Tension Analysis Of Hangers With Stepped Cross-Section Based On The State Space Method

The hangers are the key force-bearing component of through-arch bridges and half-through arch bridges.During the construction process,its tension not only controls the rationality of the whole bridge structure,but also affects the linearity of the main girder,the smoothness of the bridge deck and the safety and comfort of driving after the completion of the bridge.Therefore,the tension of hangers is an important index to evaluate the structural state of the arch bridge.The tension of hangers in bridge operation stage is also an important index to evaluate the fatigue characteristics of hangers.Therefore,accurate measurement of tension of hangers is an important work in the construction and operation of arch bridges.The main work and conclusions of this paper are as follows:(1)By simulating the hangers with stepped cross-section for arch bridges as beam model,an accurate analysis method based on the state space method was developed for the dynamic characteristics of hangers.The different cross-section characteristics and material parameters of each part of the hangers could be considered in detail as well as the complicated boundary conditions at both ends of the hangers in practical engineering.The relationship of the free vibration frequencies and tension of hangers was then obtained.It provided a theoretical basis for the so-called frequency method to measure the tension of hangers.The method was verified by the in-situ testing data and the results of FEM analysis of the hangers of a practical arch bridge.When the length of the cable segment of a hanger is greater than a certain value,this method can be combined with the classical string theory to identify the effective length of the hanger related to the length of the cable segment,which can be used to calculate the tension of hangers conveniently in practical engineering.(2)The accurate analysis theory of beam model based on state space method was extended to beam-cable hybrid model,and the reliability and accuracy of the theory were verified by comparing the results of beam-cable hybrid theory with those of in-situ testing data and and FEM analysis.Compared with the beam model,the error of the beam-cable hybrid model is larger than that of the measured results.However,when the bending stiffness of the cable body is very small,the numerical instability in the calculation process can be effectively avoided by using the beam-cable hybrid model.(3)Combined with the relevant examples,the influence of the parameters such as tension,bending stiffness and boundary conditions on the vibration frequency of the hangers were analyzed.(4)A smart phone cable tension test App based on Android system was developed in Java language.After identifying the effective length of hanger/cable of bridge by the theoretical method in this paper,the tension can be calculated conveniently with the line density,vibration frequency order and vibration frequency identified by App as the input parameters of App.The results of the horizontal hydraulic vibration platform experiment and the actual bridge tension test showed that the App has a high accuracy in obtaining frequency and calculating tension.The problems of existing cable tension testing system,such as relatively expensive,inconvenient to carry,cumbersome to install and low efficiency were solved by this App which has practical engineering value.