DOI QR코드

DOI QR Code

Accuracy of combination rules and individual effect correlation: MDOF vs SDOF systems

  • 투고 : 2011.09.07
  • 심사 : 2012.02.20
  • 발행 : 2012.04.25

초록

The accuracy of the 30% and SRSS rules, commonly used to estimate the combined response of structures, and some related issues, are studied. For complex systems and earthquake loading, the principal components give the maximum seismic response. Both rules underestimate the axial load by about 10% and the COV of the underestimation is about 20%. Both rules overestimate the base shear by about 10%. The uncertainty in the estimation is much larger for axial load than for base shear, and, for axial load, it is much larger for inelastic than for elastic behavior. The effect of individual components may be highly correlated, not only for normal components, but also for totally uncorrelated components. The rules are not always inaccurate for large values of correlation coefficients of the individual effects, and small values of such coefficients are not always related to an accurate estimation of the response. Only for perfectly uncorrelated harmonic excitations and elastic analysis of SDOF systems, the individual effects of the components are uncorrelated and the rules accurately estimate the combined response. In the general case, the level of underestimation or overestimation depends on the degree of correlation of the components, the type of structural system, the response parameter, the location of the structural member and the level of structural deformation. The codes should be more specific regarding the application of these rules. If the percentage rule is used for MDOF systems and earthquake loading, at least a value of 45% should be used for the combination factor.

