Damage-Based Design Earthquake Loads for Single-Degree-Of-Freedom Inelastic Structures
Publication: Journal of Structural Engineering
Volume 137, Issue 3
Abstract
This paper develops a new framework for modeling design earthquake loads for inelastic structures. Limited information on strong ground motions is assumed to be available only at the given site. The design earthquake acceleration is expressed as a Fourier series, with unknown amplitude and phase angle, modulated by an envelope function. The design ground acceleration is estimated by solving an inverse dynamic problem, using nonlinear programming techniques, so that the structure performance is minimized. At the same time, the design earthquake is constrained to the available information on past recorded ground motions. New measures of the structure performance based on energy concepts and damage indexes are introduced in this paper. Specifically, the structural performance is quantified in terms of Park and Ang damage indexes. Damage indexes imply that the structure is damaged by a combination of repeated stress reversals and high-stress excursions. Furthermore, the use of damage indexes provides a measure on the structure damage level, and making a decision on necessary repair possible. The material stress-strain relationship is modeled as either bilinear or elastic-plastic. The formulation is demonstrated by deriving the design earthquake loads for inelastic frame structures at a firm soil site. The damage spectra for the site are also established, to provide upper bounds of damage under possible future earthquakes.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The author thanks three anonymous reviewers for their careful reading of the paper and insightful comments they made. This research work is partly supported by research funds from the Japanese Society for the Promotion of Science. The support is gratefully acknowledged.
References
Abbas, A. M. (2006). “Critical seismic load inputs for simple inelastic structures.” J. Sound Vib., 296, 949–967.
Abbas, A. M., and Manohar, C. S. (2002). “Investigations into critical earthquake load models within deterministic and probabilistic frameworks.” Earthquake Eng. Struct. Dyn., 31, 813–832.
Abbas, A. M., and Manohar, C. S. (2005). “Reliability-based critical earthquake load models, part 2: Nonlinear structures.” J. Sound Vib., 287, 883–900.
Abbas, A. M., and Manohar, C. S. (2007). “Reliability-based vector nonstationary random critical earthquake excitations for parametrically excited systems.” Struct. Saf., 29, 32–48.
Akiyama, H. (1985). Earthquake-resistant limit-state design for buildings, University of Tokyo Press, Tokyo.
Arias, A. (1970). A measure of earthquake intensity: seismic design of nuclear power plants, MIT Press, Cambridge, MA, 438–468.
Arora, J. S. (2004). Introduction to optimum design, Elsevier Academic, San Diego.
Bommer, J. J., and Acevedo, A. B. (2004). “The use of real earthquake accelerograms as input to dynamic analysis.” J. Earthquake Eng., 8, 43–91.
Boore, D. M. (1983). “Stochastic simulation of high-frequency ground motions based on seismological models of the radiated spectra.” Bull. Seismol. Soc. Am., 73(6a), 1865–94.
Bozorgenia, Y., and Bertero, V. V. (2003). “Damage spectra: Characteristics and applications to seismic risk reduction.” J. Struct. Eng., 129(10), 1330–1340.
Bozorgnia, Y., and Bertero, V. V., eds. (2004). Earthquake engineering, CRC Press, New York.
Brune, J. N. (1970). “Tectonic stress and the spectra of seismic shear waves from earthquakes.” J. Geophys. Res., 75, 4997–5009.
Caleman, T., Branch, M. A., and Grace, A. (1999). Optimization toolbox for the use with Matlab: User’s guide, Math Works Inc., Natick, MA.
Chai, Y. H., Romstad, K. M., and Bird, S. M. (1995). “Energy-based linear damage model for high-intensity seismic loading.” J. Struct. Eng., 121(5), 857–864.
Choi, H., and Kim, J. (2006). “Energy-based design of buckling-restrained braced frames using hysteretic energy spectrum.” Eng. Struct., 28, 304–311.
Conte, J. P., and Peng, B. F. (1997). “Fully nonstationary analytical earthquake ground motion model.” J. Eng. Mech., 123, 15–24.
