Keywords: cable net, form-finding, formulation, force density, least squares, saddle.

The first section of the paper the advantages of cable net structures and an explanation as to why these structures are not widely used is presented. This section also describes the methods which are used to analyse these cable net structures and the reasons of preferring the force density method [1] for analyzing these structures to the other methods of analysis. In this section the force density method with the simple least squares approach are introduced to be an accurate way to analyze these cable net structures. This section also presents the parameters which have to be considered in the analysis and design of cable net structures. The second section presents the formulation of the force density method "nonlinear approach" which includes the main important equations of the force density method and the least squares approach. A computer program in Matlab [2] has been developed based on this previously mentioned formulation.

In the third section numerical examples [3,4] are presented that verify the program and the results of the present computer program are compared with the published results and found to be in a good agreement.

In the fourth section of the paper two parameters have been studied. The first parameter is the deviation of the net cables and the second is the error in the length of the net cables. The deviation of the net cables has been studied through two examples. The first example is a saddle cable net with regular curvature and the second is a saddle cable net with irregular curvature. It has been proved that the force density method implemented with simple least squares approach with some experience in adjusting the force densities of the edge cables connected to the inner deviated cables is more effective in reducing the cable net deviations than applying the force density method implemented with the modified damped least squares approach. The second parameters "the length error in the net cables" has been studied through three different cable net types. The first type is saddle cable net with regular curvature. The second type is saddle cable net with irregular curvature, and the third is tent cable net. The first and the second cable net types have been studied under three different cases of sag-span ratio.

In section 5, six conclusions related to the method of analysis used in this research and the two studied parameters which have been proved to be important in the analysis and design of cable net structures are presented.

1

H.-J. Schek, "The force density method for form finding and computation of general networks", Computer Methods in Applied Mechanics and Engineering, Vol.3, 115-134, 1974. doi:10.1016/0045-7825(74)90045-0

2

D. Hanselman, B. Littlefield, "Mastering MATLAB 6", USA, Prentice Hall, ISBN 0-13-019468-9.

3

F.A. Fath El-Bab, H.A. Zien El-Din, N. El-Shabasy, "Linear approach analysis of kinamatically indeterminate assemblies", Alexandria Engineering Journal, Vol. 42 No. 5 & 6, pp. 613-629, 2003.

4

G. Tibert, "Numerical Analyses of Cable Roof Structures", SE-100 44 Stockholm, Sweden, TRITA-BKN Bulletin 46, ISSN 1103-4270, 1999.

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