Keywords: cable structure, girder-stiffened structure, suspension bridge, long-span structures, discrete analysis, geometric non-linearity.

This paper presents discrete method of the analysis for different kinds of suspension bridges stiffened using a girder or a stretching cable [1]. The discrete analysis method was used to provide more flexibility to calculate suspension structures than analytical methods [2]. Discrete analysis is based on the conditions of equilibrium, applied at the nodal points of the cable. Under a uniformly distributed load the cable will take a parabolic form. In reality, the cable is loaded by concentrated forces and it takes the form of a string polygon. The conditions of equilibrium are written for every node of the polygon and the elongation of the cable was determined using the equations of deformation compatibility for every section of the cable. These conditions form a system of nonlinear equations, which give after solving all nodes displacements and internal forces for the cables and for the stiffening girder.

The discrete model of a suspension bridge [3] allows us to apply all kinds of loads, such as distributed or concentrated ones. The assumptions of the discrete method described here are: linear elastic strain-stress dependence of the material and the absence of horizontal displacements for the hangers. Hanger elongation is taken into account.

Firstly, the discrete model of the elastic cable must be described. By the action of the loads the balance situation for every node of the cable where the hanger is connected (from the equilibrium of forces) can be written. At the same time due to the relative elongation of the cable (the deriving base of discrete analysis) the same situation can be described.

The solution of these systems of non-linear equations enables us to calculate all the displacements w_i and H by the given initial cable form and boundary conditions u₀, u_n+1. The third step of calculation is to describe the deflection of the stiffening girder using the universal equation of an elastic line.

It is understandable that the deflections of points of cable and girder which are connected with the same hanger are equal (except the elongation of the hanger, this is taken into account).

Solving the system of these equations give us all the node deformations and internal forces we require. An algorithm for the calculation of the suspension bridge using these equations is presented.

Comparisons between the results from the discrete analysis, linear and nonlinear finite element analysis shows that the displacements of the bridge's girder, obtained from the discrete analysis and the nonlinear finite element analysis are practically the same and much smaller than the displacements from linear finite element analysis.

1

J. Idnurm, "Discrete Analysis of Cable-Supported Bridges", Tallinn University of Technology, Tallinn, 2004.

2

V. Kulbach, "Cable Structures. Design and Static Analysis", Estonian Academy Publishers, Tallinn, 2007.

3

V. Kulbach, J. Idnurm, S. Idnurm, "Discrete and Continuous Modelling of Suspension Bridge", Proceedings of the Estonian Academy of Sciences Engineering, 2, 121-133, 2002.

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