Structural Engineering and Mechanics

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Static and dynamic analysis of cable-suspended concrete beams

  • Kumar, Pankaj (Department of Civil Engineering, Indian Institute of Technology Delhi) ;
  • Ganguli, Abhijit (Department of Civil Engineering, Indian Institute of Technology Tirupati) ;
  • Benipal, Gurmail (Department of Civil Engineering, Indian Institute of Technology Delhi)
  • Received : 2016.11.19
  • Accepted : 2017.09.09
  • Published : 2017.12.10
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Abstract

A new theory of weightless sagging planer elasto-flexible cables under point loads is developed earlier by the authors and used for predicting the nonlinear dynamic response of cable-suspended linear elastic beams. However, this theory is not valid for nonlinear elastic cracked concrete beams possessing different positive and negative flexural rigidity. In the present paper, the flexural response of simply supported cracked concrete beams suspended from cables by two hangers is presented. Following a procedure established earlier, rate-type constitutive equations and third order nonlinear differential equations of motion for the structures undergoing small elastic displacements are derived. Upon general quasi-static loading, negative nodal forces, moments and support reactions may be introduced in the cable-suspended concrete beams and linear modal frequencies may abruptly change. Subharmonic resonances are predicted under harmonic loading. Uncoupling of the nodal response is proposed as a more general criterion of crossover phenomenon. Significance of the bilinearity ratio of the concrete beam and elasto-configurational displacements of the cable for the structural response is brought out. The relevance of the proposed theory for the analysis and the design of the cable-suspended bridges is critically evaluated.

Keywords

Acknowledgement

Supported by : Indian Institute of Technology Delhi

References

  1. Antman, S.S. (2005), Nonlinear Problems of Elasticity, Springer.
  2. Benipal, G.S. (1994), "A study on the nonlinear elastic behavior of reinforced concrete structural elements under normal loading", Ph.D. Dissertation, Department of Civil Engineering, IIT Delhi.
  3. Benipal, G.S. (1994), "Rational mechanics of cracked concrete beams", Proceedings of the National Symposium on Structural Mechanics, Bangalore, June.
  4. Coarita, E. and Flores, L. (2015), "Nonlinear analysis of structures cable-truss", IACSIT Int. J. Eng. Tech., 7(3), 160-169. https://doi.org/10.7763/IJET.2015.V7.786
  5. Deng, H.Q., Li, T.J., Xue, B.J. and Wang, Z.W. (2015), "Analysis of thermally induced vibration of cable- beam structures", Struct. Eng. Mech., 53(3), 443-453. https://doi.org/10.12989/sem.2015.53.3.443
  6. Irvine, H.M. and Caughey, T.K. (1974), "The linear theory of free vibrations of a suspended cable", Math. Phys. Sci., 341(1626), 299-315. https://doi.org/10.1098/rspa.1974.0189
  7. Kim, K.S. and Lee, H.S. (2001), "Analysis of target configurations under dead loads for cable-supported bridges", Comput. Struct., 79, 2681-2692. https://doi.org/10.1016/S0045-7949(01)00120-1
  8. Kumar, P., Ganguli, A. and Benipal, G.S. (2016), "Theory of weightless sagging elasto-flexible cables", Latin Am. J. Solid. Struct., 13(1), 155-174. https://doi.org/10.1590/1679-78252110
  9. Kumar, P., Ganguli, A. and Benipal, G.S. (2017), "Mechanics of cable-suspended structures", Latin Am. J. Solid. Struct., 14(3), 544-559. https://doi.org/10.1590/1679-78253259
  10. Lacarbonara, W. (2013), Nonlinear Structural Mechanics: Theory Dynamical Phenomenon and Modelling, Springer.
  11. Lepidi, M. and Gattulli, V. (2014), "A parametric multi-body section model for modal interactions of cable- supported bridges", J. Sound Vib., 333, 4579-4596. https://doi.org/10.1016/j.jsv.2014.04.053
  12. Menon, D. (2009), Advanced Structural Analysis, Narosa.
  13. Pandey, U.K. and Benipal, G.S. (2006), "Bilinear dynamics of SDOF concrete structures under sinusoidal loading", Adv. Struct. Eng., 9(3), 393-407. https://doi.org/10.1260/136943306777641869
  14. Pandey, U.K. and Benipal, G.S. (2011), "Bilinear elastodynamical models of cracked concrete beams", Struct. Eng. Mech., 39(4), 465-498. https://doi.org/10.12989/sem.2011.39.4.465
  15. Rega, G. (2004), "Nonlinear vibrations of suspended cables-Part I: Modelling and analysis", Appl. Mech. Rev., 57(6), 443-478. https://doi.org/10.1115/1.1777224
  16. Santos, H.A.F.A. and Paulo, C.I.A. (2011), "On a pure complementary energy principle and a force-based finite element formulation for non-linear elastic cable", Int. J. Nonlin. Mech., 46, 395-406. https://doi.org/10.1016/j.ijnonlinmec.2010.10.005
  17. Sun, B., Zhang, L., Qin, Y. and Xiao, R. (2016), "Economic performance of cable supported bridges", Struct. Eng. Mech., 59(4), 621-652. https://doi.org/10.12989/sem.2016.59.4.621
  18. Vu, T.V., Lee, H.E. and Bui, Q.T. (2012), "Nonlinear analysis of cable-supported structures with a spatial catenary cable element", Struct. Eng. Mech., 43(5), 583-605 https://doi.org/10.12989/sem.2012.43.5.583
  19. Zhang, X., and Bui, T.Q. (2015), "A fictitious crack XFEM with two new solution algorithms for cohesive crack growth modeling in concrete structures", Eng. Comput., 32(2), 473-497. https://doi.org/10.1108/EC-08-2013-0203