Study On Cable Force Optimization Method Of Concrete Cable-stayed Bridge Considering Cable Force Uncertainty

In recent years,with the maturity of finite element theory,the rapid development of computer technology,and the continuous progress of domestic cable-stayed bridge construction technology,the construction of cable-stayed bridges in China has advanced by leaps and bounds.As a cable-stayed bridge is a force-sensitive structure,how determining the optimal cable force has become a key point in the design and construction of cable-stayed bridges and a variety of cable force optimization methods have been developed.This paper summarizes and concludes the current optimization methods and proposes a method to optimize the cable force considering the construction and operation loads,and based on this method,the cable force is considered as a random variable and the structural reliability index is used as a constraint to study the influence of cable force uncertainty on the optimal cable force of cable-stayed bridges.The main research contents and conclusions are as follows:(1)In the cable-stayed bridge force optimization problem,due to the many load conditions faced by the structure in operation,the finite element calculation is used to obtain the structural response after each cable force adjustment,which will lead to a very time-consuming analysis process,in order to reduce the calculation cost,the current cable-stayed bridge force optimization method mostly adopts a simplified method or only considers a small number of live load conditions.a method to optimize the cable force considering the construction and operation loads are proposed in the paper,and the optimization model can consider all the verification elements of serviceability limit state(SLS)and ultimate limit state(ULS)required for structural design.By using the load decoupling method,the combined limit state load effects are separated into variable terms containing only the cable force and invariant terms in addition to the cable force.Through one finite element analysis,the constant term effect is obtained,and the variable term effect in the optimization process is calculated using the cable force influence matrix,so that the whole optimization process does not require repeated finite element calculations,which have high computational efficiency.(2)Taking a prestressed concrete cable-stayed bridge as an example,the optimization method in the paper is used for structural optimization design,16 load conditions can be considered according to the "General Specifications for Design of Highway Bridges and Culverts"(JTG D60-2015),with a total of 362 possible load combinations,while the safety of the structure can be ensured throughout the construction phase,and the structural safety margin in the above two limit states can be taken as the optimization objective,respectively single-objective and multi-objective optimization models are established,and intelligent optimization algorithms are used to maximize the safety margin of the structure.The optimization results show that: the cable force obtained by using the rigid cable method and bending energy minimization method does not meet the code requirements,but the cable force obtained by using this method not only meets the code requirements but also enables the structure to have a high safety reserve in the operation stage.At the same time,according to the multi-objective optimization results,the non-inferior solution set consisting of the structural stress safety margin under the SLS and the structural safety factor under the ULS is uniformly distributed in the feasible solution space,and the optimal solution can be selected from the non-inferior solution set according to different needs.(3)Based on the reliability optimization theory,the influence of the uncertainty of the cable force on the optimal cable force is further studied in the paper.Firstly,the cable force is regarded as a random variable obeying normal distribution,and by using the load decoupling method,the limit state equations based on two failure modes of SLS and ULS can be established,and the reliability indexes of stress and a bending moment of the girder are calculated by using the first second-order moment(FOSM)method and significant sampling Monte Carlo(MC)method,and by changing the value of the coefficient of variation of the cable force,the influence of the randomness of the cable force on the stress and bending moment of the girder are analyzed.The results show that The optimal cable force obtained based on the deterministic optimization model,when the cable force variation coefficient is 0.03 ～ 0.08,the component stress reliability index does not meet the code requirements,and when the variation coefficient is 0.04 ～ 0.08,the component bending moment reliability index is also lower than the specification limits,which can not meet the normal use of the actual project,indicating that it is necessary to consider the randomness of the cable force when optimizing the cable force of the cable-stayed bridge.When the variation coefficient of cable force is taken within a certain range,the optimal cable force obtained by the random optimization model can not only ensure that the structural reliability index meets the requirements of the code,but also improve the safety margin of structural stress and flexural capacity.