Steel and Composite Structures

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

An equivalent single-layer theory for free vibration analysis of steel-concrete composite beams

  • Sun, Kai Q. (School of Civil Engineering, Beijing Jiaotong University) ;
  • Zhang, Nan (School of Civil Engineering, Beijing Jiaotong University) ;
  • Liu, Xiao (School of Civil Engineering, Beijing Jiaotong University) ;
  • Tao, Yan X. (Railway Engineering Research Institute, China Academy of Railway Sciences Corporation Limited)
  • Received : 2020.07.22
  • Accepted : 2020.10.18
  • Published : 2021.02.10
⟨ Previous Next ⟩

Abstract

An equivalent single-layer theory (EST) is put forward for analyzing free vibrations of steel-concrete composite beams (SCCB) based on a higher-order beam theory. In the EST, the effect of partial interaction between sub-beams and the transverse shear deformation are taken into account. After using the interlaminar shear force continuity condition and the shear stress free conditions at the top and bottom surface, the displacement function of the EST does not contain the first derivatives of transverse displacement. Therefore, the C0 interpolation functions are just demanded during its finite element implementation. Finally, the EST is validated by comparing the results of two simply-supported steel-concrete composite beams which are tested in laboratory and calculated by ANSYS software. Then, the influencing factors for free vibrations of SCCB are analyzed, such as, different boundary conditions, depth to span ratio, high-order shear terms, and interfacial shear connector stiffness.

Keywords

Acknowledgement

The research described in this paper was financially supported by the Fundamental Research Funds for the Central Universities (2020JBM121) and the State Key Laboratory for Track Technology of High-Speed Railway, China (2018Y179).

