Main Cable Shape-Finding and Live Load Response of the Suspension Bridge with Central Buckles: An Analytical Algorithm

The stiffness of suspension bridges, which are flexible systems composed of main cables and stiffening beams, is frequently increased by adding one or more pairs of central buckles in the midspan. This study examined a suspension bridge with flexible central buckles, proposing a set of analytical calculation methods for the shape-finding of the main cable under dead load and the structural deformation and internal forces under any uniform live loads. The proposed method is based on the known bridge design parameters. First, the suspender and central buckle tension of each hanging point of the stiffening beam was determined by the multipoint rigid support continuous beam method. After assigning these tensions to the suspenders and the central buckles, the multisegment catenary theory was used to derive the equation for each main cable segment in turn. The constraint equation was established through the closure condition of the height difference within the span. The equation was then transformed into an objective function to be programmatically solved, determining the completed bridge state. To determine the live load response of the bridge, the deformation and position relationships of the main cable, main beam, and bridge towers were analyzed in sequence, with known live load parameters. Five types of constraint equations were established through the conservation of the unstrained length of each main cable segment, the coordination of the force and deformation of each suspender, the coordination of the force and deformation of each central buckle, the closure of span length and height difference in each span, and the force balance of the main beam. Then, they were converted into an objective function to be programmatically solved, leading to the live load response of the structure. Finally, a case study of a suspension bridge with a main span of 1,050 m was used to verify the feasibility and effectiveness of the proposed method. The structural deformation and internal forces provided by the analytical solution for the live load action had good accuracy, which is in good agreement with the finite-element method results.

Long-span suspension bridges, compared with traditional small- and medium-span bridges, have greater flexibility, and they are more prone to large deflection and deformation under live loads such as vehicles. To improve the structural stiffness of suspension bridges, engineers often set central buckles connecting the cable and stiffening beam in the middle of the span. The current method of calculating the live load response of suspension bridges depends on finite-element modeling. However, when purchasing and using finite-element software, it is often expensive. At the same time, the finite-element method (FEM) modeling process is relatively complex and exhibits low efficiency. In addition, Link10 element in the current commercial finite-element software ANSYS (version 16.0) cannot consider its geometric nonlinearity, which will produce deviation to the results. Therefore, this paper proposes a set of accurate live load analytical algorithms for suspension bridges with central buckles, which are solved by the same number of basic unknowns and constraint equations. It is helpful to reduce the dependence of practitioners on finite-element software and can also be used as the verification and supplement of finite-element results.