키워드

참고문헌

  1. Beyer, K. and Bommer J.J. (2007), "Selection and scaling of real accelerograms for bi-directional loading: a review of current practice and code provisions", J. Earth. Eng., 11(1), 13-45. https://doi.org/10.1080/13632460601123156
  2. Bisadi, V. and Head, M. (2010), "Orthogonal effects in nonlinear analysis of bridges subjected to multicomponent earthquake excitation", Structures Congress of the American Society of Civil Engineers, Section Bridges, 204-215.
  3. Bojorquez, E., Reyes-Salazar A., Teran-Gilmore A. and Ruiz, S.E. (2010), "Energy-based damage index for steel structures", Steel Compos. Struct, An International Journal, 10(4), 331-348. https://doi.org/10.12989/scs.2010.10.4.331
  4. Building Officials & Code Administration International (1993), 12th Edition, National Building Code.
  5. Clough, R.W. and Penzien, J. (1993), Dynamics of Structures, Second Edition, McGraHill.
  6. Gao, L. and Haldar, A. (1995) "Nonlinear seismic response of space structures with PR connections," International Journal of Microcomputers in Civil Engineering, 10(1), 27-37. https://doi.org/10.1111/j.1467-8667.1995.tb00383.x
  7. Der Kiureghian, A. (1981), "A response spectrum method for random vibration analysis of MDOF systems, Earth. Eng. Struct. D., 9(5), 419-435. https://doi.org/10.1002/eqe.4290090503
  8. Federal Emergency Management Agency (2000), State of the Art Report on Systems Performance of Steel Moment Frames Subjected to Earthquake Ground Shaking, SAC Steel Project, Report FEMA 355C.
  9. Haldar, A. and Nee, K.M. (1989) "Elasto-plastic Large Deformation Analysis of PR Steel Frames for LRFD", Compu. Struct., 31(5), 811-823. https://doi.org/10.1016/0045-7949(89)90215-0
  10. Hernandez, J.J., Lopez, O.A. (2003), "Evaluation of combination rules for peak response calculation in threecomponent seismic analysis", Earth. Eng. Struct. D., 32(10), 1585-1602. https://doi.org/10.1002/eqe.290
  11. International Code Council (2003), International Building Code (IBC), Falls Church, VA.
  12. Kondo, K. and Atluri, S.N. (1987), "Large deformation elasto-plastic analysis of frames under non-conservative loading using explicitly derived tangent stiffness based on assumed stress", Comput. Mech., 2(1), 1-25.
  13. Kunnath, S.K., Erduran, E., Chai, Y.H. and Yashinsky, M. (2008), "Effect of near-fault vertical ground motions on seismic response of highway overcrossings," J. Bridge Eng., 13(3), 282-290. https://doi.org/10.1061/(ASCE)1084-0702(2008)13:3(282)
  14. Lopez, O.A., Chopra, A.K. and Hernandez, J.J. (2000) "Critical response of structures to multi-component earthquake excitation", Earth. Eng. Struct. D., 29, 1759-1778. https://doi.org/10.1002/1096-9845(200012)29:12<1759::AID-EQE984>3.0.CO;2-K
  15. Lagaros (2010), "Multicomponent Incremental Dynamic Analysis considering variable incident angle", J. Struct. Infrastructure Eng., 6(2),77-94. https://doi.org/10.1080/15732470802663805
  16. Lopez, O.A. and Torres, R. (1996), "A clarification of orthogonal Effects in a three- dimensional seismic analysis", Earth. Spectra, 12, 357-361. https://doi.org/10.1193/1.1585887
  17. Lopez, O.A., Chopra, A.K and Hernandez, J.J. (2004), "Adapting the CQC3 rule for three seismic components with different spectra", J. Struct. Eng, ASCE, 130(3), 403-410. https://doi.org/10.1061/(ASCE)0733-9445(2004)130:3(403)
  18. Lopez, O.A., Chopra, A.K and Hernandez, J.J. (2001), "Evaluation of combination rules for maximum response calculation in multi-component seismic analysis", Earth. Eng. Struct. D., 30(9), 1379-1398. https://doi.org/10.1002/eqe.68
  19. Lopez, O.A, Hernandez J.J., Bonilla, R. and Fernandez A. (2006), "Response spectra for multi-component structural analysis, Earth. Spectra, 22(1), 85-113. https://doi.org/10.1193/1.2162898
  20. Mackie, K.R. and Cronin K.J. (2011), "Response sensitivity of highways bridges to randomly oriented multicomponent earthquake excitation", J. Earth. Eng., 15(6), 850-876. https://doi.org/10.1080/13632469.2010.551706
  21. McKenna, F. and Feneves, G.L. (2009). "Open system for earthquake engineering simulation." Pacific earthquake engineering research center, version 2.1.0.
  22. Menun, C. and Der Kiureghian, A. (2000), "Envelopes for seismic response vectors. I: Theory", J. Struct. Eng, ASCE, 126(4), 467-473. https://doi.org/10.1061/(ASCE)0733-9445(2000)126:4(467)
