The analysis of nonlinear cable net systems and their supporting structures

Abstract

The analysis of large cable net systems is feasible only with the aid of high speed digital computers. However, even computerized design of cable nets requires careful formulation and the selection of efficient solution techniques. This paper describes the solution of a general integrated structural system which includes three-dimensional beam members and cable elements that is useful to the design engineer. This solution is used to analyze an example prestressed cable structure, and results are presented to demonstrate the efficiency and accuracy of different solution techniques and to illustrate the effect of variation of important parameters. NET 3 is the general solution program. Input includes: (1) cable sizes, weights, and stress-strain characteristics; (2) initial coordinate points and cable forces due to prestressing; (3) support conditions for the cable net; (4) applied loads; and (5) data for supporting structure. The initial shape and cable forces are computed with the aid of an auxilliary program, SHAPE, given the coordinates of the cable end points, the initial prestressing forces, and an initial interior coordinate. The cable stress-strain characteristics may be linear or nonlinear. The supporting structure may be replaced with equivalent spring stiffnesses or actual three-dimensional elements. The assumptions used in the solution are: (1) cable elements are straight between nodal points and have no flexural stiffnesses; (2) the roofing and decking provide no stiffness; (3) all loads are applied at the nodal points; and (4) all supporting structural elements are elastic. It should be noted that no displacements of the cable nodal points are neglected. Even at boundaries, the elastic stiffness can be considered. Temperature changes can be analyzed to determine their effect upon the structure. Cable net structures usually have many elements and require relatively large amounts of computer time. In addition many loading and geometric conditions must be considered. To be useful as a practical design tool, it was essential that the program be as efficient as possible and require a minimum of storage. The solution utilizes a variation of the Newton-Raphson method. Initially the tangent-modulus stiffness is used. At each iteration the change in the element force is compared with the change in element force for the previous iteration to determine if the convergence rate is within a prescribed value. If it is acceptable, the stiffness for the previous iteration is used; if unacceptable for any element, tangent stiffnesses for all elements are recalculated. This technique attempts to combine the best features of the Newton-Raphson and the modified Newton-Raphson methods by increasing convergence probability and decreasing solution time. To minimize storage requirements, NET 3 has the capability of utilizing tapes in the problem solution. The storage requirements are determined internally before the solution is initiated. If the required storage exceeds that alloted for the system of equations, the solution is effected through the use of tapes. Output for the cables includes nodal point displacements, nodal point forces, and element forces; for beam elements, forces and moments are given. The solution has been verified by comparison with results by other investigators. An elliptical shaped structure, 220 by 240 ft, has been analyzed with the program to investigate the influence of several parameters. The short direction cables were prestressed, and a uniform load of 40 psf was assumed. The variables investigated include: (1) initial prestress force; (2) degree of stiffness of supporting structure; (3) cable sizes; (4) sag-span ratio; and (5) temperature change.