Advanced technique for flexible cable analysis

Abstract

Introduction. Cable structures belong to perspective roof systems. Specialized software packages for structural analysis, however, do not provide optimization tools for obtaining efficient design solutions of the cable structures. Thus, development of improved methods for design and analysis of cable systems is an important task to be solved. An advanced technique for flexible cable analysis is proposed. It includes ordinary operations of summing the coefficients and their products. The technique is applicable for non-commercial mathematical software packages with numerical simulation tools included, thus providing structural optimization capabilities.Materials and methods. The technique proposed is based on the sine-series expansion of the external load and the shape function of the flexible cable. The differential equation of cable equilibrium is thus transformed into the set of algebraic equations. The cable length is expressed in algebraic form by means of the power expressions for the sum of the series.Results. The equation for the flexible cable is derived. It includes cable ordinate, axial stiffness, relative elongation and the external load parameters. The technique for determination of the axial stiffness of the cable is proposed under the operability conditions. The techniques for finding load-induced vertical displacements, as well as the initial cable sag and the undeformed length are given. The length of the cable under load and the ordinate given the cable length are proposed.Conclusions. The technique for flexible cable analysis allows taking into account distributed transverse external loads. For a combined load the coefficients of the series are the sum of the particular load coefficients. The technique is intended for automated structural solution. It allows facilitating the preliminary design stage, thus providing optimal parameters determination and in-depth design study implementation. Further development of the proposed technique encompasses the fields of non-shallow cable analysis, multy-chord cable systems, cable structures with stiffening girders, strutted cable systems and spatial roof structures.

Keywords

• sine-series expansion
• fourier series
• shallow cable
• flexible cable
• cable length
• shape function
• deformation