Cosenza, C., Manfredi, G., and Ramasco, R. (1993). “The use of damage functionals in earthquake engineering: a comparison between different methods.” Earthquake Eng. Struct. Dyn., 22, 855–868.
COSMOS. (2005). “Consortium organizations for strong-motion observation systems.” 〈http://db.cosmos-eq.org/scripts/default.plx〉 (May 2008).
Decanini, L. D., and Mollaioli, F. (2001). “An energy-based methodology for the assessment of seismic demand.” Soil Dyn. Earthquake Eng., 21, 113–137.
Drenick, R. F. (1977). “The critical excitation of nonlinear systems.” J. Appl. Mech., 44(E2), 333–336.
Fajfar, P. (1992). “Equivalent ductility factors, taking into account low-cyclic fatigue.” Earthquake Eng. Struct. Dyn., 21, 837–848.
Fajfar, P., and Krawinklere, H., eds. (1997). Seismic design methodologies for the next generation of codes, Taylor & Francis, Rotterdam, Balkema.
Ghobara, A., Abou-Elfath, H., and Biddah, A. (1999). “Response-based damage assessment of structures.” Earthquake Eng. Struct. Dyn., 28, 79–104.
Goel, R. K. (1997). “Seismic response of asymmetric systems: energy-based approach.” J. Struct. Eng., 123(11), 1444–1453.
Hanks, T. G., and McGuire, R K. (1981). “The character of high frequency ground motions based on seismic shear waves.” Bull. Seismol. Soc. Am., 71(6), 2071–2095.
He, W.-L., and Agrawal, A. K. (2008). “Analytical model of ground motion pulses for the design and assessment of seismic protective systems.” J. Struct. Eng., 134(7), 1177–1188.
Housner, G. W., and Hudson, D. E. (1958). “The Port Hueneme earthquake of March 18, 1957.” Bull. Seismol. Soc. Am., 48, 163–168.
Iyengar, R. N. (1972). “Worst inputs and a bound on the highest peak statistics of a class of non-linear systems.” J. Sound Vib., 25, 29–37.
Kalkan, E., and Kunnath, S. K. (2006). “Effects of fling step and forward directivity on seismic response of buildings.” Earthquake Spectra, 22(2), 367–390.
Kalkan, E., and Kunnath, S. K. (2008). “Relevance of absolute and relative energy content in seismic evaluation of structures.” Adv. Struct. Eng., 11(1), 1–18.
Kiureghian, A. D., and Crempien, J. (1989). “An evolutionary model for earthquake ground motion.” Struct. Saf., 6, 235–246.
Mahin, S. A., and Bertero, V. V. (1981). “An evaluation of inelastic seismic design spectra.” J. Struct. Div., 107(ST9), 1777–1795.
McGuire, R. K. (1995). “Probabilistic seismic hazard analysis and design earthquake: closing the loop.” Bull. Seismol. Soc. Am., 85(5), 1275–1284.
Mehanny, S. S., and Deierlein, G. G. (2000). “Modeling of assessment of seismic performance of composite frames with reinforced concrete columns and steel beams.” John Blume Earthquake Research Center Rep. No. 135, Dept. of Civil and Environmental Engineering, Stanford Univ., Stanford, CA.
Moustafa, A. (2002). “Deterministic/Reliability-based critical earthquake load models for linear/nonlinear engineering structures,” Ph.D. thesis, Dept. of Civil Engineering, Indian Institute of Science, Bangalore, India.
Moustafa, A. (2010). “Discussion of analytical model of ground motion pulses for the design and assessment of seismic protective systems.” J. Struct. Eng., 136(2), 229–230.
Nakashima, M., Saburi, K., and Tsuji, B. (1996). “Energy input and dissipation behavior of structures with hysteretic dampers.” Earthquake Eng. Struct. Dyn., 25, 483–496.
Newmark, N. M., and Hall, W. J. (1982). “Earthquake spectra and design, Monograph.” Earthquake Engineering Research, Berkeley, CA.
