobjective Optimization of Cable Forces and Counterweights for Universal Cable-Stayed Bridges

Zhangming Wang,Nan Zhang,Qikai Sun,Xianting Du,Shilei Wang,Bin Yu

doi:10.1155/2021/6615746

Abstract

In cable-stayed bridges, especially asymmetric bridges, counterweights are always made to work together with cable pretension forces to get a reasonable finished state. To solve the optimization problem of the cable-stayed bridge considering the counterweights, the integrated optimization method (IOM) for estimating cable forces and counterweights is proposed. In this method, the counterweights are proposed to act on the anchor points. After that, the summary of the minimum weighted total bending energy and the summary of the counterweights are considered as two objective functions of a multiobjective problem. Finally, the dynamic weighted coefficient method is used to solve this problem and realize the Pareto solution set. IOM presents detailed procedures in a simple numerical model and is then applied to the Yong-ding special-shaped cable-stayed bridge. The results show that not only IOM can realize the priority selection of the loading position of the counterweights but also get a better reasonable finish state because of the introduction of the counterweight dimension; the dynamic weighted coefficient method can quickly find the Pareto optimal solution set and be further screened by decision-makers; counterweight is very helpful to reduce torsion and other spatial effects in cable-stayed bridges. IOM can be used as a universal optimization method for cable-stayed bridges.

Highlights

Cable-stayed bridges are statically indeterminate structures, and their structural behavior is greatly influenced by cable pretension forces. erefore, the determination of cable pretension forces is critical in the design procedure.with the development of cable-stayed bridges in recent years toward large-span, spatialization and artistry, and various cable-stayed bridges of strange shapes appear more and more frequently [1,2,3]
Based on the above research, this paper proposes a universal integrated optimization method (IOM) that can consider counterweights and suitable for asymmetric cablestayed bridges
In order to solve the reasonable finish state of an asymmetric cable-stayed bridge, this paper proposes the integrated optimization method (IOM) considering the counterweights on the anchor point: (1) Compared with the hill-climbing algorithm, IOM has high efficiency and good convergence. e assumption of counterweights on anchor point is applicable to all cable-stayed bridges, and it can be converted to uniform weight based on simple structural mechanics

Summary

Introduction

Cable-stayed bridges are statically indeterminate structures, and their structural behavior is greatly influenced by cable pretension forces. erefore, the determination of cable pretension forces is critical in the design procedure.with the development of cable-stayed bridges in recent years toward large-span, spatialization and artistry, and various cable-stayed bridges of strange shapes appear more and more frequently [1,2,3]. Ere have been several methods proposed in the literature for determining pretension forces of cable-stayed bridges [6, 7], which can be divided into four types: the optimization methods for specified structural conditions, the minimum bending energy methods, the unit load methods, and the mathematical optimization methods. Wang et al [8] aimed at zero vertical displacements of anchor points and proposed the zero displacement method of cable-stayed bridges; Chen et al [9] proposed the force equilibrium method later. In this method, the additional bending moments of the girder can be considered, so it is more rational than the zero displacement method. The additional bending moments of the girder can be considered, so it is more rational than the zero displacement method. e

Methods

Results

Conclusion