Tracy H. Zhang (hzhang@hotmail.com)

and

Steven L. McCabe

Department of Civil and Environmental Engineering,

University of Kansas

Lawrence, Kansas 66045

This paper reports on a project that has developed two methods to analyze and design cable tensile structures. The analysis module includes FEM solution and a method to refine a 2D-computer model to determine 3D state. Results are compared to these two ways.

Tensile structures have gained much popularity in recent decades due to their notable advantages, which include superiority to cover long spans and efficiency in the use of materials. However, the analysis process is particularly challenging. Specifically the necessity of the form-finding procedure and the analysis of cable and membrane using large displacement theory make tensile structure analysis a complicated and time-consuming process. The absence of flexural rigidity in the membrane makes it impossible to produce the shape of a tension structure prior to loading. Because the displacement is generally large in magnitude, the small deflection theory is inadequate for large displacements. The combination of the applied loads and internal stresses, which depend upon the curvature of the shape, give rise to a set of nonlinear equilibrium equations. The stress- strain relationship of membrane materials is highly non-linear. Fortunately this relation is nearly linear within the allowable stress range of most structural membranes. Practical analysis generally does not require accounting for non-linear material properties. The nonlinearly is of the geometrical type and the strains generally remain within the limits of linear stress-strain relations of the material. The deformations associated with applied loads usually influence the resolution of those forces, making load analysis a geometrically non-linear problem.

The solution is application Finite Element Method and the solution obtained for the minimum energy configuration. Using a Largrangian formulation instead of standard finite element formulations. Tension Structures are usually modeled using two-dimensional elements with different properties in the warp and fill directions. However, designers often find it convenient to analytically model a membrane surface as a network of cables or bars. Uniaxial elements are simpler to formulate and analyze than biaxial elements. If the analysis mesh is set with nodes on the principal surface curvatures and the element properties are adjusted to reflect the effective tributary area and stress, the behavior of a membrane surface can generally be adequately examined with cable elements. Accounting for biaxial interaction, such as the effect of Poisson’s ratio requires special adjustment during the analysis. However these are usually not significant.

Parsons Brinckerhoff Company created the other method when they designed and constructed a canopy in New Jersey. Basically, the natural shape of the fabric can be generated by refining a 2D-computer model to determine 3D state using a geometric nonlinear analysis program.

This project results will simplify the complex design process of tension structures and save time for designers. The utilization of this result will make the design of tension structures a more straightforward processes and allowing development of new results for the structures.

Graduate Research Assistant

Department of Civil & Environmental Engineering
2006 Learned Hall
University of Kansas
Lawrence, Kansas 66045-2225
USA

Phone: (O) (785) 864-3853