Optimization of cable pre-tension forces in long-span cable-stayed bridges considering the counterweight

•Optimization approach is presented for determining the cable pre-tension forces.•The load and the range of the counterweight are considered as design variables.•A variable-step search algorithm is proposed for solving the optimization problem.•Considering the counterweight can reduce the maximum moment significantly. Over the past 20 years, many long-span cable-stayed bridges with asymmetric spans have been constructed, and the counterweight is always used to balance the self-weight of the main span. This paper presents an optimization method to determine the cable pre-tension forces in long-span cable-stayed bridges considering the counterweight. This method includes: finite element (FE) model, formulation of the optimization problem and optimization algorithm. FE model is established considering the geometrical nonlinearity. The optimization problem is formulated with the objective of minimum weighted total bending energy. In addition, the constraints for the cable pre-tension forces, the bending moment of the girder and the tower, the load of the counterweight, the bearing reactions of the transition piers and auxiliary piers are all implemented in the optimization model. The optimization algorithm solves the optimization problem through the variable-step search along each design variable including the cable pre-tension forces, the load and the range of the counterweight. The efficiency and the accuracy of the proposed method are demonstrated by an application example and the results exhibit the importance of considering counterweight in the design of asymmetric cable-stayed bridges.