Strut And Tie Model Analysis Of One-Box Two-Cell Concrete Cable-Pylon Anchorage Zone In Cable-Stayed Bridge Based On The Topology Optimization

The long-span cable-stayed bridge has been developed rapidly in recent decades.With the increase of the span of the cable-stayed bridge,the cable force has gradually increased,which becomes a new challenge to the design of the bridge tower.And the cable-pylon anchorage zone is the important part of the cable-stayed bridge.The rationality of the structure design is important for the security of the whole bridge.However,the geometry of the cable-pylon anchorage zone is complex and the mechanical behavior also is unclear.And there is no theoretical method for designing the cable-pylon anchorage zone.Hence,it brings challengs for bridge designers to design the structure.Nowdays,finite element analysis（FEA）and model test method are the common way for the structure design.However,it may cost a lot of money and time.This dissertation has investigated the theoretical method for design the cable-pylon anchorage zone based on the Strut-and-Tie model（STM）.The topology optimization has been introduced to generate the STM.Further,the STM has been introduced in the design of the Cao’e River cable-stayed Bridge.The main content of the dissertation is as follows.（1）The Evolutionary Structure Optimization（ESO）algorithm has been introduced in detail,and the strut-and-tie model（STM）of the single-box double-cell cable-pylon anchorage zone in the bridge tower is obtained by the traditional ESO method.The principle stress flow distribution of the structure is obtained by finite element analysis（FEA）.Through comparing the STM based on the classical ESO method with the principle stress flow distribution,the irrationality of STM was verified.The reason why the traditional ESO algorithm is not suitable for the one-box two-cell anchorage zone has been analyzed in detail.To get the rational STM of the structure,the removal criterion of ESO method has been analyzed,and an improved ESO method has been proposed.Based on the improved ESO method,the new STM of the one-box two-cell anchorage zone has been generated.By comparing the new STM and the principle stress flow distribution of the structure,the rationality of the new STM has been proved.What’more,to further verify the rationality of the new STM,the crack propagation model of structure was established.By comparing the location of the crack and the ties in STM,the rationality of the new STM has been substantiated.Moreover,the STM of the one-box two-cell anchorage zone has been proposed for the first time.（2）To verify the rational STM of the one-box two-cell anchorage zone can be applied in the practical engineering.This dissertation has introduced the STM to design the cable-pylon anchorage zone in Cao’e River Bridge.Based on the STM,the calculation method of the number of the prestressed tendon in the cable-pylon anchorage zone has been proposed,and the location of the prestressed tendon also has been presented.Birdge designers can follow the calculation process given in this dissertation to calculate the reinforcement in the one-box two cell anchorage zone.Further,to verify the correctness of the reinforcement layout of the structure,a full-scale test model has been constructed.The test model design was introduced in detail.The result of the test model shows that the arrangement of four U-shaped prestressed steel strands and six linear prestressed steel strands in the one-box two-cell anchorage zone is rational.Meanwhile,the result of the full-scale test model of the Cao’e River Bridge shows that the STM of the one-box two-cell anchorage zone can be used in the practical engineering.（3）The mechanical behavior of the anchorage zone in bridge tower is complex,while the STM method is an effective way to analyze the structure.This dissertation detailed analyzed the influence of the structural geometrical parameters on the internal force of the important tie members in STM of the structure.Firstly,based on the crack propagation model of the structure,the important tie members in STM has been determined.Then,the structural geometrical parameters in the cable-pylon anchorage zone of a total of 68 long-span cable-stayed bridges has been collected.Based on the statistical method,the value range of the geometrical parameters of the structure have been obtained.The influence of the geometrical parameters of the structure on the internal force of the important tie members in STM has been analyzed.The calculation formulations of the internal force of the important tie members under the influence of single geometrical parameter was obtained.Moreover,the method of calculating the single influence factors is proposed to solve the problem of the multi-parameters.The calculation formulations of the internal force of the important tie members under the influence of multi-geometrical parameters was presented.Lastly,an numerical example has been analyzed to verify the accuracy of the calculation formulations.The calculation formulations proposed in this dissertation is suitable for the one-box two-cell anchorage zone in bridge tower,which is useful for bridge designers to design the cable-pylon anchorage zone.（4）Based on the minimum strain energy principle,the analytical equation for solving the optimum STM of the one-box two-cell anchorage zone in bridge tower has been proposed.The analytical formulations for calculating the internal force of tie members in the optimum STM of the structure also has been presented.Firstly,based on the equilibrium equation of the nodes in the STM,the analytical expressions of the internal force of the tie and strut members with respect to the parameters（θ₁,θ₂,θ₃,θ₄ andθ₅）in STM was presented.Then,through analyzing the geometric relationship between the strut and tie members in STM,the analytical expressions of the length of the tie members with respect to the parameters（h,θ₁,θ₂,θ₃ andθ₄）in STM was obtained.Lastly,based on the minimum strain energy principle and by solving the partial differential equations,the analytical equation for solving the optimum STM of the one-box two-cell anchorage zone was derived.The accuracy of the analytical equation derived in this dissertation was verified by an engineering example.（5）Based on the optimum STM of the one-box two-cell anchorage zone,the calculation method of the width of the strut members in STM was proposed.Further,the macro STM model of the one-box two-cell anchorage zone was presented.Based on the macro STM model,the method of predicting the ultimate bearing capacity and shear strength capacity of the structure is given.The Cao’e River Bridge was introduced to be analyzed.The ultimate bearing capacity of the anchorage zone in Cao’e River Bridge was calculated in detail.The maximum cable force which the structure can bear is 13455k N and the safety coefficient is2.07.Due to the STM method follows the lower limit of plasticity,hence,the prediction result based on the STM method is conservative,which is applicable to practical engineering.Meanwhile,based on the macro STM model,the concept of shear strength capacity of the one-box two-cell anchorage zone was proposed for the first time.The shear strength capacity of the anchorage zone in Cao’e River Bridge was calculated in detail.The shear strength capacity of the structure is 8140.9k N.Through the prediction analysis of ultimate bearing capacity and shear strength capacity of Cao’e River Bridge,it is found that increasing the linear prestressed steel strand in the cable-pylon anchorage zone of Cao’e River Bridge is beneficial to improve the ultimate bearing capacity and shear strength capacity.