Time-Dependent Analysis of Prestressed Cable Nets
Publication: Journal of Structural Engineering
Volume 142, Issue 7
Abstract
In this paper, time-dependent nonlinear numerical and analytical computational models suitable for rheological analysis of prestressed cable nets subjected to creep effects are presented. The principal aim of this contribution is to describe a developed design computational tool for a theoretical simulation of the time-dependent behavior of cable nets and predict their rheological characteristics. For this purpose, a modified finite-element method for the time-dependent analysis of materially linear and geometrically nonlinear cable nets is proposed. Creep constitutive equations in the logarithmic form are incorporated into the finite-element model to express the current lengths of cables as the functions of creep strain increments. As an extension of the Irvine approach, a geometrically nonlinear time-dependent analytical static solution of taut flat cable nets over an orthogonal square plan is presented. The cable net is replaced by an equivalent membrane. Creep strain is incorporated into the compatibility equation of the structure. Examples are presented. Results of time-dependent analyses of cable nets confirmed the required functionality and performance of the developed numerical and analytical computational models.
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Acknowledgments
This work is part of Research Project No. 1/0321/12, partially founded by the Scientific Grant Agency of the Ministry of Education of the Slovak Republic and the Slovak Academy of Sciences. The present research has been carried out within the project: Centre of excellent integrated research for progressive building structures, materials and technologies, supported by European Union Structural funds.
References
ABAQUS [Computer software]. Dassault Systèmes Simulia Corp., Johnston, RI.
ADINA [Computer software]. ADINA R&D, Watertown, MA.
Andreu, A., Gil, L., and Roca, P. (2006). “A new deformable catenary element for the analysis of cable net structures.” Comput. Struct., 84(29-30), 1882–1890.
ANSYS [Computer software]. Canonsburg, PA ANSYS.
ASCE. (2010). “Structural applications of steel cables for buildings.” ASCE/Structural Engineering Institute, Reston, VA.
Barnes, M. (1994). “Form and stress engineering of tension structures.” Struct. Eng. Rev., 6(3-4), 175–202.
Buchholdt, H. A. (1998). Introduction to cable roof structures, 2nd Ed., Cambridge University Press, Cambridge, MA.
Deng, H., Jiang, Q. F., and Kwan, A. S. K. (2005). “Shape finding of incomplete cable-strut assemblies containing slack and prestressed elements.” Comput. Struct., 83(21-22), 1767–1779.
Firt, V. (1982). Statics, form-finding and dynamics of air-supported membrane structures, Academia Press, Prague, Czech Republic.
Gasparini, D., and Gautam, V. (2002). “Geometrically nonlinear static behaviour 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.
Grundig, L., and Bahndorf, J. (1988). “The design of wide-span roof structures using micro-computers.” Comput. Struct., 30(3), 495–501.
Husiar, B., and Switka, R. (1986). “Creep and relaxation in net structures.” Proc., IASS Symp. on Membrane Structures and Space Frames, Vol. 2, Elsevier, New York, 63–70.
Irvine, H. M. (1981). Cable structures, MIT Press, Cambridge, MA.
Jayaraman, H. B., and Knudson, W. C. (1981). “A curved element for the analysis of cable structures.” Comput. Struct., 14(3-4), 325–333.
Kanno, Y., Ohsaki, M., and Ito, J. (2002). “Large-deformation and friction analysis of non-linear elastic cable networks by second-order cone programming.” Int. J. Numer. Methods Eng., 55(9), 1079–1114.
Kao, R., and Perrone, N. (1972). “Large deflection of flat arbitrary membranes.” Comput. Struct., 2(4), 535–546.
Kassimali, A., and Parsi-Feraidoonian, H. (1987). “Strength of cable trusses under combined loads.” J. Struct. Eng., 907–924 .
Kaveh, A., Rahami, H., and Nikbakht, M. (2010). “Vibration analysis of regular structures by graph products: Cable networks.” Comput. Struct., 88(9-10), 588–601.
Kmet, S. (1994). “Rheology of prestressed cable structures.” Advances in finite element techniques, M. Papadrakakis and B. H. V. Topping, eds., Civil-Comp Press, Edinburgh, Scotland, 185–200.
Kmet, S. (2004). “Non-linear rheology of tension structural element under single and variable loading history. I: Theoretical derivations.” Struct. Eng. Mech. Int. J., 18(5), 565–589.
Kmet, S., and Holickova, L. (2004). “Non-linear rheology of tension structural element under single and variable loading history. II: Creep of steel rope—Examples and parametrical study.” Struct. Eng. Mech. Int. J., 18(5), 591–607.
Kmet, S., and Mojdis, M. (2013). “Time-dependent analysis of cable domes using a modified dynamic relaxation method and creep theory.” Comput. Struct., 125, 11–22.
Krishna, P. (1977). Cable-suspended roofs, McGraw-Hill, New York.
