An iterative calculation method for hanger tensions and the cable shape of a suspension bridge based on the catenary theory and finite element method

Abstract

Construction of suspension bridges and their structural analysis are challenged by the presence of elements (chains or main cables) capable of large deflections leading to a geometric nonlinearity. For an accurate prediction of the main cable geometry of a suspension bridge, an innovative iterative method is proposed in this article. In the iteration process, hanger tensions and the cable shape are, in turns, used as inputs. The cable shape is analytically predicted with an account of the pylon saddle arc effect, while finite element method is employed to calculate hanger tensions with an account of the combined effects of the cable-hanger-stiffening girder. The cable static equilibrium state is expressed by three coupled nonlinear governing equations, which are solved by their transformation into a form corresponding to the unconstrained optimization problem. The numerical test results for the hanger tensions in an existing suspension bridge were obtained by the proposed iterative method and two conventional ones, namely, the weight distribution and continuous multiple-rigid-support beam methods. The latter two reference methods produced the respective deviations of 10% and 5% for the side hangers, respectively, which resulted in significant errors in the elevations of the suspension points. To obtain more accurate hanger tensile forces, especially for the side hangers, as well as the cable shape, the iterative method proposed in this article is recommended.

Study on the curve error of acoustic transmission path in anechoic chamber

“…In general, the problem of the drooping wire rope under gravity is simplified as a catenary [16]. In this paper, the sound transmission device that connects the microphone to the suspension and hangs on a wire rope with the help of pulleys.…”

Calculation Method and Construction Process of Main Cable Alignment of Self Anchored Suspension Bridge

“…The static equilibrium state of cable is expressed by three coupled nonlinear control equations, which are transformed into the form corresponding to unconstrained optimization problem. His method is too complicated to be practical [3]. Xiao R presents a five-step algorithm for determining the reasonable state of space cable suspension bridges without theoretical derivation or original program design.…”

A Novel Shape Finding Method for the Main Cable of Suspension Bridge Using Nonlinear Finite Element Approach

“…A shape finding or form finding process is therefore conducted to determine the shape and internal forces of the main cable through minimizing the dead-load-induced deformation of the bridge. Moreover, the increase of the main cable dimension and the reduction of the cable design safety factor require a more refined estimation of the cable configuration and internal forces in the structural components [3].…”

“…The equations describing the analytical relations between the axial forces and the strained/unstrained lengths of a cable segment under the action of the self-weight can be found in many pioneering studies, e.g., [14]. These equations were then widely employed to develop various shape finding approaches for the main cable of the suspension bridge, such as the initial force method or segmental catenary method (SCM) [3,[15][16][17][18], the target configuration under dead load (TCUD) method [19], the improved TCUD method [20], the Generalized TCUD method [21], the coordinate iteration method [22], and the perturbation approach [23,24]. The unstrained length of each main cable segment in these methods is unknown and solved in the successive nonlinear equations using the nonlinear finite element iteration [15,16,[25][26][27][28][29].…”