HYSTERETIC ENERGY TO ENERGY INPUT RATIO SPECTRUM IN NONLINEAR SYSTEMS

Abstract

Even though some empirical formulas for hysteretic energy (EH) to energy input (EI) ratio have been proposed in the literature, they all assume that this ratio is the same for any period range and do not consider either the ground motion properties or the structural properties. This paper presents a study on EH/EI in inelastic single-degree-of-freedom (SDOF) systems and relates it to the inelastic multidegree-of-freedom (MDOF) systems subject to severe earthquake ground motions. The response analyses are carried out through nonlinear dynamic time-history (NDTH) analyses on SDOF systems and steel moment resisting frames as MDOF systems for ninety EQGMs recorded on different soils. A spectrum for EH/EI ratio with different strength indices in SDOF systems is proposed based on the analyses results

Keywords

• Hysteretic energy, Energy spectrum, NDTH analysis, nonlinear systems, SDOF systems, MDOF systems

DOĞRUSAL OLMAYAN SİSTEMLERDE HİSTERETİK ENERJİ /ENERJİ ORANI SPEKTRUMU

Abstract

Literatürde histeretik enerji (EH)/enerji oranı (EI) için bazı ampirik bağıntılar olmasına rağmen, tüm bu bağıntılar anılan oranı her bir periyot aralığı için sabit kabul etmekte ve deprem yer hareketi özellikleri veya yapısal özellikleri gözönüne almamaktadır. Bu çalışma, doğrusal olmayan tek serbestlik dereceli sistemler için EH/EI oranlarının hesabı üzerinedir ve çeşitli deprem yer hareketine maruz doğrusal olmayan çok serbestlik dereceli sistemlere adaptasyonu ile ilgilidir. Bu bağlamda, tek serbestlik dereceli sistemler ile çok serbestlik dereceli sistemlerin (moment aktaran çerçeveler) dinamik analizleri farklı zeminlerde kaydedilmiş doksan adet deprem hareketi dikkate alınarak doğrusal olmayan zaman tanım alanında hesap yöntemi ile gerçekleştirilmiş, analiz sonuçları doğrultusunda tek serbestlik dereceli sistemlere ait EH/EI oranı için spektrum önerilmiştir

Keywords

• Histeretik enerji, Enerji spektrumu, Doğrusal olmayan zaman tanım alanında hesap, Doğrusal olmayan sistemler, tek serbestlik dereceli sistemler, Çok serbestlik dereceli sistemler

References

1. Bertero, V.V. and Teran-Gilmore, A. Use of Energy Concepts in Earthquake-Resistant Analysis and Design: Issues and Future Directions, Advances in Earthquake Engineering Practice, Short Course in Structural Engineering, Architectural and Economic Issues, University of California, Berkeley, 1994.
2. Housner, G.W. Limit Design of Structures to Resist Earthquakes, Proceedings of the First World Conference on Earthquake Engineering, Berkeley, California, 1956, 5-1-5-13.
3. Zahrah, T.F. and Hall, W.J. Seismic Energy Absorption in Simple Structures, Structural Research Series No.501, 1982, Civil Engineering Studies, University of Illinois, Urbana- Champaign, Illinois.
4. Akiyama, H. Earthquake-Resistant Limit-State Design for Buildings, University of Tokyo Press, 1985.
5. Fajfar, P. and Vidic, T., and Fischinger, M. Seismic Demand in Medium- and Long-period Structures, Earthquake Engineering and Structural Dynamics, v.18, 1989, pp.513-537.
6. Kuvamura, H. and Galambos, T.V. Earthquake Load for Structural Reliability, Journal of Structural Engineering, v.115, no.6, 1989, pp.1446-1463.
7. Uang, C.M. and Bertero, V.V. Evaluation of Seismic Energy in Structures, Earthquake Engineering and Structural Dynamics, v.19, 1990, pp.77-90.
8. Manfredi, G. Evaluation of seismic energy demand, Earthquake Engineering and Structural Dynamics, v.30, 2001, pp.485-499.

9. Riddell, R. and Garcia, J.E. Hysteretic energy spectrum and damage control, Earthquake Engineering and Structural Dynamics, v.30, 2001, pp.1791-1816.
10. Cruz MF and Lopez OA. Plastic energy dissipated during an earthquake as a function of structural properties and ground motion characteristics, Engineering Structures , v.22, 2000, pp.784-792.
11. Shen, J. and Akbas, B. Seismic Energy Demand in Steel Moment Frames, Journal of Earthquake Engineering, v.3, no.4, 1999, pp.519-559.
12. Shen J, Hao H, and Akbas B. Hysteresis Energy in Moment Frames, Shen J., Editor. The Engineering Science of Structures, A Special Volume Honoring Sidney A. Guralnick. Illinois Institute of Technology: April, 2000, pp.112-138.
13. Fajfar, P., Vidic, T., and Fischinger, M. On Energy Demand and Supply in SDOF Systems, Workshop on Nonlinear Seismic Analysis of Reinforced Concrete Buildings, Bled, Slovenia, Yugoslavia, 1992.
14. Fajfar, P., and Vidic, T. Consistent Inelastic Design Spectra: Hysteretic and Input Energy, Earthquake Engineering and Structural Dynamics, v.23, 1994, pp.523-537.
15. Akbas, B., Shen, J., and Hao, H. Energy approach in performance-based seismic design of steel moment resisting frames for basic safety objective, The Structural Design of Tall Buildings, v.10, 2001, p.193-217.
16. Prakash, V., Powell, G.H., and Campbell, S. DRAIN-2DX: Base Program Description and User Guide, Version 1.10, Rep. No. UCB/SEMM-93/17, University of California, Berkeley, 1993.
17. Sari, A. Energy Consideration in Ground Motion Attenuation and Probabilistic Seismic Hazard Studies, Ph.D. Thesis, Department of Civil Engineering, University of Texas at Austin, 2003.
18. Ohtori, Y., R. E. Christenson, B. F. Spencer, et al. Benchmark Control Problems for Seismically http://www.nd.edu/~quake/benchmarks/bench3def/, 2000. Excited Nonlinear Buildings.
19. Akbas, B. Temiz, H., Tugsal, U.M., and Kara, F.I. Hysteretic Energy Demand in Low-, Medium-, and High-rise Steel Moment Resisting Frames, Earthquake Symposium-2005, Kocaeli, Turkey (in Turkish).
20. AISC-LRFD. Load and Resistance Factor Design, American Institute of Steel Construction, Chicago, 1999.