Research On Theoretical Calculation Method Of Tie Force Of Tied Arch Bridge Based On Frequency Method

Currently,steel cables are widely used in cable-stayed bridges such as cable-stayed bridges,suspension bridges,tied-arch bridges,etc.,and are the main structural components of these projects.For tie-arch bridges,whether they are under construction or already in normal operation,it is necessary to quickly and accurately identify the cable force of the hangers,which is convenient for the construction of bridges to provide safe construction protection,and provide reliable assessment of the health status of bridges in service.in accordance with.Therefore,the suspension force of the tied arch bridge is the key and difficult point in the current project.The frequency method is one of the most widely used cable force identification methods.In this paper,the theoretical method of cable force identification based on frequency measurement is studied on the basis of suspender mounting and cable truss debugging of1-64m tied arch bridge on Xige Railway Overpass Bridge of Wulan Mining Special Line in Qinghai Province.The main completed research work has the following aspects:(1)From the consideration of the ordinary differential equations of the vibration of the derrick bending stiffness,has nothing to do with the boundary conditions is deduced formula of cable force identification and unified the formula is just in front of the string vibration theory formula of cable force identification multiplied by a coefficientK_n.And can use any order of frequency for cable force recognition,and the hinged boundary conditions at both ends into the theoretical calculation formula to obtain the same display force calculation formula with Euler's beam theory.(2)Two kinds of boundary conditions,the consolidation at the two ends and the consolidation at the one end,are brought into the theoretical calculation formula,and two different transcendental equations are obtained.The iterative solution and the curve fitting of the transcendental equation are combined with MATLAB to obtain the coefficients under different boundary conditionsK_n.Thus,the display expression of the force identification formula is established.(3)Through the finite element software Midas Civil,three suspender models with different lengths were established.Three different tensile forces were applied to calculate the vibration frequencies at the two ends of the consolidation and one end of the joint is constricted by two kinds of boundary conditions.Then use the theoretical formula deduced in this paper for cable force identification.Comparing with Mehrabi and Tabatabai's proposed cable force recognition formula considering cable sag effect and flexural rigidity,the results show that the proposed formula has higher precision and is more applicable to all types of suspenders and frequencies.(4)Considering the difference of bending stiffness,unit length quality and flexible cable section of the anchorage section of the suspender,a three-section suspension suspender vibration model is established,and the frequency equation between the natural vibration frequency and the cable force is derived.(5)Because the frequency equation of the three-section suspender is complex and inconvenient to calculate,the three-section suspension suspender vibration model is simplified,and the anchor end is simplified as an elastic support perpendicular to the direction of the suspender.The vibration model of the longitudinally-stretched transverse elastic support strut was established.Considering the combined effect of the flexural rigidity and the elastic support of the strut,the dynamic response equation of the strut was deduced,and the formula of the force identification was obtained.(6)The suspending force cable identification formula proposed in this paper is applied to the suspender installation and cable tension adjustment process of the 1-64m tied arch bridge on Xige Railway Overpass Bridge of Wulan Mining Special Line in Qinghai Province,and compared with the corresponding cable force theoretical values.The results show that the cable force identification formula established in this paper has high accuracy,and it is more suitable for the short suspender and the frequency of natural vibration of all order suspenders in the project.It is worthy of being applied and popularized in engineering examples.