  23. Menun, C. and Der Kiureghian, A. (1998), "A replacement for the 30%, 40% and SRSS rules for multicomponent seismic analysis", Earth. Spectra, 14(1), 153-156. https://doi.org/10.1193/1.1585993
  24. Newmark, N.M. (1975) "Seismic design criteria for structures and facilities, Trans-Alaska pipeline system", Proceedings of the U.S. National Conference on Earthquake Engineering, pp. 94-103.
  25. Newmark, N.M. and Hall, W.J. (1982), Earthquake Spectra and Design, Monograph Series, Earthquake Engineering Institute, Berkeley CA, USA.
  26. Nielson, B. G. and DesRoches, R. (2006), "Influence of modeling assumptions on the seismic response of multispan simply supported steel girder bridges in moderate seismic zones," Eng. Struct., 28(8), 1083-1092. https://doi.org/10.1016/j.engstruct.2005.12.014
  27. Penzien, J. and Watabe, M. (1975), "Characteristics of 3-dimensional earthquake ground motions," Earthquake Engineering and Structural Dynamics, 3(4), 365-373.
  28. Reglamento de construcciones del Distrito Federal (2004), Normas Tecnicas Complementarias de Diseno por Sismo, Gaceta Oficial del Distrito Federal.
  29. Reyes-Salazar, A., Haldar, A. and Romero-Lopez, M.R. (2000), "Force reduction factor for SDOF and MDOF", Joint Specialty Conference on Probabilistic Mechanics and Structural, ASCE, Paper 063.
  30. Reyes-Salazar, A. (1997) " Inelastic Seismic Response and Ductility Evaluation of Steel Frames with Fully, Partially Restrained and Composite Connections," PhD. thesis Department of Civil Engineering and Engineering Mechanics, University of Arizona, Tucson, Arizona.
  31. Reyes-Salazar, A. and Haldar, A. (1999), "Nonlinear seismic response of steel structures with semi-rigid and composite connections", J. Constr. Steel Res., 51, 37-59. https://doi.org/10.1016/S0143-974X(99)00005-X
  32. Reyes-Salazar, A. and Haldar, A. (2000), "Dissipation of energy in steel frames with pr connections", Struct. Eng. Mech, An International Journal, 9(3), 241-256. https://doi.org/10.12989/sem.2000.9.3.241
  33. Reyes-Salazar, A. and Haldar, A. (2001a) "Energy dissipation at PR frames under seismic loading", J. Struct. Eng, ASCE, 127(5), 588-593. https://doi.org/10.1061/(ASCE)0733-9445(2001)127:5(588)
  34. Reyes-Salazar, A. and Haldar, A. (2001b), "Seismic response and energy dissipation in partially restrained and fully restrained steel frames: An analytical study", Steel, Compos. Struct., An International Journal, 1(4), 459-480. https://doi.org/10.12989/scs.2001.1.4.459
  35. Reyes-Salazar, A., Juarez-Duarte, J.A., Lopez-Barraza, A. and Velázquez-Dimas, J.I. (2004), "Combined effect of the horizontal components of earthquakes for moment resisting steel frames", Steel, Compos. Struct, An International Journal, 4(3), 89-209.
  36. Reyes-Salazar, A., Lopez-Barraza, A., Lopez-Lopez, L.A. and Haldar, A. (2008), "Multiple-components seismic response analysis-a critical review", J. Earth. Eng., 12(5), 779-799. https://doi.org/10.1080/13632460701672979
  37. Rigato, A. B. and Medina, R. A. (2007), "Influence of angle of incidence on seismic demands for inelastic single-storey structures subjected to bi-directional ground motions," Engineering Structures, 29(10), 2593-2601. https://doi.org/10.1016/j.engstruct.2007.01.008
  38. Rosenblueth, E. (1980), Design of Earthquake Resistance Structures, Pentech Press Ltd.
  39. Rosenblueth, E. and Contreras, H. (1977), "Approximate design for multi-component earthquakes", J. Eng. Mech. Division, ASCE, 103, 895-911.
  40. Salmon, C.G., Johnson, J.E. and Malhas, F.A. (2009), Steel Structures Design and Behavior, 5th Edition, Pearson, Prentice Hall, New Jersey.
  41. Smeby, W. and DerKiureghian, A. (1985), "Modal combination rules for multi-component earthquake excitation", Earth. Eng. Struct. D., 13(1), 1-12. https://doi.org/10.1002/eqe.4290130103
  42. Shi, G. and Atluri, S.N. (1988), "Elasto-plastic large deformation analysis of spaces-frames", Inter. J. Numer Meth. Eng., 26, 589-615. https://doi.org/10.1002/nme.1620260306
  43. Uniform Building Code (1994), Structural Engineering Design Provisions Vol. 2, International Conference of Building Officials.
  44. Wilson, E.L., Suharwardy, I. and Habibullah, A. (1995), "A clarification of the orthogonal effects in a threedimensional seismic analysis", Earth. Spectra, 11(4), 659-666. https://doi.org/10.1193/1.1585831
  45. Wilson, E.L., Der Kiureghian, A. and Bayo, E.P., (1981), "A replacement for the SRSS method in seismic analysis", Earth. Eng. Struct. D., 9(2), 187-194. https://doi.org/10.1002/eqe.4290090207