Kwan, A. S. K. (1998). “A new approach to geometric nonlinearity of cable structures.” Comput. Struct., 67(4), 243–252.
Lewis, W. J. (2003). Tension structures: Form and behavior, Thomas Telford, London.
Lewis, W. J., Jones, M. S., and Rushton, K. R. (1984). “Dynamic relaxation analysis of the non-linear static response of pretensioned cable roofs.” Comput. Struct., 18(6), 989–997.
Lopez-Garcia, O., Carnicero, A., Torres, V., and Jimenez-Octavio, J. R. (2008). “The influence of cable slackening on the stiffness computation od railway overheads.” Int. J. Mech. Sci., 50(7), 1213–1223.
Luo, X. Q., Zhang, Q. L., and Chen, L. (2012). “Form-finding of a mixed structure with cable nets and tubular trusses.” J. Constr. Steel Res., 72, 192–202.
Malerba, P. G., Patelli, M., and Quagliaroli, M. (2012). “An extended force density method for the form finding of cable systems with new forms.” Struct. Eng. Mech. Int. J., 42(2), 191–210.
MATLAB [Computer software]. MathWorks, Natick, MA.
Maurin, B., and Motro, R. (1988). “The surface stress density method as a form-finding tool for tensile membranes.” Eng. Struct., 20(8), 712–719.
Møllmann, H. (1974). Analysis of hanging roofs by the displacement method, Polyteknisk Forlag, Lyngby, Denmark.
Otto, F. (1973). Tensile structures: Design, structures and calculation of buildings of cables, nets and membranes, MIT Press, Cambridge, MA.
Pauletti, R. M. O., and Pimenta, P. M. (2008). “The natural force density method for the shape finding of taut structures.” Comput. Methods Appl. Mech. Eng., 197(49-50), 4419–4428.
Raknes, S. B., Deng, X., Bazilevs, Y., Benson, D. J., Mathisen, K. M., and Kvamsdal, T. (2013). “Isogeometric rotation-free bending-stabilized cables: Statics, dynamics, bending strips and coupling with shells.” Comput. Methods Appl. Mech. Eng., 263, 127–143.
Salehi Ahmad Abad, M., Shooshtari, A., Esmaeili, V., and Naghavi Riabi, A. (2013). “Nonlinear analysis of cable structures under general loadings.” Finite Elem. Anal. Des., 73, 11–19.
Sanchez, J., Serna, M. A., and Morer, P. (2007). “A multi-step force-density method and surface-fitting approach for the preliminary shape design of tensile structures.” Eng. Struct., 29(8), 1966–1976.
Schek, H. J. (1974). “The force density method for form finding and computation of general networks.” Comput. Methods Appl. Mech. Eng., 3(1), 115–134.
Schleyer, F. K. (1969). Tensile structures, Vol. 2, MIT Press, Cambridge, MA.
SCIA Engineer. (2013). “SCIA engineer manuals.” Columbia, MD.
Shore, S., and Bathish, G. N. (1967). Space structures, Blackwell, London.
Switka, R., and Husiar, B. (1984). “Discrete analysis of rheological models.” J. Theor. Appl. Mech., 22(1-2), 209–233.
Talvik, I. (2001). “Finite element modelling of cable networks with flexible supports.” Comput. Struct., 79(26-28), 2443–2450.
Topping, B. H. V., and Ivanyi, P. (2007). Computer aided design of cable membrane structures, Saxe-Coburg, Stirlingshire, Scotland.
Tworzydlo, W. W. (1987). “Analysis of large deformations of membrane shells by the generalized finite difference method.” Comput. Struct., 27(1), 39–59.
Vassilopoulou, I., and Gantes, C. J. (2011). “Nonlinear dynamic behavior of saddle-form cable nets under uniform harmonic load.” Eng. Struct., 33(10), 2762–2771.
Wakefield, D. S. (1999). “Engineering analysis of tension structures: Theory and practice.” Eng. Struct., 21(8), 680–690.
Wang, Z., Li, T., and Cao, Y. (2013). “Active shape adjustment of cable net structures with PZT actuators.” Aerosp. Sci. Technol., 26(1), 160–168.
Wood, R. D. (2002). “A simple technique for controlling element distortion in dynamic relaxation form-finding of tension membranes.” Comput. Struct., 80(27-30), 2115–2120.
Zhou, B., Accorsi, M., and Leonard, J. W. (2004). “Finite element formulation for modeling sliding cable elements.” Comput. Struct., 82(2-3), 271–280.
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Published In
Journal of Structural Engineering
Volume 142 • Issue 7 • July 2016
Copyright
© 2016 American Society of Civil Engineers.
History
Received: Dec 21, 2014
Accepted: Nov 3, 2015
Published online: Feb 16, 2016
Published in print: Jul 1, 2016
Discussion open until: Jul 16, 2016
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