Analysis Of Main Cable Shape Of Suspension Bridge Based On Unstressed Length Of Cable

The distribution of inner forces in the completed structure is directly influenced by the main cable shape of a suspension bridge.And the main cable shape determines the unstressed lengths of main cable and hanger cable,the location of cable clamp,these parameters are involved in the design and construction process of suspension bridge.It is difficult to adjust the geometric form of cable once the erection of the main cable of the suspension bridge is finished.So,it is important to calculate and analyze the empty cable shape and unstressed cable length precisely to reach the ideal completed state of suspension bridge.Taking a self-anchored concrete suspension bridge as the engineering background,the main cable shape and the unstressed length of the cable are analyzed and calculated by the node equilibrium analytical method and finite element iterative calculation method.The node equilibrium analytical method simplifies the suspension bridge into the stiffening beam system and the main cable system.And then the vertical equilibrium equations at the anchorage point and the main cable sling point are given,a set of non-linear simultaneous equations are represented.Use trial-error-correction solution method to solve the nonlinear equations,the cable shape of the suspension bridge is obtained.The unstressed length of cable members can be evaluated by solving the cubic equation when their nominal tension and the chord length are given.The unstressed length of the main cable of midspan is the initial value of the iterative calculation in the finite element calculation.With assumption of the unstressed length of the midspan main cable according to the calculation results by the node equilibrium analytical method,obtain the reasonable dead load sling force by the rigid support continuous beam method,establishment of the full-bridge finite element model and simulation of the construction step of the suspension bridge by the general FEM program,the iterative calculation is carried out to obtain the unloaded cable line,the main cable line and the unstressed length of the cable.The results of node equilibrium analytical calculation and finite element iterative calculation show that:(1)The free-cable shape is catenary,and the cable shape of bridge completed state is neither a catenary line nor a parabola shape,it is,between the two,a cable polygon of multi-section catenary.(2)The error values of the node ordinate obtained by the node equilibrium analytical method and the finite element method for solving the main cable shape are less than 1cm,and the solution error is small.Therefore,using the node equilibrium analytical method to calculate the main cable shape of the bridge completed state has enough accuracy.(3)The error value of the unstressed length of the main cable by the node equilibrium analytical method and the finite element method is less than 3cm,so the two methods can be mutually verified.The analytical solution can be used as the criterion for the initial value assumption in the finite element iterative calculation.The exact setting of the iterative initial value can make the iterative calculation converge faster and effectively reduce the number of iterations.(4)According to the bridge design elevation of the stiffening beam,the dead load sling force is obtained by the rigid support continuous beam method.Calculation result proves that the sling force of bridge state is relatively evenly distributed except for the slight undulation near the pier.But due to the setting of pre-camber to the stiffening beam,the sling force under one-stage dead load is not equal.(5)The node equilibrium analytical method can only obtain the cable shape of the bridge state and the unstressed length of the cable,and the accuracy of the solution is limited.The finite element method can simulate the construction process of the suspension bridge to obtain the shape and internal forces of various construction stages and completed state of the bridge.So,it is more specific and precise to use finite element method to guide the actual project.(6)The horizontal force of the main cable in the bridge completed state obtained by the analytical method and the finite element method is 72299.60 kN and 72730.23 kN,respectively,and the error rate is only 0.59%.The bending moment of the stiffening beam in bridge completed state obtained by the analytical method and the finite element method satisfy the target bridge completed state of dead load internal force.