Nonlinear Model for Cable Trusses Based on Polynomial Shape Functions and Energy Approach
Publication: Journal of Structural Engineering
Volume 142, Issue 7
Abstract
Biconcave cable trusses are widely utilized in engineering applications, representing an economical solution for large span roofs. The most common modeling approach is via the finite-element method (FEM). Analytical approaches have been proposed for biconcave cable trusses to provide good approximations while reducing the number of variables of the problem, but most of them do not take into account the slackening of cables. The approach proposed in this paper is based on the classical Ritz approach, using polynomial functions to approximate the deformed shape of the cable truss. The equilibrium configuration is found via minimization of total potential energy. The approach is suitable for most load conditions (distributed and concentrated). The model takes into account the nonlinearities attributable to the slackening of both vertical harnesses and bracing cables. The number of variables is reduced compared to a FEM approach, while the results show a good agreement with the FEM solution. This general approach provides a consistent frame from which previously presented closed-form solutions can be derived as particular cases. A previously studied, 60-m-span plane structure is simulated under different load conditions. The results are compared to previous works and to the results of the FEM approach, showing good consistency.
Get full access to this article
View all available purchase options and get full access to this article.
References
Bradshaw, R. (2005). “History of the analysis of cable net structures.” Metropolis and Beyond: Proc., 2005 Structures Congress, ASCE, Reston, VA.
Brew, J. S., and Lewis, W. J. (2003). “Computational form-finding of tension membrane structures—Non-finite element approaches. Part 1: Use of cubic splines in finding minimal surface membranes.” Int. J. Numer. Methods Eng., 56, 651–668.
Buchholdt, H. A. (1999). Introduction to cable roof structures, 2nd Ed., Thomas Telford, London.
Gasparini, D., and Gautam, V. (2002). “Geometrically nonlinear static behavior of cable structures.” J. Struct. Eng., 1317–1329.
Greco, L., and Cuomo, M. (2012). “On the force density method for slack cable nets.” Int. J. Solids Struct., 49(13), 1526–1540.
Greco, L., Impollonia, N., and Cuomo, M. (2014). “A procedure for the static analysis of cable structures following elastic catenary theory.” Int. J. Solids Struct., 51(7–8), 1521–1533.
Irvine, H. M. (1981). Cable structures, MIT Press, Cambridge, MA.
Kassimali, A., and Parsi-Feraidoonian, H. (1987). “Strength of cable trusses under combined loads.” J. Struct. Eng., 907–924.
Kmet, S., and Kokorudova, Z. (2006). “Nonlinear analytical solution for cable truss.” J. Eng. Mech., 119–123.
Kmet, S., and Kokorudova, Z. (2009). “Non-linear closed-form computational model of cable trusses.” Int. J. Non-Linear Mech., 44(7), 735–744.
Lasdon, L. S., Warren, A. D., Jain, A. M., and Ratner, M. (1978). “Design and testing of a generalized reduced gradient code for nonlinear programming.” ACM Trans. Math. Software, 4(1), 34–50.
Maier, G., and Contro, R. (1975). “Energy approach to inelastic cable-structure analysis.” J. Eng. Mech. Div., 101, 531–548.
Otto, F., and Schleyer, F. K. (1972). Tension structures, Ullstein, Berlin (in German).
Such, M., Jimenez-Octavio, J. R., Carnicero, A., and Lopez-Garcia, O. (2009). “An approach based on the catenary equation to deal with static analysis of three dimensional cable structures.” Eng. Struct., 31(9), 2162–2170.
Yeniay, O. (2005). “A comparative study on optimization methods for the constrained nonlinear programming problems.” Math. Problems Eng., 2005(2), 165–173.
Information & Authors
Information
Published In
Copyright
© 2016 American Society of Civil Engineers.
History
Received: Jan 10, 2015
Accepted: Nov 24, 2015
Published online: Feb 8, 2016
Published in print: Jul 1, 2016
Discussion open until: Jul 8, 2016
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.