Email this article Methods for multi-segment continuous cable analysis
DOI: https://doi.org/10.20528/cjsmec.2023.02.001
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Cables are invaluable members for some applications of engineering. The specialty is due to its behavior under transverse loads. Having almost no rigidity in transverse direction makes cables different from other structural elements. In most applications, cables are assumed to be two force members. However, not only its weight but also its application with roller supports makes them different structural elements. Generally, cables are assembled as single-segmented cables (SSC) where they are fixed at their ends. However, in most of the SSC applications, cables have intermediate supports which can be rollers or sliders. These type of cable applications are called as multi-segment continuous cables (MSCC). In MSCC systems, the cable fixed at its ends and supported by a number of intermediate rollers. Total length of cable is constant, and the intermediate supports are assumed to be frictionless and stationary. In this problem, the critical issue is to find the distribution of the cable length among the segments in the final equilibrium state, so reactions at all supports can be found. Two methods are proposed for the segment length adjustment based on the stress continuity among the cable. These methods are named as direct stiffness method and tension distribution method (relaxation method). Results calculated from the proposed methods are verified by both the reference benchmark problems and commercial finite element program.
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Andreu, A., Gil, L., & Roca, P. (2006). A new deformable catenary element for the analysis of cable net structures. Computer & Structures, 84(29–30), 1882–1890. https://doi.org/10.1016/j.compstruc.2006.08.021
Aufaure, M. (1993). A finite element of cable passing through a pulley. Computers & Structures, 46(5), 807–812. https://doi.org/https://doi.org/10.1016/0045-7949(93)90143-2
Aufaure, M. (2000). Three-node cable element ensuring the continuity of the horizontal tension; A clamp-cable element. Computers and Structures, 74(2), 243–251. https://doi.org/10.1016/S0045-7949(99)00015-2
Bel Hadj Ali, N., Sychterz, A. C., & Smith, I. F. C. (2017). A dynamic-relaxation formulation for analysis of cable structures with sliding-induced friction. International Journal of Solids and Structures, 126–127, 240–251. https://doi.org/10.1016/j.ijsolstr.2017.08.008
Christou, P., Michael, A., & Elliotis, M. (2014). Implementing slack cables in the force density method. Engineering Computations (Swansea, Wales), 31(5), 1011–1030. https://doi.org/10.1108/EC-03-2012-0054
Dehghan, M., & Abbaszadeh, M. (2016). Analysis of the element free Galerkin (EFG) method for solving fractional cable equation with Dirichlet boundary condition. Applied Numerical Mathematics, 109, 208–234. https://doi.org/10.1016/j.apnum.2016.07.002
Demir, A. (2011). Form finding and structural analysis of cables with multiple supports. Middle East Technical University.
Dinçer, A. E., & Demir, A. (2020). Application of Smoothed Particle Hydrodynamics to Structural Cable Analysis. In Applied Sciences (Vol. 10, Issue 24). https://doi.org/10.3390/app10248983
Dischinger, F. (1949). Hängebrücken fur Schwerste Verkehrslasten. Der Bauingenieur, 24, 65–107.
Ernst, H. J. (1965). Der E-Modul von Seilen unter Brucksichtigung des Durchhangers. Der Bauingenieur, 40(2), 52–55.
Fleming, J. F. (1979). Nonlinear static analysis of cable-stayed bridge structures. Computers & Structures, 10(4), 621–635. https://doi.org/https://doi.org/10.1016/0045-7949(79)90006-3
Hajdin, N., Michaltsos, G. T., & Konstantakopoulos, T. G. (1998). About the equivalent modulus of elasticity of cables of cable-stayed bridges. Sci. J. Facta Universitatis Arc and Civil Eng Series, 1(5), 569–575.
Jayaraman, H. B., & Knudson, W. C. (1962). A curved element for the analysis of cabe structures. Trans. Am. Soc. Civ. Eng., 127, 267–281.
Ju, F., & Choo, Y. S. (2005). Super element approach to cable passing through multiple pulleys. International Journal of Solids and Structures, 42(11–12), 3533–3547. https://doi.org/10.1016/j.ijsolstr.2004.10.014
Judge, R., Yang, Z., Jones, S. W., & Beattie, G. (2012). Full 3D finite element modelling of spiral strand cables. Construction and Building Materials, 35, 452–459. https://doi.org/10.1016/j.conbuildmat.2011.12.073
McDonald, B. M., & Peyrot, A. H. (1988). Analysis of Cables Suspended in Sheaves. Journal of Structural Engineering, 114(3), 693–706. https://doi.org/10.1061/(asce)0733-9445(1988)114:3(693)
McDonald, B. M., & Peyrot, A. H. (1990). Sag‐Tension Calculations Valid for Any Line Geometry. Journal of Structural Engineering, 116(9), 2374–2386. https://doi.org/10.1061/(asce)0733-9445(1990)116:9(2374)
Michalos, J., & Birnstiel, C. (1962). Movements of a cable due to changes in loading. Trans. Am. Soc. Civ. Eng., 127, 267–281.
Noguchi, H., & Kawashima, T. (2004). Meshfree analyses of cable-reinforced membrane structures by ALE–EFG method. Engineering Analysis with Boundary Elements, 28(5), 443–451. https://doi.org/https://doi.org/10.1016/S0955-7997(03)00098-5
O’Brien, W. T., & Francis, A. J. (1964). Cable movements under two-dimensional loads. Journal of Structural Division ASME, 90, 89–124.
Peyrot, A. H., & Goulois, A. M. (1979). Analysis of cable structures. Computers and Structures, 10(5), 805–813. https://doi.org/10.1016/0045-7949(79)90044-0
Polat, U. (1981). Nonlinear computer analysis of guyed towers and cables. Middle East Technical University.
Prawoto, Y., & Mazlan, R. B. (2012). Wire ropes: Computational, mechanical, and metallurgical properties under tension loading. Computational Materials Science, 56, 174–178. https://doi.org/10.1016/j.commatsci.2011.12.034
Ren, W.-X., Huang, M.-G., & Hu, W.-H. (2008). A parabolic cable element for static analysis of cable structures. Engineering Computations: Int J for Computer-Aided Engineering, 25, 366–384. https://doi.org/10.1108/02644400810874967
Salehi, A. A. M., Shooshtari, A., Esmaeili, V., & Naghavi Riabi, A. (2013). Nonlinear analysis of cable structures under general loadings. Finite Elements in Analysis and Design, 73, 11–19. https://doi.org/https://doi.org/10.1016/j.finel.2013.05.002
Skop, R. A., & O’Hara, G. J. (1970). The method of imaginary reactions: a new technique for analyzing structural cable systems. Marine Technology Society Journal, 4(1), 21–30.
Thai, H.-T. T., & Kim, S.-E. E. (2011). Nonlinear static and dynamic analysis of cable structures. Finite Elements in Analysis and Design, 47(3), 237–246. https://doi.org/https://doi.org/10.1016/j.finel.2010.10.005
Tibert, G. (1999). Numerical analyses of cable roof structures. KTH.
Yang, Y. B. . B. B., & Tsay, J.-Y. (2007). Geometric nonlinear analysis of cable structures with a two-node cable element by generalized displacement control method. International Journal of Structural Stability and Dynamics, 07(04), 571–588. https://doi.org/10.1142/S0219455407002435
Zhou, B., Accorsi, M. L., & Leonard, J. W. (2004). Finite element formulation for modeling sliding cable elements. Computers and Structures, 82(2–3), 271–280. https://doi.org/10.1016/j.compstruc.2003.08.006
