Optimization On Cable Tensions Of Completed Cable-stayed Bridges With Mixed Stiffening Girders

In recent years, with the continuous development and application of high-strength materials, and the progress in structure analytical and construction methods, modern cable-stayed bridges have developed rapidly in the world. In some bids for long-span bridges, the cable-stayed bridges with mixed stiffening girders have gradually shown their advantages due to their light weight, excellent performance and convenient construction. The stiffening girder adopts two different materials longitudinally. The junction section of two materials is near the pylon tower. The combination of two materials can effectively take advantage of the strengths of steel and concrete, reduce cost and enhance the spanning capability of the stiffening girder.The optimization on cable tension of cable-stayed bridges with mixed stiffening girders is the key issue in design, because cable tension greatly determines the pattern of the inner forces in completed state. This paper summarizes previous methods and conducts optimization on cable tensions under dead load and under both of dead and live loads respectively according to the feature of cable-stayed bridges with mixed stiffening girders. The research contents are as follows:1) Optimization on cable tensions of completed cable-stayed bridges with mixed stiffening girders considering moment limit at junction section under dead load. Using the sum of the bending and tension-compression strain energy within tower and stiffening girder as objective function, the initial cable tensions as design variables, and the cable tensions under completed stage and the moment at the junction section of steel and concrete stiffening girders as constraint conditions, this paper determined cable tensions under the completed stage. During the optimization process, the internal forces and displacements of bridge structures under completed stage were investigated by changing the moment limit at junction section. The most reasonable moment limit at junction section and the optimal cable tensions were determined.2) Optimization on cable tensions of completed cable-stayed bridges with mixed stiffening girders due to dead and live loads. On the basis of cable tension optimization due to dead load, considering the action of live load and using the stress balanced method, this paper obtained the feasible moment ranges of the critical sections of stiffening girder, which were used as the constraint conditions of final optimization. With the initial cable tensions as design variables, and horizontal displacement of tower top as object function, the cable tensions were determined.This paper employed an actual cable-stayed bridge with single tower and asymmetrical cable configuration as project case, established the spatial finite element model by a general finite element program (ANSYS). The optimization model was solved by sub-problem and first-order methods. The calculating result shows that the most reasonable completed state under dead load can be obtained by assigning the moment limit at junction section within the range of 0.3-0.5 times of the minimum and maximum moment through the stiffening girder. The optimized state has the features with the gradually increased cable tensions from the tower through the side supports, smooth moment distribution within the stiffening girder, and the smaller moment at junction section. Comprehensive optimization method with combination of the cabal tension optimization under dead load, the stressed balanced method and the constraint optimization method with the horizontal displacement of tower top as object function, takes all of dead load, live load and prestress load into consideration, and makes the completed state very reasonable.