Study Of Hybrid Element Of Thin-walled Beam And Its Application In Double Non-linear Analysis Of Cable-Stayed Bridges

Cable-stayed bridges get into good graces of people because of their great spanning capability and beautiful sight. With the development of scientific technology and increasing demands of the society, cable-stayed bridge has great increase in number and span; its structure form is increasingly diversiform. There are numerous rivers in China, which brings cable-stayed bridge a good future in application. As a kind of flexible structure, practice shows that geometry-nonlinear must be taken into account in the design and calculation of cable-stayed bridge. For carrying capability analysis, material nonlinear has to be taken into account, too. In the comparison of schemes and preliminary design, data are changed often, so that the amount of calculation work is huge. Though current software has powerful functions, it is still difficult to get accurate results in a short time. Therefore, there is an urgent need for a set of calculation methods and software for design of cable-stayed bridges, which should be simple, applied and able to meet engineering demands. The main girders and towers of cable-stayed bridges are usually thin-walled box girder structures, which have complex stress state. The classic beam theory has difficulty in reflecting the deformation characteristic of thin-walled box girders accurately. In this thesis, the author made an in-depth study of the analysis theories and calculation methods of thin-walled box girder and cable, put forward new calculation theory and methods, and applied them into the non-linear analysis of cable-stayed bridges. The main innovative achievements are listed in the following:1. On the basis of extensive reading, an in-depth study was made on the non-linear characteristic of cable-stayed bridges, the calculation theories and methods of thin-walled box girders, and the existing problems in the above -mentioned subjects; hybrid variation principle was fixed to be the theoretical basis of the thin-walled beam element of this paper.2. A two-node spatial non-linear thin-walled box girder element isput forward, which is based on Hellinger-Reissner hybrid variation principle. The non-linear FEM (finite element method) equation, elastic rigidity matrix, geometry matrix and pre-stress load column matrix were formulated. In the element, axial deformation, double flexural, shear deformation, restraining torsion warping and section-distortion were all taken into account, which lead to a comprehensive reflection of deformation characteristic of thin-walled box girders. The corresponding program was designed, and some simple examples were given. The results of the examples show that the element is simple, accurate and effective.3. A method named equivalent load of cut-down plastic stress was put forward, which extended the above two-node spatial non-linear thin-walled hybrid beam element to material non-linear field. The plastic constructive equation suited for thin-walled box beam was derived, the increment of plastic cut-down stress and its resultant, the plastic cut-down stress and its resultant were formulated. The calculation steps were listed out. The method simplifies calculation by translates the impairment of structure rigidity, caused by plasticity, into an equivalent load. The corresponding program was designed, and some simple examples were given. The results of the examples show that the theory and the method are correct, simple and applicable.4. A spatial catenary cable element was brought forward, which was built strictly according to the natural geometric shape of cables. The rigidity matrix and node force column matrix of the cable element were formulated; the arithmetic of two kinds of cable problems was given; the master-slave relationship of the relative nodes between cable element and beam element was considered. Corresponding program was designed and some simple examples were given. The results of the examples show that the catenary cable element simulates the geometric non-linear behavior accurately, the results are actual and believable.5. All the above-mentione...