Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Estimation of modal correlation coefficients from background and resonant responses

  • Denoel, V. (National Fund for Scientific Research, University of Liege, Department of Architecture, Geology, Environment and Construction)
  • Received : 2008.03.27
  • Accepted : 2009.06.04
  • Published : 2009.08.20
⟨ Previous Next ⟩

Abstract

A new simple relation for the estimation of modal correlation coefficients is presented. It is obtained from the decomposition of covariances of modal responses into background and resonant contributions, as it is commonly done for the variances. Thanks to appropriate assumptions, the modal correlation coefficients are estimated as weighted sums of two limit values, corresponding to the background and resonant responses respectively. The weighting coefficients are expressed as functions of the background-to-resonant ratios, which makes the proposed formulation convenient and easily accessible. The simplicity of the mathematical formulation facilitates the physical interpretation. It is for example proved that modal correlation coefficients can be non negligable even in case of well separated natural frequencies, which is sometimes unclear in the litterature. The new relation is mainly efficient in case of large finite element models. It is applied and validated on a finite element buffeting analysis of the Viaduct of Millau, the highest bridge deck ever built so far.

Keywords

References

  1. Aslani, H. and Miranda, E. (2005), "Probability based seismic response analysis", Eng. Struct., 27, 1151-1163 https://doi.org/10.1016/j.engstruct.2005.02.015
  2. ATC-40 Report (1996), Seismic Evaluation and Retrofit of Concrete Buildings, Vol. 1, 2, Applied Technology Council, Redwood City, California
  3. Bertero, V.V. (1977), "Strength and deformation capacities of buildings under extreme environments", Structural Engineering and Structural Mechanics, K.S. Pister, ed., Prentice Hall, Englewood Cliffs, NJ, 211-215
  4. Bradley, B.A., Dhakal, R.P., Mander, J.B. and Li, L. (2008), "Experimental multi-level seismic performance assessment of 3D RC frame designed for damage avoidance", Earthq. Eng. Struct. Dyn., 37(1), 1-20 https://doi.org/10.1002/eqe.741
  5. Chopra, A.K. (1995), Dynamics of Structures: Theory and Applications to Earthquake Engineering, Prentice-Hall: Upper Saddle River, NJ
  6. Chopra, A.K. and Goel, R.K. (2002), "A modal pushover analysis procedure for estimating seismic demands for buildings", Earthq. Eng. Struct. Dyn., 31(3), 561-582 https://doi.org/10.1002/eqe.144
  7. Chopra, A.K. and Goel, R.K. (2004), "Evaluation of modal and FEMA pushover analyses: Vertically 'regular' and irregular generic frames", Earthq. Spectra, 20(1), 255-271 https://doi.org/10.1193/1.1647580
  8. Dhakal, R.P., Mander, J.B. and Mashiko, N. (2006), "Identification of critical ground motions for seismic performance assessment of structures", Earthq. Eng. Struct. Dyn., 35(8), 989-1008 https://doi.org/10.1002/eqe.568
  9. Dhakal, R.P., Singh, S. and Mander, J.B. (2007), "Effectiveness of earthquake selection and scaling method in New Zealand", Bulletin New Zealand Soc. Earthq. Eng., 40(3), 160-171
  10. FEMA-273 (1997), "NEHRP guidelines for the seismic rehabilitation of buildings", Federal Emergency Management Agency, Washington, D.C
  11. FEMA-350 (2000), "Recommended seismic design criteria for new steel moment frame buildings", Federal Emergency Management Agency Washington, D.C
  12. FEMA-356 (2000), "Prestandard and commentary for the seismic rehabilitation of buildings", Federal Emergency Management Agency, Washington, D.C
  13. FEMA-440 (2005), "Improvement of nonlinear static seismic analysis procedures", Federal Emergency Management Agency, Redwood City, California
  14. Goel, R.K. and Chopra, A.K. (2005), "Extension of modal pushover analysis to compute member forces", Earthq. Spectra, 21(1), 125-139 https://doi.org/10.1193/1.1851545
  15. Gupta, B. and Kunnath, S.K. (2000), "Adaptive spectra-based pushover procedure for seismic evaluation of structures", Earthq. Spectra, 16(2), 367-391 https://doi.org/10.1193/1.1586117
  16. HAZUS (1999), "Earthquake loss estimation methodology", Technical Manual, National Institute of Building Sciences for Federal Emergency Management Agency, Washington, DC
