Analysis of Some Geometrically Nonlinear Catenary Structures

Abstract

The behavior of a cable truss is generally considered as being analytically nonlinear. This thesis follows Irvine’s procedures to derive the nonlinear and linear analytical solutions of cable truss systems, taking into account the geometry, pretension, boundary condition and temperature difference. After the final closed-form solution is achieved, the resultant increase in horizontal component of cable force in both top and bottom chords of a cable truss can be solved correspondingly, with which the deflection at midspan of the cable truss can be further figured out. This kind of work is done by transforming the solution into computer program. With the help of numerical method, it is found there is obvious difference between the results of nonlinear solution and linear solution. Besides, 10 different cases are assumed and solved to see the effect that parameters related to the solutions will have on the difference of the result from those two kinds of approaches, in which the considered parameters include the span-to-sag ratio, span-to-camber ratio, pretension in chords and temperature difference in both top and bottom chords. It is found the difference of resultant horizontal force in bottom chord for a biconcave cable truss from the two approaches and the difference of resultant force in top chord for a biconvex cable truss from the two approaches are most sensitive to the change of any of the considered parameters. However, it should be noted all the results and the conclusions are obtained within a limited range.