Nonlinear analysis of cable structures

Abstract

Large structures are widely used in the modem construction industry for infra-structure facilities development. Among these, long span structures with cables are becoming increasingly popular. In this category of structures deformations are large and estimations based on small deformation theory in the normal analysis are inadequate. The large deformation analysis results in nonlinear behavior where principle of superposition does not hold. In geometrical nonlinear analysis, the equations of equilibrium are based on the deformed geometry after the load application. The length of a curved deflected line is longer than the initial length and the basic assumptions used in linear analysis may cause inaccuracies when the deformations are very large. It is also essential that bending effects of cables are considered. Here we deal with large deformations, but small strain problems with linear stress strain relationships. Although there are many methods found in literature to analyze cables exhibiting large deformation nonlinear behavior, it is hard to find a universal approach to describe the exact behavior of a cable considering all geometrical nonlinearity issues. The analysis described in this study recognizes all such influences contributing to geometrical non-linearity. The procedure developed is versatile and gives a state-of the- art analytical tool. This work fills a void in the current practice recognizing large deformation issues without any knowledge of small or large strains as opposed to what is required in commercial software. A numerical solution procedure has been evolved to solve the resulting nonlinear nonhomogeneous integral differential equation. The procedure is converging and a computer program has been developed for practical use. The results are compared with those in literature to validate the findings and to ensure the accuracy of the new large deformation nonlinear analysis technique.