  17. Ibarra, L.F. and Krawinkler, H. (2004), "Global collapse of deteriorating MDOF systems", Proc. 13th World Conf. on Earthquake Engineering, Vancouver, B.C., Canada, Paper No. 116
  18. IS:1893 (Part 1) (2002), "Indian standard criteria for earthquake resistant design of structures, Part 1- General provisions and buildings", Indian Standards Institution, New Delhi
  19. IS:456 (1978), "Indian standard code of practice for plain and reinforced concrete for general building construction", Indian Standards Institution, New Delhi
  20. Jaiswal, K.S., Sinha, R. and Goyal, A. (2002), "World Housing Encyclopedia Report. Country: India. Housing type: Reinforced concrete frame building with masonry infill walls designed for gravity loads", EERI, Created on: 6/5/2002, Last Modified: 7/2/2003
  21. Kent, D.C. and Park, K.R. (1971), "Flexural members with confined concrete", J. Struct. Div., ASCE, 97(ST7), 1969-1989
  22. Kircil, M.S. and Polat, Z. (2006), "Fragility analysis of mid-rise RC frame buildings", Eng. Struct., 28, 1335-1345 https://doi.org/10.1016/j.engstruct.2006.01.004
  23. Mander, J.B., Dhakal, R.P., Mashiko, N. and Solberg, K.M. (2007), "Incremental dynamic analysis applied to seismic financial risk assessment of bridges", Eng. Struct., 29(10), 2662-2672 https://doi.org/10.1016/j.engstruct.2006.12.015
  24. Murty, C.V.R., Rai, D.C., Bajpai, K.K. and Jain, S.K. (2001), "Anchorage details and joint design in seismic RC frames", Ind. Concrete J., 274-280
  25. Park, Y.J., Reinhorn, A.M. and Kunnath, S.K. (1987), "IDARC: Inelastic damage analysis of reinforced concrete frame - shear-wall structures", Technical Report NCEER-87-0008, State University of New York at Buffalo
  26. Park, Y.J., Reinhorn, A.M. and Kunnath, S.K. (2006), "IDARC-2D V6.0 computer program, Inelastic damage analysis of RC building structures", State University of New York
  27. Porter, K., Kennedy, R. and Bachman, R. (2007), "Creating fragility functions for performance based earthquake engineering", Earthq. Spectra, 23(2), 471-489 https://doi.org/10.1193/1.2720892
  28. Rai, D.C., Thakkar, S.K. and Ramesh, U. (2006), "Behavior of seismic and non-seismic RC frames under cyclic loads", Ind. Concr. J., 46-52
  29. Shinozuka, M., Feng, M.Q., Lee, J. and Naganuma, T. (2000), "Statistical analysis of fragility curves", J. Eng. Mech., 126(12), 1224-1231 https://doi.org/10.1061/(ASCE)0733-9399(2000)126:12(1224)
  30. Shome, N. (1999), "Probabilistic seismic demand analysis of nonlinear structures", Ph.D. dissertation, Stanford University
  31. Sivaselvan, M.V. and Reinhorn, A.M. (1999), "Hysteretic models for cyclic behavior of deteriorating inelastic structures", Tech. Rep. MCEER-99-0018, Multidisciplinary Ctr. for Earthquake Engrg. Res., State University of New York at Buffalo, N.Y
  32. Smyth, A., Altay, G., Deodatis, G., Erdik, M., Franco, G. and Gulkan, P. (2004), "Benefit-cost analysis for earthquake mitigation: Evaluating measures for apartment houses in Turkey", Earthq. Spectra, 20(1), 171-203 https://doi.org/10.1193/1.1649937
  33. Solberg, K.M., Dhakal, R.P., Mander, J.B. and Bradley, B.A. (2008), "Rapid expected annual loss estimation methodology for structures", Earthq. Eng. Struct. Dyn., 37(1), 81-101 https://doi.org/10.1002/eqe.746
  34. Vamvatsikos, D. and Cornell, A.C. (2002), "Incremental dynamic analysis", Earthq. Eng. Struct. Dyn., 31(3), 491-514 https://doi.org/10.1002/eqe.141

Cited by

  1. Statistical buffeting response of flexible bridges influenced by errors in aeroelastic loading estimation vol.104-106, 2012, https://doi.org/10.1016/j.jweia.2012.03.036
  2. Response of an oscillator to a random quadratic velocity-feedback loading vol.147, 2015, https://doi.org/10.1016/j.jweia.2015.09.008
  3. An efficient approach to the evaluation of wind effects on structures based on recorded pressure fields vol.124, 2016, https://doi.org/10.1016/j.engstruct.2016.06.023
  4. Multiple timescale spectral analysis vol.39, 2015, https://doi.org/10.1016/j.probengmech.2014.12.003
  5. An asymptotic expansion-based method for a spectral approach in equivalent statistical linearization vol.38, 2014, https://doi.org/10.1016/j.probengmech.2014.08.003