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1、Study on nonlinear analysis of a highly redundant cable-stayed bridge1AbstractA comparison on nonlinear analysis of a highly redundant cable-stayed bridge is performed in the study. The initial shapes including geometry and prestress distribution of the bridge are determined by using a two-loop iter
2、ation method, i.e., an equilibrium iteration loop and a shape iteration loop. For the initial shape analysis a linear and a nonlinear computation procedure are set up. In the former all nonlinearities of cable-stayed bridges are disregarded, and the shape iteration is carried out without considering
3、 equilibrium. In the latter all nonlinearities of the bridges are taken into consideration and both the equilibrium and the shape iteration are carried out. Based on the convergent initial shapes determined by the different procedures, the natural frequencies and vibration modes are then examined in
4、 details. Numerical results show that a convergent initial shape can be found rapidly by the two-loop iteration method, a reasonable initial shape can be determined by using the linear computation procedure, and a lot of computation efforts can thus be saved. There are only small differences in geom
5、etry and prestress distribution between the results determined by linear and nonlinear computation procedures. However, for the analysis of natural frequency and vibration modes, significant differences in the fundamental frequencies and vibration modes will occur, and the nonlinearities of the cabl
6、e-stayed bridge response appear only in the modes determined on basis of the initial shape found by the nonlinear computation.2. Nonlinear analysis2.1. Initial shape analysisThe initial shape of a cable-stayed bridge provides the geometric configuration as well as the prestress distribution of the b
7、ridge under action of dead loads of girders and towers and under pretension force in inclined cable stays. The relations for the equilibrium conditions, the specified boundary conditions, and the requirements of architectural design should be satisfied. For shape finding computations, only the dead
8、load of girders and towers is taken into account, and the dead load of cables is neglected, but cable sag nonlinearity is included. The computation for shape finding is performed by using the two-loop iteration method, i.e., equilibrium iteration and shape iteration loop. This can start with an arbi
9、trary small tension force in inclined cables. Based on a reference configuration (the architectural designed form), having no deflection and zero prestress in girders and towers, the equilibrium position of the cable-stayed bridges under dead load is first determined iteratively (equilibrium iterati
10、on). Although this first determined configuration satisfies the equilibrium conditions and the boundary conditions, the requirements of architectural design are, in general, not fulfilled. Since the bridge span is large and no pretension forces exist in inclined cables, quite large deflections and v
11、ery large bending moments may appear in the girders and towers. Another iteration then has to be carried out in order to reduce the deflection and to smooth the bending moments in the girder and finally to find the correct initial shape. Such an iteration procedure is named here the shape iteration.
12、 For shape iteration, the element axial forces determined in the previous step will be taken as initial element forces for the next iteration, and a new equilibrium configuration under the action of dead load and such initial forces will be determined again. During shape iteration, several control p
13、oints (nodes intersected by the girder and the cable) will be chosen for checking the convergence tolerance. In each shape iteration the ratio of the vertical displacement at control points to the main span length will be checked, i.e., |spanmi oitsctrldilevertca|The shape iteration will be repeated
14、 until the convergence tolerance, say 10-4, is achieved. When the convergence tolerance is reached, the computation will stop and the initial shape of the cable-stayed bridges is found. Numerical experiments show that the iteration converges monotonously and that all three nonlinearities have less i
15、nfluence on the final geometry of the initial shape. Only the cable sag effect is significant for cable forces determined in the initial shape analysis, and the beam-column and large deflection effects become insignificant.The initial analysis can be performed in two different ways: a linear and a n
16、onlinear computation procedure. 1. Linear computation procedure: To find the equilibrium configuration of the bridge, all nonlinearities of cable stayed bridges are neglected and only the linear elastic cable, beam-column elements and linear constant coordinate transformation coefficients are used. The shape iteration is carried out without considering the equilibrium iteration. A reasonable convergent initial shape is found, and a lot of computation efforts can be saved.2. Nonli