References

  1. Bathe, K.J. (1996), Finite element procedures. Prentice Hall, Englewood Cliffs, New Jersey.
  2. Chakrabarti, A., Sheikh, A.H., Griffith, M. and Oehlers, D.J. (2012), "Analysis of composite beams with partial shear interactions using a higher order beam theory", Eng. Struct. 36(2012), 283-291. https://doi.org/10.1016/j.engstruct.2011.12.019.
  3. Chakrabarti, A., Sheikh, A.H., Griffith, M. and Oehlers, D.J. (2013), "Dynamic response of composite beams with partial shear interaction using a higher-order beam theory", J. Struct. Eng.-ASCE, 139(1), 47-56. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000603.
  4. Cho, M. and Parmerter, R.R. (1992), "An efficient higher-order plate theory for laminated composites", Compos. Struct., 20(1992), 113-123. https://doi.org/10.1016/0263-8223(92)90067-M.
  5. Cosmin, G.C. and Stefan, M.B. (2017), "Practical nonlinear inelastic analysis method of composite steel-concrete beams with partial composite action", Eng. Struct., 134(2017) 74-106. https://doi.org/10.1016/j.engstruct.2016.12.017.
  6. Fu, C. and Yang, X. (2018), "Dynamic analysis of partial-interaction Kant composite beams by weak-form quadrature element method", Arch. Appl. Mech., 88(1), 2179-2198. https://doi.org/10.1007/s00419-018-1443-1.
  7. Gattesco, N. (1999), "Analytical modeling of nonlinear behavior of composite beams with deformable connection", J. Constr. Steel Res., 52(2), 102-112. http://dx.doi.org/10.1016/j.engstruct.2016.12.017.
  8. Girhammar, U.A., Pan, D.H. and Gustafsson, A. (2009), "Exact dynamic analysis of composite beams with partial interaction", Int. J. Mech. Sci., 51(8), 565-582. https://doi.org/10.1016/j.ijmecsci.2009.06.004.
  9. Grundberg, S., Girhammar, U.A. and Hassan, O.A.B. (2014), "Dynamics of axially loaded and partially interacting composite beams", Int. J. Struct. Stab. Dy., 14(1), 1350047. https://doi.org/10.1142/S0219455413500478.
  10. He, G.H. and Yang, X. (2015), "Dynamic analysis of two-layer composite beams with partial interaction using a higher order beam theory", Int. J. Mech. Sci., 90(2015), 102-112. http://dx.doi.org/10.1016/j.ijmecsci.2014.10.020
  11. He, G.H., Wang, D.J. and Yang, X. (2016), "Analytical solutions for free vibration and buckling of composite beams using a higher order beam theory", Acta Mech. Solida Sin., 29(3), 300-315. https://doi.org/10.1016/S0894-9166(16)30163-X.
  12. Hou, Z.M., Xia, H. and Zhang, Y.L. (2012), "Dynamic analysis and shear connector damage identification of steel-concrete composite beams", Steel Compos. Struct., 13(4), 327-341. https://doi.org/10.12989/scs.2012.13.4.327.
  13. Huang, C.W. and Su, Y.H. (2008), "Dynamic characteristics of partial composite beams", Int. J. Struct. Stab. Dy., 8(4), 665-685. https://doi.org/10.1142/S0219455408002946
  14. Kant, T. and Gupta, A. (1988), "A finite element model for a higher-order shear-deformable beam theory", J. Sound Vib., 125(2), 193-202. https://doi.org/10.1016/0022-460X(88)90278-7.
  15. Kant, T., Owen, D.R.J. and Zienkiewicz, O.C. (1982), "A refined higher-order C0 plate bending element", Comput. Struct., 15(2), 177-183. https://doi.org/10.1016/0045-7949(82)90065-7.
  16. Newmark, N.M., Siess, C.P. and Viest, I.M. (1951), "Test and analysis of composite beams with incomplete interaction", Proc. Soc. Exp. Stress Anal., 9(1), 75-92.
  17. Nguyen, Q.H., Hjiaj, M. and Grognec, P.L. (2012), "Analytical approach for free vibration analysis of two-layer Timoshenko beams with interlayer slip", J. Sound Vib., 331(12), 2949-2961. https://doi.org/10.1016/j.jsv.2012.01.034_.
  18. Reddy, J.N. (1984), "A simple higher-order theory for laminated composite plates", J. Appl. Mech. ASME, 51(1984), 745-752. https://doi.org/10.1115/1.3167719.
  19. Ren X.H., Chen W.J. and Wu Z. (2011), "A new zig-zag theory and C0 plate bending element for composite and sandwich plates", Arch Appl. Mech., 81(2011) 185-197. https://doi.org/10.1007/s00419-009-0404-0.
  20. Schnabl, S., Saje, M., Turk, G. and Planinc, I. (2007), "Analytical solution of two-layer beam taking into account interlayer slip and shear deformation", J. Struc.t Eng.-ASCE, 133(6), 886-894. https://doi.org/10.1061/_ASCE_0733-9445_2007_133:6_886_.
  21. Schnabl, S., Saje, M., Turk, G. and Planinc, I. (2007), "Locking-free two-layer Timoshenko beam element with interlayer slip", Finite Elem. Anal. Des., 43(9), 705-714. https://doi.org/10.1016/j.finel.2007.03.002.
  22. Sciuva, M. Di (1986), "Bending, vibration and buckling of simply supported thick multilayered orthotropic plates: an evaluation of a new displacement model". J. Sound Vib., 105(1986), 425-442. https://doi.org/10.1016/0020-7683(70)90076-4.
  23. Sheremet'ev, M.P. and Pelekh, B.L. (1964), "Construction of an Improved Theory of Plates", Inzhenernyi Zhurnal, 1964, 4(3), 34-41.
  24. Timoshenko, S.P. (1921), "On the correction for shear of differential equation for transverse vibrations of bars of prismatic bars", Philos. Mag., 41(5) 744-746. https://doi.org/10.1080/14786442108636264.
  25. Uddin, M. A., Sheikh, A. H., Brown, D., Bennett, T. and Uy, B. (2018), "Geometrically nonlinear inelastic analysis of steel-concrete composite beams with partial interaction using a higher-order beam theory", Int. J. Non-Lin. Mech., 100(2018), 34-47. https://doi.org/10.1016/j.ijnonlinmec.2018.01.002.
  26. Uddin, M.A., Sheikh, A.H., Brown, D., Bennett, T. and Uy, B. (2017), "Large deformation analysis of two layered composite beams with partial shear interaction using a higher order beam theory", Int. J. Mech. Sci., 122(2017), 331-340. https://doi.org/10.1016/j.ijmecsci.2017.01.030.
  27. Wu, Y.F., Xu, R.Q. and Chen, W.Q. (2007), "Free vibrations of the partial-interaction composite members with axial force", J. Sound Vib. 299(4), 1074-1093. https://doi.org/10.1016/j.jsv.2006.08.008.
  28. Xu, R. and Wang, G. (2012), "Variational principle of partial-interaction composite beams using Timoshenko's beam theory", Int. J. Mech. Sci., 60(1), 72-83. http://dx.doi.org/10.1016/j.ijmecsci.2012.04.012.
  29. Xu, R. and Wu, Y. (2007), "Static dynamic and buckling analysis of partial interaction composite members using Timoshenko's beam theory", Int. J. Mech. Sci., 49(10), 1139-1155. https://doi.org/10.1016/j.ijmecsci.2007.02.006.

Cited by

  1. Exact Dynamic Characteristic Analysis of Steel-Concrete Composite Continuous Beams vol.2021, 2021, https://doi.org/10.1155/2021/5577276