Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Detection of a concentrated damage in a parabolic arch by measured static displacements

  • Greco, Annalisa (Department of Civil and Environmental Engineering, University of Catania) ;
  • Pau, Annamaria (Department of Structural and Geotechnical Engineering, La Sapienza University of Rome)
  • Received : 2009.10.17
  • Accepted : 2011.06.22
  • Published : 2011.09.25
⟨ Previous Next ⟩

Abstract

The present paper deals with the identification of a concentrated damage in an elastic parabolic arch through the minimization of an objective function which measures the differences between numerical and experimental values of static displacements. The damage consists in a notch that reduces the height of the cross section at a given abscissa and therefore causes a variation in the flexural stiffness of the structure. The analytical values of static displacements due to applied loads are calculated by means of the principle of virtual work for both the undamaged and damaged arch. First, pseudo-experimental data are used to study the inverse problem and investigate whether a unique solution can occur or not. Various damage intensities are considered to assess the reliability of the identification procedure. Then, the identification procedure is applied to an experimental case, where displacements are measured on a prototype arch. The identified values of damage parameters, i.e., location and intensity, are compared to those obtained by means of a dynamic identification technique performed on the same structure.

Keywords

References

  1. Bakhtiari-Nejad, F., Rahai, A. and Esfandiari, A. (2005), "A structural damage detection method using static tests data", Eng. Struct., 27(12), 1784-1793. https://doi.org/10.1016/j.engstruct.2005.04.019
  2. Baldacci, R. (1970), Scienza Delle Costruzioni, Utet, Torino.
  3. Banan, M.R., Banan, M.R. and Hjelmstad, D.D. (1994), "Parameter estimation of structures from static response. I. Computational aspects" J. Struct. Eng., 120(11), 3243-3258. https://doi.org/10.1061/(ASCE)0733-9445(1994)120:11(3243)
  4. Banan, M.R., Banan, M.R. and Hjelmstad, D.D. (1994), "Parameter estimation of structures from static response. II. Numerical simulation studies", J. Struct. Eng., 120(11), 3259-3283. https://doi.org/10.1061/(ASCE)0733-9445(1994)120:11(3259)
  5. Buda, G. and Caddemi, S. (2007), "Identification of concentrated damages in Euler-Bernoulli beams under static loads", J. Eng. Mech., 133(8), 942-956. https://doi.org/10.1061/(ASCE)0733-9399(2007)133:8(942)
  6. Caddemi, S. and Morassi, A. (2005), "Detecting damage in beams by static tests", Key Eng. Mater., 293-294, 493-500. https://doi.org/10.4028/www.scientific.net/KEM.293-294.493
  7. Caddemi, S. and Greco, A. (2006), "The influence of instrumental errors on the static identification of damage parameters for elastic beams", Comput. Struct., 84(26-27), 1696-1708. https://doi.org/10.1016/j.compstruc.2006.03.010
  8. Caddemi, S. and Morassi, A. (2007), "Crack detection in elastic beams by static measurements", Int. J. Solids Struct., 44, 5301-5315. https://doi.org/10.1016/j.ijsolstr.2006.12.033
  9. Cerri, M.N. and Vestroni, F. (2003), "Identification of damage due to open cracks by changes of measured frequencies", Proceedings of the XVI AIMETA Congress of Theoretical and Applied Mechanics, September.
  10. Cerri, M.N. and Ruta, G.C. (2004), "Detection of localised damage in plane circular arches by frequency data", J. Sound Vib., 270, 39-59. https://doi.org/10.1016/S0022-460X(03)00482-6
  11. Chondros, T.G. and Dimarogonas, A.D. (1998), "A continuous cracked beam vibration theory", J. Sound Vib., 215(1), 17-34. https://doi.org/10.1006/jsvi.1998.1640
  12. Christides, S. and Barr, D.S. (1984), "One-dimensional theory of cracked Bernoulli-Euler beams", Int. J. Mech. Sci., 26(11-12), 639-648. https://doi.org/10.1016/0020-7403(84)90017-1
  13. Di Paola, M. and Bilello, C. (2004), "An integral equation for damage identification of Euler-Bernoulli beams under static loads", J. Eng. Mech., 130(2), 225-234. https://doi.org/10.1061/(ASCE)0733-9399(2004)130:2(225)
  14. Farrar, C. and Worden, K. (2007), "An introduction to structural health monitoring", Philos. T. R. Soc., 365, 303-315. https://doi.org/10.1098/rsta.2006.1928
  15. Friswell, M.I. (2007), "Damage identification using inverse methods", Philos. T. R. Soc., 365, 393-410. https://doi.org/10.1098/rsta.2006.1930
  16. Greco, A. and Pau, A. (2008), "Influence of axial deformability on the dynamic response of damaged parabolic arches", Proceedings of the XVII Italian Congress of Computational Mechanics, Alghero, September. (in Italian)
  17. Hjelmstad, K.D. and Shin, S. (1997), "Damage detection and assessment of structures from static response", J. Eng. Mech., 123(6), 568-576. https://doi.org/10.1061/(ASCE)0733-9399(1997)123:6(568)
  18. Oh, B.H. and Jung, B.S. (1998), "Structural damage assessment with combined data of static and modal tests", J. Struct. Eng., 124(8), 956-965. https://doi.org/10.1061/(ASCE)0733-9445(1998)124:8(956)
  19. Lee, B.K., Lee, T.E. and Ahn, D.S. (2004), "Freee vibrations of arches with inclusion of axial extension, shear deformation and rotatory inertia in Cartesian coordinates", KSCE J. Struct. Eng., 8(1), 43-48.
  20. Ostachowicz, W.M. and Krawczuk, M. (1991), "Analysis of the effects of cracks on the natural frequencies of a cantilever beam", J. Sound Vib., 150(2), 191-201. https://doi.org/10.1016/0022-460X(91)90615-Q
  21. Pau, A., Greco, A. and Vestroni, F. (2011), "Numerical and experimental detection of a concentrated damage in a parabolic arch by measured frequency variations", J. Vib. Control, 17(4), 605-614. https://doi.org/10.1177/1077546310362861
  22. Rucka, M. and Wilde, K. (2006), "Crack identification using wavelets on experimental static deflection profiles", Eng. Struct., 28, 279-288. https://doi.org/10.1016/j.engstruct.2005.07.009
  23. Sanayei, M. and Onipede, O. (1991), "Damage assessment of structures using static test data", AIAA J., 29(7) 1174-1179. https://doi.org/10.2514/3.10720
  24. Sanayei, M.S. and Scampoli, F. (1991), "Structural element stiffness identification from static test data", J. Eng. Mech., 117(5), 1021-1036. https://doi.org/10.1061/(ASCE)0733-9399(1991)117:5(1021)
  25. Sanayei, M. and Saletnik, M.J. (1996), "Parameter estimation of structures from static strain measurements. I: Formulation", J. Struct. Eng., 122(5), 555-562. https://doi.org/10.1061/(ASCE)0733-9445(1996)122:5(555)
  26. Sanayei, M., Imbaro, G.R., McClain, J.A.S. and Brown, L.C. (1997), "Structural model updating using experimental static measurements", J. Struct. Eng., 123(6), 792-798. https://doi.org/10.1061/(ASCE)0733-9445(1997)123:6(792)
  27. Shenton, H.W. and Hu, III, X. (2006), "Damage identification based on dead load redistribution: Methodology", J. Struct. Eng., 132(8), 1254-1263. https://doi.org/10.1061/(ASCE)0733-9445(2006)132:8(1254)
  28. Tseng, S. (2000), "Damage assessment of linear structures by a static approach, II: Numerical simulation studies", Struct. Eng. Mech., 9(2), 195-208. https://doi.org/10.12989/sem.2000.9.2.195
  29. Viola, E., Artioli, E. and Dilena, M. (2005), "Analytical and differential quadrature results for vibration analysis of damaged circular arches", J. Sound Vib., 288, 887-906. https://doi.org/10.1016/j.jsv.2005.01.027
  30. Wang, X., Hu, N., Fukunaga, H. and Yao, Z.H. (2001), "Structural damage identification using static test data and changes in frequencies", Eng. Struct., 23(6), 610-621. https://doi.org/10.1016/S0141-0296(00)00086-9
  31. Zimmerman, D.C. and Simmermacher, T. (1995), "Model correlation using multiple static load and vibration tests", AIAA J., 33(11), 2182-2188. https://doi.org/10.2514/3.12813

