Optimal Combination for Modal Pushover Analysis by Using Genetic Algorithm

Authors: K. Shakeri, M. Mohebbi

Abstract:

In order to consider the effects of the higher modes in the pushover analysis, during the recent years several multi-modal pushover procedures have been presented. In these methods the response of the considered modes are combined by the square-rootof- sum-of-squares (SRSS) rule while application of the elastic modal combination rules in the inelastic phases is no longer valid. In this research the feasibility of defining an efficient alternative combination method is investigated. Two steel moment-frame buildings denoted SAC-9 and SAC-20 under ten earthquake records are considered. The nonlinear responses of the structures are estimated by the directed algebraic combination of the weighted responses of the separate modes. The weight of the each mode is defined so that the resulted response of the combination has a minimum error to the nonlinear time history analysis. The genetic algorithm (GA) is used to minimize the error and optimize the weight factors. The obtained optimal factors for each mode in different cases are compared together to find unique appropriate weight factors for each mode in all cases.

Keywords: Genetic Algorithm, Modal Pushover, Optimalweight.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1081511

References:

[1] Seismic evaluation and retrofit of concrete buildings, ATC, ATC-40. Redwood City, CA: Applied Technology Council, 1996.
[2] Prestandard and commentary for the seismic rehabilitation of buildings, FEMA, FEMA 356. Washington, DC: Federal Emergency Management Agency, 2000.
[3] Eurocode-8: Design of structures for earthquake resistance, Part 1, Pr- EN 1998-1, Final Draft, Brussels (BEL): European Committee for Standardization; 2003.
[4] S. Otani, H. Hiraishi, M. Midorikawa and M. Teshigawara, "New seismic design provisions in Japan," In: Proc. Uzumeri symposium, ACI Annual Convention. Canada, 2000.
[5] M. Saiidi and M.A. Sozen, "Simple non-linear seismic analysis of RC structures," ASCE J Struct Div 1981;107(ST5):937-951.
[6] P. Fajfar and P. Gašperšič, "The N2 method for the seismic damage analysis of RC buildings," Earthquake Eng & Struct Dyn 1996;25(1):31- 46.
[7] A. Gupta and H. Krawinkler, "Estimation of seismic drift demands for frame structures," Earthquake Eng & Struc Dyn 2000;29(9):1287-1305.
[8] H. Krawinkler and G.D.P.K. Seneviratna, "Pros and cons of a pushover analysis of seismic performance evaluation," Eng Struct 1998;20(4- 6):452-464.
[9] S. Kim and E. D-Amore, "Push-over analysis procedures in earthquake engineering," Earthq Spectra 1999;15(3):417-434.
[10] A.M. Mwafy and A.S. Elnashai, "Static pushover versus dynamic collapse analysis of RC buildings," Eng Struct 2001;23:407-424.
[11] Improvement of nonlinear static seismic analysis procedures, FEMA, FEMA 440. Washington, DC: Federal Emergency Management Agency, 2005.
[12] T.F. Paret, K.K. Sasaki, D.H. Elibeck and S.A. Freeman, "Approximate inelastic procedures to identify failure mechanism from higher mode effects," in Proc. the eleventh world conference on earthquake engineering. 1996.
[13] K.K. Sasaki, S.A. Freeman and T.F. Paret, "Multi-mode pushover procedure (MMP) - a method to identify the effects of higher modes in a pushover analysis," in Proc. sixth US. national conference on earthquake engineering. 1998.
[14] A.S. Moghadam, "A pushover procedure for tall buildings," in Proc. the twelfth European conference on earthquake engineering. 2002.
[15] A.K. Chopra and R.K. Goel, "A modal pushover analysis procedure for estimating seismic demands for buildings," Earthquake Eng & Struct Dyn 2002;31:561-582.
[16] K. Shakeri, M.A. Shayanfar and A.S. Moghadam, "An efficient method for optimum combination of modes required for pushover analysis," in Proc. the 9th Canadian conference on earthquake engineering. 2007.
[17] E. Hernandez-Montes, O-S. Kwon and M.A. Aschheim, "An energybased formulation for first-and multiple-mode nonlinear static (Pushover) analyses," J Earthquake Eng 2004;8:69-88.
[18] A.K. Chopra, R.K. Goel and C. Chinatanapakdee, "Evaluation of a modified MPA procedure assuming higher modes as elastic to estimate seismic demands," Earthq Spectra 2004;20(3):757-778.
[19] B. Gupta and S.K. Kunnath, "Adaptive spectra-based pushover procedure for seismic evaluation of structures," Earthq Spectra 2000;16(2):367-391.
[20] M.N. Aydino─ƒlu, "An incremental response spectrum analysis procedure based on inelastic spectral displacements for multi-mode seismic performance evaluation," Bull Earthquake Eng 2003;1:3-36.
[21] E. Kalkan and S.K. Kunnath, "Adaptive modal combination procedure for nonlinear static analysis of building structures," J Struct Eng ASCE 2006;132(11):1721-1731.
[22] A.S. Elnashai, "Advanced inelastic static (pushover) analysis for earthquake applications," Struct Eng Mech 2001;12(1):51-69.
[23] S. Antoniou and R. Pinho, "Advantages and limitations of adaptive and non-adaptive force-based pushover procedures," J Earthquake Eng 2004;8(4):497-522.
[24] S. Antoniou, R. Pinho, "Development and verification of a displacement-based adaptive pushover procedure," J Earthquake Eng 2004;8(5):643-661.
[25] K. Shakeri, M.A. Shayanfar and T. Kabeyasawa, "A story shear-based adaptive pushover procedure for estimating seismic demands of buildings," Eng. Struct. 2010:32(1) 174-183.
[26] J.H. Holland, "Adaptation in natural and artificial systems," Ann Arbor: The University of Michigan Press. 1975.
[27] D.E. Goldberg, "Genetic algorithms in search, optimization and machine Learning. Addison -Wesley Publishing Co., Inc. Reading, Mass. 1989.
[28] Z. Michalewicz, "Genetic algorithms + data structures=evolution programs," New York: Springer-Verlag. 1996.
[29] J.E. Baker, "Adaptive selection methods for genetic algorithms," in Proc. ICGA, 1985, 1: 101-111.
[30] W.M. Jenkins, "A decimal-coded evolutionary algorithm for constrained optimization," Comp. and Struct., 2002, 80:471-480.
[31] State of the art report on systems performance of steel moment frames subject to earthquake ground shaking, FEMA 355C. Sacramento, CA: SAC Joint Venture; 2000.
[32] V. Prakash, G.H. Powell and S. Campbell, "DRAIN-2DX base program description and user guide," Version 1.10, Report No. UCB/SEMM- 93/17. Berkeley, CA: Department of Civil Engineering, University of California at Berkeley; 1993.
[33] A. Gupta and H. Krawinkler, "Seismic demands for performance evaluation of steel moment resisting frame structures (SAC Task 5.4.3)," Report no. 132. Palo Alto, CA: John A. Blume Earthquake Engineering Center, Stanford University; 1999.
[34] M.A. Lopez-Menjivar and R. Pinho, "A review of existing pushover methods for 2-D reinforced concrete buildings," Pavia (Italy): Rose School; 2004.