A Refined Analysis Method Of Main Cable For Long-Span Suspension Bridge

With the increasing span length of suspension bridge, the safety factor of main cable was decreased from the original4.0to the current2.0. Therefore it is necessary to perform more accurate calculation of suspension bridge. In order to achieve the purposes of precise calculation, two new elements were developed combined with the structure characteristics of suspension bridge, and the calculation model is more consistent with the actual situation. On the basis of the segmental catenary theory and nonlinear finite element method, a series of research work was carried on around the geometric nonlinear analysis of suspension bridges, the contact nonlinear between cable and saddle, the alignment of the spatial main cable.Firstly, the plane cable segmental catenary theory was extended to the spatial cable system. The calculation methods of tangential point position between spatial cable and space saddle and the iterative algorithm of spatial main cable configuration were established. A corresponding spatial cable program, which can comprehensively consider of the space saddle, splay saddle, anchor span strand, has been developed using the numerical analytical method. The unstressed length of main cable and anchor span strand, tangential point and jacking force of strand can also be figured out accurately by using the program. The program can be used to analyse the spatial cable shape in both the finished bridge stage and the cable finished stage.Secondly, based on the analysis of cable and saddle constraint relation, two new elements, saddle element and anchorage-anchor span element, have been put forward for suspension bridge finite element calculation. The saddle element is used for contact nonlinear analysis between main cable and saddle on tower, and the anchorage-anchor span element is used for contact nonlinear analysis between anchor span strands, side-span main cable and splay saddle. The new elements automatically satisfy the condition that the main cable should be always tangent to saddle. First of all, on the condition that the total unstressed length of cable between two nodes remains constant, the current state of the element is determined and the location of the tangent points are obtained. After that, according to the spatial catenary theory and the geometric relation between cable and saddle, the accurate element nodal force can be derived. At the same time, with increment instead of differential, the element tangent stiffness matrix can be deduced depending on the definition of the stiffness matrix. Calculation shows that the new elements have high calculation precision. The computational simulation problem of contact nonlinear between cable and saddle has been well solved through the introduction of the two new elements. Finally, a combinational method of increment and iteration based on the total method for the element rod end resisting force was chosen to solve the equilibrium equation. The precision of calculation doesn’t rely on tangent stiffness matrix and no accumulative error would occur. The calculation method of rod end resisting force and tangent stiffness matrix according to total node displacement was described. The rotation transform relationship when the vector occurring spatial limited rotation was derived from the introduction of Euler-Rodrigues formulation. The method to determine the co-rotational coordinate system and total beam end rotation angle of space beam element was introduced. An improved method, which divides the unbalanced force vector into prescribed parts and makes them act gradually in one load step, was proposed. The processing methods for the element with rigid arms, relaxation of degree of freedom, master-slave constraint, were introduced. A calculation program including catenary cable element, space beam element, saddle element and anchorage-anchor span element which can satisfy the geometric nonlinear analysis of suspension bridges was developed.Calculation analysis demonstrates that the effect of saddle should be accurately considered in the calculation of suspension bridge. If using the traditional bar system FEM without considering the change of tangent point location, the calculation error of the final bridge shape will be greater than the erection accuracy requirements, and moreover, the calculation error occurring in the construction process may be greater than that of finished bridge state. The calculation accuracy of suspension bridge has been improved through the introduction of the two new elements. It provides more accurate calculation basis for construction control.