Static Analysis Of Tensegrity

Study of physical behavior and static analysis of tensegrity structures

Aparna Harichandran1, Yamini Sreevalli2

1, 2School of Mechanical and Building Sciences, VIT

University, Chennai-600048

[e-mail]

2 [e-mail] Abstract — This paper deals with the physical behavior of Tensegrity structures while erection, in equilibrium state and in loading. Physical modeling of a tensegrity prism is done and static analysis is performed by graphical method. The result is compared with the static analysis by mathematical modeling. There is reduction in degrees of freedom in physical model due to limitations of joints of the tensegrity model.

Keywords—Form finding; Icosahedron; Octahedron; Static analysis; Tensegrity

A tensegrity system is developed when a set of discontinuous compressive members interacts with a set of continuous tensile members to define a stable volume in space. Let us call the compressive members as bars and the tensile members as strings. Most bar–string configurations which can be formed are not in equilibrium, and if actually constructed will collapse to a different shape. Only bar–string configurations in a stable equilibrium will be called tensegrity structures.

The members of a tensegrity structure are either always in tension or always in compression. Since the tensile members form a continuous network, tensile forces are transmitted throughout the structure. The compression members are discontinuous. The compression members are not subject to the great buckling loads they would be otherwise since they do not have to transmit loads over long distances. Because of that they can be made more slender without sacrificing structural integrity. The tensegrity structures have lots of applications from temporary terrestrial construction to large on -orbit space structures due to the self erecting behaviour and a range of adaptive

Considering only a particular minimal form, in which three cables and one bar meet at each node. We refer the tensegrity structure with nine cables and three bars as T-3 prism and the one with twelve cables and four bars as T-4 prism. The prism transforms from a compact bundle of bars into a full three -dimensional framework as the last cable is pulled in tension. It changes from a form-finding structure to a pre stressed system. When all members except the last cable is connected, the system will remain as a loose bundle of bars and cables. The construction is first described for a structure in which the axial deformation of bars and cables is negligible. The displacement of the last pair of nodes is initially unrestrained, in that no structural resisting forces are developed at those nodes as the other cables and bars move with that displacement. At some specific separation length the two nodes can no longer approach one another, because the whole system has fall into a geometry in which a three dimensional truss has been formed. Any attempt to bring the nodes closer together becomes a force along that line of action that acts to pre stress all members in the truss. The structure has thereby reached its tensegrity geometry through a "form-finding" behaviour. The tensegrity geometry achieved is unique. Every member length, except for that of the last cable, has been