Cited by

  1. Closed form solutions of a multi-cracked circular arch under static loads vol.121, 2017, https://doi.org/10.1016/j.ijsolstr.2017.05.026
  2. Structural models for the evaluation of eigen-properties in damaged spatial arches: a critical appraisal vol.86, pp.11, 2016, https://doi.org/10.1007/s00419-016-1151-7
  3. Closed-form solution based genetic algorithm software: Application to multiple cracks detection on beam structures by static tests vol.64, 2018, https://doi.org/10.1016/j.asoc.2017.11.040
  4. Numerical and statistical analysis about displacements in reinforced concrete beams using damage mechanics vol.10, pp.3, 2012, https://doi.org/10.12989/cac.2012.10.3.307
  5. The influence of damage on the eigen-properties of Timoshenko spatial arches vol.190, 2017, https://doi.org/10.1016/j.compstruc.2017.04.012
  6. Damage identification on spatial Timoshenko arches by means of genetic algorithms vol.105, 2018, https://doi.org/10.1016/j.ymssp.2017.11.040
  7. A procedure for the identification of multiple cracks on beams and frames by static measurements vol.25, pp.8, 2018, https://doi.org/10.1002/stc.2194
  8. On profile reconstruction of Euler–Bernoulli beams by means of an energy based genetic algorithm pp.1435-5663, 2020, https://doi.org/10.1007/s00366-018-00693-x
  9. Experimental investigation into brick masonry arches' (vault and rib cover) behavior reinforced by FRP strips under vertical load vol.67, pp.5, 2018, https://doi.org/10.12989/sem.2018.67.5.481
  10. Natural frequencies of parabolic arches with a single crack on opposite cross-section sides vol.25, pp.7, 2011, https://doi.org/10.1177/1077546319825681
  11. Exact closed-form static solutions for parabolic arches with concentrated damage vol.90, pp.4, 2020, https://doi.org/10.1007/s00419-019-01633-x
  12. A Novel Stochastic Approach for Static Damage Identification of Beam Structures Using Homotopy Analysis Algorithm vol.21, pp.7, 2011, https://doi.org/10.3390/s21072366