A Refined Analysis Method Of Asymmetric Main Cable For Long-span Single-tower Ground-anchored Suspension Bridge

As a novel type of suspension bridge,the long-span single-tower ground-anchored suspension bridge can fully adapt to the complex terrain conditions in the mountain-canyon region.Because this type of suspension bridge has only one tower,and the span of the main cable and the span of the stiffening girder in the mid-span are different,compared with the traditional suspension bridge,there are great differences in the main cable alignment calculation and construction control.Based on the engineering background of the Hutiao Gorge Jinsha River Bridge,and in view of the asymmetric structural characteristics of the bridge,this paper studies the analytical calculation method of the spatial main cable shape,the control calculation during the construction process and the finite element calculation method of the main cable shape.The main contents are as follows:(1)An analytical calculation method of spatial asymmetric main cable shape considering the influence of cable clamp is proposed.Through the stress analysis of the coupling effect between the main cable,the suspender and the stiffening girder,the space suspender stress can be obtained,and the ground anchor cable is designed based on the principle of maintaining the elevation of the cable clamp point or the unstressed length;The iterative calculation process of main cable configuration is divided into calculation stage of design,calculation stage of finished bridge,and calculation stage under load.During the iterative calculation process,the unstressed length of the main cable in the space saddle groove is corrected,and the influence of the spatial force of the cable clamp on the shape calculation is considered.This method establishes a calculation model for the main cable shape that is more in line with the actual situation of this type of suspension bridge,achieving accurate calculation of the main cable shape of the finished bridge and the load state of this type of suspension bridge,and achieving the goal of precise calculating the spatial asymmetric main cable shape.(2)A calculation method of the erection linetype of cable and the pre-displacement of the cable saddle considering the deviation of the single tower is proposed.The longitudinal deflection stiffness of the bridge tower is calculated by sectioning the box shaped variable cross-section of the bridge tower,and apply it to the establishment of the equilibrium conditions for the single tower cable saddle.This method improves the calculation accuracy of the erection linetype of cable and the pre-displacement of the cable saddle of the single tower suspension bridge,and reduces the influence of the unbalanced force of the cable saddle on the tower column.A strain incremental cable stress adjustment method considering the coupling effect of composite saddle anchor span cable is proposed,and based on this,a multi-round optimization adjustment method to prevent the slippage of cable is proposed.This method considers the coupling relationship between the composite saddle anchor span cable and the mid-span main cable,as well as the coupling relationship between the cable,achieving precise calculation of the cable force of the composite cable saddle anchor span cable,and improving the accuracy and efficiency of the cable adjustment of the anchor span cable.(3)Based on the geometrically exact beam theory,a method for constructing a cable-clamp assembled finite element for calculating the plane main cable shape is proposed.The kinematics of plane beam is accurately described with large rotation angle and large deformation by using the theory of geometrically exact beam,and the tangent stiffness matrix of the beam element is obtained by using the incremental virtual work equations;The cable clamp is regarded as a rigid component,and the beam end displacement is amplified to obtain the expression of the external load vector and the internal stress vector of the composite element.The tangent stiffness matrix of the non-rigid component is connected through the node displacement on the rigid component,and then the tangent stiffness matrix of various composite elements is obtained.This finite elements construction method achieves accurate description of the large rotation angle and the large deformation of the composite components of the plane main cable and cable clamp,improving the calculation accuracy and efficiency of the plane main cable shape.(4)Based on cubic spline interpolation,a method for constructing a geometrically exact Euler-Bernoulli beam element for calculating the spatial main cable shape is proposed.Cubic spline interpolation is used to describe the interpolation vector in element,which can make the interpolation curve smoother at the endpoint of the element and more accurately simulate the shape of the spatial main cable.Quaternion is used to describe the rotation of the cross section inside the element in the inertial coordinate system and the section coordinate system.The quaternion of the section inside the element is described by two quaternion rotations of the quaternion of the end section,then the curvature vectors and angular velocity vectors of the element cross-section can be accurately derived.Decomposing the curvature vectors and angular velocity vectors in the direction of the basis vectors to obtain the degree components rotating around the three basis vectors,then the expressions of the time derivatives of the three centroid curvature represented by the generalized velocity array are obtained.Then,the control equation of geometrically exact Euler-Bernoulli beam element is derived by the principle of virtual work rate.This element construction method achieves accurate description of the large rotation angle and the large deformation of the spatial main cable,which can accurately simulate the actual shape of the spatial main cable,improve the calculation accuracy of the spatial main cable shape,and can be used for spatial force calculation of flexible beam structures.