Browse > Article
http://dx.doi.org/10.12989/sem.2009.32.6.725

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)
Publication Information
Structural Engineering and Mechanics / v.32, no.6, 2009 , pp. 725-740 More about this Journal
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
modal correlation; correlation coefficient; CQC; SRSS; buffeting analysis; background response; resonant response; Viaduct of Millau;
Citations & Related Records

Times Cited By Web Of Science : 0  (Related Records In Web of Science)
Times Cited By SCOPUS : 2
연도 인용수 순위
  • Reference
1 Vamvatsikos, D. and Cornell, A.C. (2002), "Incremental dynamic analysis", Earthq. Eng. Struct. Dyn., 31(3), 491-514   DOI   ScienceOn
2 Aslani, H. and Miranda, E. (2005), "Probability based seismic response analysis", Eng. Struct., 27, 1151-1163   DOI   ScienceOn
3 ATC-40 Report (1996), Seismic Evaluation and Retrofit of Concrete Buildings, Vol. 1, 2, Applied Technology Council, Redwood City, California
4 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
5 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   DOI   ScienceOn
6 Chopra, A.K. (1995), Dynamics of Structures: Theory and Applications to Earthquake Engineering, Prentice-Hall: Upper Saddle River, NJ
7 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   DOI   ScienceOn
8 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   DOI   ScienceOn
9 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   DOI   ScienceOn
10 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
11 FEMA-273 (1997), "NEHRP guidelines for the seismic rehabilitation of buildings", Federal Emergency Management Agency, Washington, D.C
12 FEMA-350 (2000), "Recommended seismic design criteria for new steel moment frame buildings", Federal Emergency Management Agency Washington, D.C
13 FEMA-356 (2000), "Prestandard and commentary for the seismic rehabilitation of buildings", Federal Emergency Management Agency, Washington, D.C
14 FEMA-440 (2005), "Improvement of nonlinear static seismic analysis procedures", Federal Emergency Management Agency, Redwood City, California
15 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
16 Goel, R.K. and Chopra, A.K. (2005), "Extension of modal pushover analysis to compute member forces", Earthq. Spectra, 21(1), 125-139   DOI   ScienceOn
17 Gupta, B. and Kunnath, S.K. (2000), "Adaptive spectra-based pushover procedure for seismic evaluation of structures", Earthq. Spectra, 16(2), 367-391   DOI   ScienceOn
18 HAZUS (1999), "Earthquake loss estimation methodology", Technical Manual, National Institute of Building Sciences for Federal Emergency Management Agency, Washington, DC
19 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
20 IS:456 (1978), "Indian standard code of practice for plain and reinforced concrete for general building construction", Indian Standards Institution, New Delhi
21 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
22 Kent, D.C. and Park, K.R. (1971), "Flexural members with confined concrete", J. Struct. Div., ASCE, 97(ST7), 1969-1989
23 Kircil, M.S. and Polat, Z. (2006), "Fragility analysis of mid-rise RC frame buildings", Eng. Struct., 28, 1335-1345   DOI   ScienceOn
24 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   DOI   ScienceOn
25 Porter, K., Kennedy, R. and Bachman, R. (2007), "Creating fragility functions for performance based earthquake engineering", Earthq. Spectra, 23(2), 471-489   DOI   ScienceOn
26 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
27 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
28 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
29 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
30 Shinozuka, M., Feng, M.Q., Lee, J. and Naganuma, T. (2000), "Statistical analysis of fragility curves", J. Eng. Mech., 126(12), 1224-1231   DOI   ScienceOn
31 Shome, N. (1999), "Probabilistic seismic demand analysis of nonlinear structures", Ph.D. dissertation, Stanford University
32 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
33 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   DOI   ScienceOn
34 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   DOI   ScienceOn