Cable Systems and Tensile Structures

The present dissertation focuses on and investigates the behaviour of the structural category referred to as tensile structures, paying particular attention to the cable ones. During the years the design of the structures has been conducted to lighter systems and the tensile structures rapidly increased thanks to their advantages as technical and time construction. To the other side, since the particular response to the external solicitation, the mechanical behaviour of these structures encouraged the researchers to find analytical and numerical methods proper to study, describe and analyze them. In this research, once identified and described the different typologies of tensile structures, specific issues related to the statics of cable ones are dealt with an enhanced analysis of the current methodologies used to solve and manage these structural systems. Composed of seven chapters, after an introduction about the issue and the main goal, the thesis starts from a recognization of the several types belonging to the analyzed structural categories, including cable, membrane, tensegrity and tensairity structures. One reports the features of each of them, highlighting the differences through some existing architectural examples, from the ancient to nowadays time. Subsequently, the attention is paid to statics of cable structures including simple cables, cables with opposite curvature and cable nets. Starting from a literature review, the selected approaches are analytically developed and demonstrated, focusing on both equilibrium and form-finding problems and highlighting advantages and disadvantages of each method, to have a suitable background to develop and introduce proper calculus models to solve the non-linear relationships characterizing these structures. The study aims to deal with the main problems concerning the cable systems, as find the equilibrated and compatible configuration under external loads’ action without the small displacements assumption, governing the non-linear relationship between forces and displacements, and taking into account the relevance of the deformations. Moreover, a fundamental scope of this research is to develop procedures suitable both in 2D and 3D cases, for several kinds of cable structures, and possible future computational implementation. Related to these main goals, different procedures are proposed and described. Basing on the optimization approaches, one refers to the Total Potential Energy, finding the solution through a constrained minimization concerning the Kuhn-Tucker conditions. The method is applied to a 2D structure and a numerical example is reported to highlight the main features of the proposed methodology. Moreover, the static response of plane and three-dimensional structures is evaluated by a calculus model under large displacements and in matrix form. The non-linear relationship between forces and displacements is identified and then it is solved through a step by step procedure, linearizing the equation governing the problem at each infinitesimal load’s step. Firstly developed for a 2D structure, the approach is extended to a three-dimensional one highlighting its worth for several types of these systems. Finally, an overview of the dynamic effects of tensile cable structure is explained, applying a modal analysis to a study case