Otani, S. (1981). “Hysteretic models of reinforced concrete for earthquake response analysis.” Journal of the Faculty of Engineering, University of Tokyo, Series B, 36(2), 407–441.
Park, Y. J., and Ang, A. H.-S. (1985). “Mechanistic seismic damage model for reinforced concrete.” J. Struct. Eng., 111(4), 722–739.
Park, Y. J., Ang, A. H.-S., and Wen, Y. K. (1985). “Seismic damage analysis of reinforced concrete buildings.” J. Struct. Eng., 111(4), 740–757.
Park, Y. J., Ang, A. H.-S., and Wen, Y. K. (1987). “Damage-limiting aseismic design of buildings.” Earthquake Spectra, 3(1), 1–26.
Philippacopoulos, A. J., and Wang, P. C. (1984). “Seismic inputs for nonlinear structures.” J. Eng. Mech., 110, 828–836.
Powell, G. H., and Allahabadi, R. (1988). “Seismic damage predictions by deterministic methods: concepts and procedures.” Earthquake Eng. Struct. Dyn., 16, 719–734.
Quek, S. T., Teo, Y. P., and Balendra, T. (1990). “Non-stationary structural response with evolutionary spectra using seismological input model.” Earthquake Eng. Struct. Dyn., 19, 275–288.
Reiter, L. (1990). Earthquake hazard analysis, Columbia University Press, New York.
Riddell, F. (1995). “Inelastic design spectra accounting for soil conditions.” Earthquake Eng. Struct. Dyn., 24, 1491–1510.
Sarkar, A. (2003). “Linear stochastic dynamical system under uncertain load: inverse reliability analysis.” J. Eng. Mech., 129(6), 665–671.
Shinozuka, M. (1970). “Maximum structural response to seismic excitations.” J. Eng. Mech. Div., Am. Soc. Civ. Eng., 96(5), 729–738.
Shinozuka, M., and Henry, L. (1965). “Random vibration of a beam column.” J. Eng. Mech. Div., Am. Soc. Civ. Eng., 91(5), 123–154.
Structural Engineers Association of California. (SEAOC), (2002). “Performance based seismic design engineering of buildings.” Vision 2000 Rep., Sacramento, CA.
Takeda, T., Sozen, M. A., and Nielsen, N. N. (1970). “Reinforced concrete response to simulated earthquakes.” J. Struct. Div., 96(ST12), 2557–2573.
Takewaki, I. (2001). “Probabilistic critical excitation for MDOF elastic-plastic structures on compliant ground.” Earthquake Eng. Struct. Dyn., 30, 1345–1360.
Takewaki, I. (2002). “Seismic critical excitation method for robust design: A review.” J. Struct. Eng., 128, 665–672.
Takewaki, I. (2004). “Bound of earthquake input energy.” J. Struct. Eng., 130, 1289–1297.
Takewaki, I. (2007). Critical excitation methods in earthquake engineering, Elsevier Science, The Netherlands.
Uang, C-M., Bertero, and V. V. (1990). “Evaluation of seismic energy in structures.” Earthquake Eng. Struct. Dyn., 19, 77–90.
Westermo, B. D. (1985). “The critical excitation and response of simple dynamic systems.” J. Sound Vib., 100, 233–242.
Wong, K. K. F., and Yong, R. (2002). “Earthquake response and energy evaluation of inelastic structures.” J. Eng. Mech., 128(3), 308–317.
Yamaguchi, H., and El-Abd, A. (2003). “Effect of energy input characteristics on hysteretic damper efficiency.” Earthquake Eng. Struct. Dyn., 32, 827–843.
Zahrah, T. F., and Hall, W. J. (1984). “Earthquake energy absorption in sdof structures.” J. Struct. Eng., 110, 1757–1772.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 137 • Issue 3 • March 2011
Pages: 456 - 467
Copyright
© 2011 American Society of Civil Engineers.
History
Received: Jun 23, 2008
Accepted: Mar 30, 2009
Published online: Feb 15, 2011
Published in print: Mar 1, 2011
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.