Discrete and continuous analysis of different cable structures

Abstract

Continuous and discrete analysis of different cable structures is under investigation in our report. In cases of distributed loads the non-linear conditions of equilibrium and equations of deformation compatibility are taken as initial equations [1]. To eliminate the horizontal displacements, the equations of deformation compatibility were used in integrated form; corresponding integrals (du/dx)dx were replaced by respective displacements of supporting structures under action of cable forces. Determination of deflections and inner forces for certain cable structures under action of distributed vertical loads may be carried out by means of exact analysis. A girder-stiffened structure has also an exact solution but in the form of complicated transcendental equations. A simpler, compact solution may be found with a proper approximation of the deflection function in the form of trigonometric dependences. Continuous analysis may be also applied to spatial cable structures in the form of hypar-networks with elliptical contour beam [2]. Suitable approximation of the deflection function with use of Galyorkin procedures brings us to values of the network’s deflection and cable forces very near to exact ones.

In discrete analysis of girder-stiffened cable structures, the condition of equilibruim is to be composed for every node and the equation of deformations compatibility for every section of the cable [3]. For every joint on stiffening girder were used equation which consider girder’s node’s deformations, internal force in the hangers and load, which is balanced by the stiffening girder. The load may be by distributed load or concentrated force, and may be applied on any point of girder. Using this equations, and moment equilibrium conditions for girder’s supports, were calculated vertical displacements of cable nodes and displacements of girder nodes. Using iteration can be found such value of cable force, which gives actual displacement for every node. After found cable force, all required parameters can be calculated. Examples of analysis of hypar-network and the bridge for a 6100 m strait crossing are presented in the full text of our paper.