Structural Engineering and Mechanics

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Exact closed-form equations for internal forces functions of bridge-type structures

  • Received : 2019.12.21
  • Accepted : 2021.08.11
  • Published : 2021.10.25
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Abstract

Influence lines and internal forces functions are vital tools for designing and monitoring engineering structures. This research explored a static method to derive exact closed-form equations for internal forces functions of bridge-type structures, continuous beams, and bridge frames, considering the bending flexibility. For this aim, first, we achieved member-end moment functions by applying the moment-rotation relationships in conjunction with the rotation propagation method. Then, substituting these functions into the static equilibrium equations provided the desired functions in terms of both the unit load and intended cross-section positions all over the structure, subjected to concentrated loads. Finally, the authors solved three illustrative examples to clarify the dominance of their suggested method for constructing both influence line and internal forces diagrams of statically indeterminate structures.

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References

  1. Belegundu, A. (1988), "The adjoint method for determining influence lines", Comput. Struct., 29(2), 345-350. https://doi.org/10.1016/0045-7949(88)90269-6.
  2. Buckley, E. (1997), "Basic influence line equations for continuous beams and rigid frames", J. Struct. Eng., 123(10), 1416-1420. https://doi.org/10.1061/(ASCE)0733-9445(1997)123:10(1416)
  3. Catbas, F.N., Zaurin, R., Gul, M. and Gokce, H.B. (2012), "Sensor networks, computer imaging, and unit influence lines for structural health monitoring: case study for bridge load rating", J. Bridge Eng., 17(4), 662-670. https://doi.org/10.1061/(asce)be.1943-5592.0000288.
  4. Chen, Z.W., Cai, Q.L. and Zhu, S. (2018), "Damage quantification of beam structures using deflection influence lines", Struct. Control Hlth. Monit., 25(11), e2242. https://doi.org/10.1002/stc.2242.
  5. Chen, Z.W., Cai, Q.L., Lei, Y. and Zhu, S.Y. (2014), "Damage detection of long-span bridges using stress influence lines incorporated control charts", Sci. China Tech. Sci., 57(9), 1689-1697. https://doi.org/10.1007/s11431-014-5623-0.
  6. Dowell, R.K. (2009), "Closed-form moment solution for continuous beams and bridge structures", Eng. Struct., 31(8), 1880-1887. https://doi.org/10.1016/j.engstruct.2009.03.012.
  7. Fiorillo, G. and Ghosn, M. (2015), "Application of influence lines for the ultimate capacity of beams under moving loads", Eng. Struct., 103, 125-133. https://doi.org/10.1016/j.engstruct.2015.09.003.
  8. Ghali, A., Neville, A.M. and Brown, T.G. (2009), Structural Analysis A Unified Classical and Matrix Approach, Taylor and Francis.
  9. Hirachan, J. (2006), Development of Experimental Influence Lines for Bridges, University of Delaware, United States.
  10. Hosseini-Tabatabaei, M.-R., Rezaiee-Pajand, M. and Mollaeinia, M.R. (2020), "Bridge-type structures analysis using RMP concept considering shear and bending flexibility", Struct. Eng. Mech., 74(2), 189-199. https://doi.org/10.12989/sem.2020.74.2.189.
  11. Hosseini-Tabatabaei, M.R. and Rezaiee-Pajand, M. (2012), "Analysis of continuous beams and bridge frames based on propagating rotations", J. Iran. Soc. Civil Eng., 14(34), 53-61.
  12. Hozhabrossadati, S.M. and Aftabi Sani, A. (2016), "Application of Green's functions for constructing influence lines", J. Eng. Mech., 142(3), 04015097-04015091-04015015. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001016.
  13. Huang, J. and Shenton III, H.W. (2008). "Experimentally determined continuous displacement influence lines for bridges", Structures Congress 2008: Crossing Borders.
  14. Jepsen, M.S. and Damkilde, L. (2016), "A direct and fully general implementation of influence lines/surfaces in finite element software", Adv. Eng. Softw., 120, 55-61. https://doi.org/10.1016/j.advengsoft.2016.04.006.
  15. Karnovsky, I.A. and Lebed, O. (2010), Advanced Method of Structural Analysis, Springer.
  16. Megson, T.H.G. (2014), Influence Lines Chap20, Elsevier Ltd.
  17. Orakdogen, E. and Girgin, K. (2005), "Direct determination of influence lines and surfaces by F.E.M.", Struct. Eng. Mech., 20(3), 279-292. https://doi.org/10.12989/sem.2005.20.3.279.
  18. Shihua, B. and Yaoging, G. (2008), Structural Mechanics, Wuhan University Press, Wuhan.
  19. Wang, N.B., He, L.X., Ren, W.X. and Huang, T.L. (2017), "Extraction of influence line through a fitting method from bridge dynamic response induced by a passing vehicle", Eng. Struct., 151, 648-664. https://doi.org/10.1016/j.engstruct.2017.06.067.
  20. Yang, D., Chen, G. and Du, Z. (2015), "Direct kinematic method for exactly constructing influence lines of forces of statically indeterminate structures", Struct. Eng. Mech., 54(4), 793-807. https://doi.org/10.12989/sem.2015.54.4.793.
  21. Zhao, H., Uddin, N., Shao, X., Zhu, P. and Tan, C. (2015), "Field-calibrated influence lines for improved axle weight identification with a bridge weigh-in-motion system", Struct. Infrastr. Eng., 11(6), 721-743. https://doi.org/10.1080/15732479.2014.904383.
  22. Zhu, S., Chen, Z., Cai, Q., Lei, Y. and Chen, B. (2014), "Locate damage in long-span bridges based on stress influence lines and information fusion technique", Adv. Struct. Eng., 17(8), 1089-1102. https://doi.org/10.1260/1369-4332.17.8.1089