Study On Bending Stiffness Effect And Secondary Stress Of Main Cable Of Long Span Suspension Bridge

With the merits of large spanning ability, light weight, aesthetical structure, good aseismic performance, diversified structure and good terrain adaptability, suspension bridge is the first choice among ultra-long-span bridges. With rapid development of long-span suspension bridge construction, the cross-sectional dimension of main cable is increasing. For example, the diameter of main cable of Hong Kong Tsing Ma Bridge or Akashi Kaikyo Bridge has reached 1.1m. Affected by the saddles, cable clamps, wire wrapping and other factors, the bending stiffness of large cross-section main cable has a more complicated influence on geometry shape and internal force. Besides axial tensile stress generated by dead loads and live loads, main cable is also subjected to additional secondary stress, such as bending stress while changing saddles’position, and non-uniform axial stress caused by manufacturing and construction. And secondary stress is an important basis for determining the safety factor of the main cable. Being the major bearing component of suspension bridge, main cable must be analyzed rigorously and precisely, which is important for the safety and durability of main cable and the accuracy of the construction monitoring. By developing the geometric nonlinear finite element program, a profound and systematic research on bending stiffness and secondary stress of the main cable of long-span suspension bridge is conducted on the base of model test and field test. The main contents, methods and results are as follows:(1)The main cable is discretized into the slender beam elements with small deflection. Stiffness matrix of the slender beam element is derived from the dead load condition, in which the influence of the bending stiffness affected by axial force and the axial stiffness correction factor caused by bending moment is taken into account. The calculation method of main cable shape is based on the slender beam element and then the finite element program is developed. The results show that the influence that the bending stiffness has on the main cable shape is mostly located at the middle span, the position near the pylon and the hanging point with large sling force. And the error of main cable shape calculation becomes larger while the sag-span ratio gets bigger. According to the main cable of Xihoumen Suspension Bridge,9 different suspension cable models are designed which consist of different diameters and different quantity of steel wires respectively. Deformation under the static loads and free vibration characteristics are measured. Reliability of the calculation method based on the slender beam element is verified through the results of model test. And the qualitative results for the influence of bending stiffness on main cable deformation are obtained as well as those for bending stiffness values.(2) A novel original curvature beam element has been developed to address the following issues which primarily refer to the bending stiffness of the main cable and its original curvature. Based on the virtual work increment equation, the tangent stiffness matrix of the original curvature beam element is derived. The geometric nonlinear finite element program for the main cable is developed based on the Updated Lagrangian (U.L.) formulation. The correction of main cable shape in saddle and the variation of bending stiffness with the construction process are implemented in the program. Finite element model of the main cable of Nanjing Yangtze River Forth Bridge is established in according to the program. The results show that the vertical deformation of main cable under dead loads decreases with the bending stiffness taken into account, so that the calculation deviation of main cable shape caused by the bending stiffness can be able to fit the requirements of precision in the finished bridge state. The bending moment and the bending stress of main cable on the hanging points near the pylon and the limit hangers are significant in the finished bridge state.(3) Main cable is composed by discrete wires that tend to slip during the bending deformation. Based on this characteristic, the layered slipping element model is proposed and established, likewise, the calculation method of ultimate friction between layers is developed. A test stand and loading system are designed for the axial tension and bending model test of parallel cable strand. Section layered stress and deformation of the cable strand composed of 61 wires are tested under the axial tension and bending moment. The results show that:①Section layered stress and deformation characteristics of the cable strand can be realistically simulated by the layered slipping element model; ②The non-uniform stress and deformation of the cable strand are obviously influenced by its uniform wrapping force and axial force after wire slippage; ③Only if all the wires slip along the longitudinal direction of the cable strand, can the non-uniform stress be affected by the cable strand length; ④The slope which is between the non-uniform stress and the rotation angle at the extremity reflects the bending stiffness of the cable strand, and it decreases with the expansion of the interlayer slip region; ⑤With the same rotation angle at the extremity, the larger uniform wrapping force or the smaller axial force of cable strand is, the larger the bending stiffness of cable strand and the non-uniform stress are, as well as the deformation.(4) The stress of the main cable is measured on site for several sections which are near the pylon saddle during the stiffening girder lifting process of the Nanjing Yangtze River Fourth Bridge. The field measurement results show that secondary stress is mainly composed by the non-uniform axial stress. Secondary stress accumulates gradually in the fixed-end with the construction process, and its tendency is consistent with the rotation angle change of the main cable at the pylon saddle. According to the test data, secondary stress formula with the rotation angle is fitted, and the secondary stress is calculated by the fitting formula for a small amount of construction cases in which there is no test data. Finally, the variation curve of secondary stress of the main cable is obtained for the whole construction process of the Nanjing Yangtze River Fourth Bridge. Testing and fitting results show that the maximum secondary stress of the main cable at the both sides outlet of the pylon saddle is 171MPa and 136MPa respectively in the finished bridge state. Ratio of the secondary stress to average axial stress is 0.26 and 0.21. There is significant difference between the testing results and theoretical results, which is worth of attention by bridge designers and maintenance staffs.