DOI QR코드

DOI QR Code

Nondestructive damage evaluation of deep beams

  • Received : 2017.08.08
  • Accepted : 2017.09.02
  • Published : 2017.09.25

Abstract

This paper presents a Level III damage evaluation methodology, which simultaneously, identifies the location, the extent, and the severity of stiffness damage in deep beams. Deep beams are structural elements with relatively high aspect (depth-to-length) ratios whose response are no longer based on the simplified Euler-Bernoulli theory. The proposed methodology is developed on the bases of the force-displacement relations of the Timoshenko beam theory and the concept of invariant stress resultants, which states that the net internal force existing at any cross-section of the beam is not affected by the inflicted damage, provided that the external loadings in the undamaged and damaged beams are identical. Irrespective of the aspect ratios, local changes in both the flexural and the shear stiffnesses of beam-type structures may be detected using the approach presented in this paper.

Keywords

References

  1. Ashraf, FA. (1997), "Tests of reinforced concrete continuous deep beams", ACI Struct. J., 94(1), 3-12.
  2. Berman, A. and Flannely, W.G. (1971), "Theory of incomplete models of dynamic structures", AIAA J., 9(8), 1481-1487. https://doi.org/10.2514/3.49950
  3. Cawley, P. and Adams, R.D. (1997), "The locations of defects in structures from measurements of natural frequencies", J. Strain Anal., 14(2), 49-57.
  4. Choi, S., Park, S. and Stubbs, N. (2005), "Nondestructive damage detection in structures using changes in compliance", Int. J. Solids Struct., 42(15), 4494-4513. https://doi.org/10.1016/j.ijsolstr.2004.12.017
  5. Choi, S., Sooyong. P., Yoon, S. and Stubbs, N. (2005), "Nondestructive damage identification in plate structures using changes in modal compliance", NDT & E Int., 38(7), 529-540. https://doi.org/10.1016/j.ndteint.2005.01.007
  6. Dansheng, W., Hongping, Z., Chuanyao, C. and Yong, X. (2007), "An impedance analysis for crack detection in the Timoshenko beam based on the anti-resonance technique", Acta Mechanica Solida, Sinica, 20(3), 228-235. https://doi.org/10.1007/s10338-007-0727-8
  7. Dincal, S. and Stubbs, N. (2013), "Damage evaluation of Timoshenko beams using invariant stress resultants", Eng. Struct., 56, 2052-2064. https://doi.org/10.1016/j.engstruct.2013.08.022
  8. Hjelmstad, K.D. and Shin, S. (1996), "Crack identification in a cantilever beam from modal response", J. Sound Vib., 198(5), 527-545. https://doi.org/10.1006/jsvi.1996.0587
  9. Karve, P.M., Na, S.W. and Kang, J.W. (2011), "The inverse medium problem for Timoshenko beams and frames: Damage detection and profile construction in the time-domain", Comput. Mech., 47(2), 117-136. https://doi.org/10.1007/s00466-010-0533-x
  10. Kim, B.H. (2002), "Local damage detection using modal flexibility", Ph.D. Dissertation, Texas A&M University, College Station, Texas.
  11. Kim, J.T. and Stubbs, N. (2002), "Improved damage identification method based on modal information", J. Sound Vib., 252(2), 223-238. https://doi.org/10.1006/jsvi.2001.3749
  12. Kim, J.T. and Stubbs, N. (2003), "Crack detection in beam-type structures using frequency data", J. Sound Vib., 259(1), 145-160. https://doi.org/10.1006/jsvi.2002.5132
  13. Kim, J.T. and Stubbs, N. (2003), "Nondestructive crack detection algorithm for full-scale bridges", J. Struct. Eng. - ASCE, 129(10), 1358-1366. https://doi.org/10.1061/(ASCE)0733-9445(2003)129:10(1358)
  14. Kong, F.K. (1990), Reinforced concrete deep beams, Blackie and Son Ltd, Glasgow, Scotland.
  15. Kreyszig, E. (1999), "Advanced engineering mathematics", 8th Ed., Wiley, New York.
  16. Labuschagne, A., Rensburg, N.F.J. and Merwe, A.J. (2009), "Comparison of linear beam theories", Math. Comput. Modell., 49, 20-30. https://doi.org/10.1016/j.mcm.2008.06.006
  17. Lifshitz, J.M. and Rotem, A. (1969), "Determination of reinforcement unbonding of composites by a vibration technique", J. Compos. Mater., 3(3), 412-423. https://doi.org/10.1177/002199836900300305
  18. Oh, J.K. and Shin, S.W. (2001), "Shear strength of reinforced high-strength concrete deep beams", ACI Struct. J., 98(2), 164-173.
  19. Pandey, A.K. and Biswas, M. (1994), "Damage detection in structures using changes in flexibility", J. Sound Vib., 169(1), 3-17. https://doi.org/10.1006/jsvi.1994.1002
  20. Pandey, A.K., Biswas, M. and Samman, M.M. (1991), "Damage detection from changes in curvature mode shapes" J. Sound Vib., 145(2), 321-332. https://doi.org/10.1016/0022-460X(91)90595-B
  21. Park, J.W. and Daniel, K. (2007), "Strut-and-tie model analysis for strength prediction of deep beams", ACI Struct. J., 104(6), 657-666.
  22. Reddy, J.N. (1997) "On locking-free shear deformable beam finite elements", Comput. Method. Appl. M., 149, 113-132. https://doi.org/10.1016/S0045-7825(97)00075-3
  23. Rogowsky, D.M. and MacGregor, J.G. (1986), "Design of reinforced concrete deep beams", Concrete Int. , 8(8), 49-58.
  24. Rytter, A. (1993), "Vibrational based inspection of civil engineering structures", Ph.D. Dissertation, University of Aalborg., Denmark.
  25. Sayyad, A.S. (2011), "Comparison of various refined beam theories for bending and free vibration analysis of thick beams", Appl. Comput. Mech., 5, 217-230.
  26. Stubbs, N., Kim, J.T. and Topole, K. (1992), "An efficient and robust algorithm for damage localization in offshore platforms", Proceedings of the 10th ASCE Structures Congress, San Antonio, Texas., April.
  27. Swamidas, S.J., Yang, X. and Seshadri, R. (2004), "Identification of cracking in beam structures using Timoshenko and Euler formulations", J. Eng. Mech. -ASCE, 130(11), 1297-1308. https://doi.org/10.1061/(ASCE)0733-9399(2004)130:11(1297)
  28. Ugural, A.C. and Fenster, S.K. (2003), "Advanced strength and applied elasticity", 4th Ed., Prentice Hall, New Jersey.
  29. Zhang, Z. and Aktan, A.E. (1995) "The damage indices for constructed facilities", Proceedings of the 13th International Modal Analysis Conference, Nashville, Tennessee, February.
  30. Zimmerman, D.C. and Kaouk, M. (1994), "Structural damage detection using minimum rank update theory", J. Vib. Acoust., 116(2), 222-231. https://doi.org/10.1115/1.2930416