Nonlinear Modified Influence Matrix Method For Determining Construction Cable Force Of Long-span Cable-stayed Bridge

The geometrical nonlinear effect is obvious in long-span cable-stayed bridges.This effect makes it complicated to determinate the cable force of the construction stage and to reach the reasonable bridge completed state.This paper has optimized the influence matrix method and has studied the determination of the construction cable force based on the modified influence matrix method.Based on the principle of the influence matrix,the influence matrix equation has been derived involving the support method and the cantilever method of the longspan cable-stayed bridge.The influence factors of cable force have been divided into four kinds: the weight of the newly assembled beam,cable tensioning,temporary construction loads and remove of temporary construction loads.The movement of the temporary load and the change of the boundary constraint have been converted into the loads acting on the structure,so the solution of the cable force influence matrix has been unified in this way.At the same time,the solution method of the nonlinear problem has been considered on the basis of linear value adjustment,and the nonlinear modified influence matrix method has been derived,which is suitable for the construction of long-span cable-stayed bridges and takes the geometrical nonlinear effect into account.A three-tower cable-stayed bridge with two main spans of 616 m has been taken as the engineering background.The finite element model has been established by ANSYS,and the construction stages have been divided.On the basis of calculating the reasonable bridge force,the model has been solved and compared by using the influence matrix method and the nonlinear modified influence matrix method.The results show that:(1)The side span is constructed by the support method.During the construction process,only the post-tensioned cables will affect the pre-tensioned cables.And the middle span is constructed by the cantilever method.During the construction process,the weight of the newly assembled beam,cable tensioning,temporary construction loads and remove of temporary construction loads all have certain influence on the cable force.Among them,the weight of the newly assembled beam has the greatest influence on the cable force,followed by cable tensioning.(2)Among the cable force of the completed bridge obtained by forwarding analysis,the calculated force value of the middle cables on both sides of the side tower most conforms to the target value.And the cable force error value of the two side cables of the side tower is generally smaller than that of the middle tower.The maximum error values are generally distributed around the towers,the piers and the closure segment.(3)Geometric nonlinearity in the construction of the long-span cable-stayed bridge has a significant impact on the construction cable calculation,and there will exist large errors in the results if the geometric nonlinear effect is ignored.(4)The modified influence matrix method can effectively solve the problem of the geometric nonlinear cable force calculation in the long-span cable-stayed bridge.Based on the geometric nonlinear influence matrix method,the calculated results not only reduce the maximum error of a single cable but also make the cable force curve more approximate to the reasonable cable force curve.The above conclusions prove that the cable force calculated by the nonlinear modified influence matrix method can be used as an engineering guide.Based on the idea of linear approximation and nonlinear correction,this method can quickly approach the target value by a small amount of iterative calculation after obtaining the influence matrix,and it greatly reduces the iterative calculation amount in the determination of the construction cable force.According to the engineering requirenments,a certain part of the cable force can be adjusted slightly later.