Nonlinear Analysis of Cable Truss Structures under Static Loads

Abstract

In this thesis, the linear and nonlinear cable truss equations of the biconvex and biconcave cable truss structures under four types of static loads, i.e. uniformly distributed vertical load applied over entire span, uniformly distributed vertical load applied on partial span, uniformly distributed vertical load applied over left half span and vertical point load, are derived using the compatibility equation suggested by Wang and Er (2013, 2014). Here, the effects of elastic deformations, temperature changes and elastic supports are taken into consideration. Computer programs are written, Newton–Raphson iteration method and Gaussian elimination method are applied to obtain the additional horizontal components of the top and bottom cable tension forces caused by the external force in the coupled nonlinear cable truss structures and linear cable truss structures, respectively. The additional vertical deflections caused by the external force also are analyzed according to the vertical equilibrium for the loaded cable trusses. The numerical results, i.e. the horizontal components of cable forces and vertical deflection of the symmetric and asymmetric cable trusses under various loads with different span-to-sag ratios, the horizontal components of cable forces and vertical deflection of the cable trusses with different loads obtained by linear and nonlinear analyses are presented, compared, and discussed. Through the investigation, it is shown that the linear cable truss theory has some limitations. When the deflection is large, which is normal for the flexible cable truss catenary structures, nonlinear cable truss theory is to be used in order to obtain relatively accurate results. Otherwise, the error can be too large to be acceptable with linear cable truss theory.