A New Method for Estimating the Input-Energy of MDOF Structures

Document Type : Research

Authors

1 University of Tabriz, Tabriz, Iran.

2 Associate Professor, University of Tabriz, Tabriz, Iran.

Abstract

Input-energy is the amount of energy that is imposed by an earthquake on a structure and its correlation with structural damage has been studied and demonstrated by many researchers. Since studies concerning seismic energy in multi-degree-of-freedom systems are relatively limited compared with single-degree-of-freedom, in this paper, firstly a theoretical exact method is discussed to calculate the input-energy of the multi-degree-of-freedom elastic oscillators. It is proved that unlike the general rule in mechanics, the superposition theorem is valid for input-energy in conventional modal analysis. To estimate the input-energy, an approach based on PHSA to predict the Fourier amplitude spectrum, is proposed. The results indicate that the modal mass ratio is not the only decisive parameter in input-energy. Modal input-energy decomposition also confirms the possibility of greater input-energy of higher modes in comparison with fundamental ones or the ones with the higher mass participation ratio, especially for tall buildings located in the near-field seismic zones.

Keywords

References

1. Ucar, T. and O. Merter, Derivation of energy-based base shear force coefficient considering hysteretic behavior and P-delta effects. Earthquake Engineering and Engineering Vibration, 2018. 17(1): p. 149-163. [DOI:10.1007/s11803-018-0431-3]
2. Decanini, L.D. and F. Mollaioli, An energy-based methodology for the assessment of seismic demand. Soil Dynamics and Earthquake Engineering, 2001. 21(2): p. 113-137. [DOI:10.1016/S0267-7261(00)00102-0]
3. Davarnia, D. and B. Farahmand Azar, A new method for scaling of earthquake records using input energy of structures. The Structural Design of Tall and Special Buildings,Under Publication.
4. Akbas, B., J. Shen, and H. Hao, Energy appproach in peformance‐based seismic design of steel moment resisting frames for basic safety objective. The Structural Design of Tall and Special Buildings, 2001. 10(3): p. 193-217. [DOI:10.1002/tal.172]
5. Uang, C.M. and V.V. Bertero, Evaluation of seismic energy in structures. Earthquake Engineering & Structural Dynamics, 1990. 19(1): p. 77-90. [DOI:10.1002/eqe.4290190108]
6. Uang, C.-M. and V.V. Bertero, Use of energy as a design criterion in earthquake-resistant design. Vol. 88. 1988: Earthquake Engineering Research Center, University of California Berkeley, USA.
7. Teran-Gilmore, A., Performance-based earthquake-resistant design of framed buildings using energy concepts. 1996, University of California, Berkeley.
8. Leelataviwat, S., S.C. Goel, and B.i. Stojadinovic, Toward performance-based seismic design of structures. Earthquake spectra, 1999. 15(3): p. 435-461. [DOI:10.1193/1.1586052]
9. Trifunac, M., T. Hao, and M. Todorovska. Energy of earthquake response as a design tool. in Proc. 13th Mexican National Conf. on Earthquake Engineering. 2001.
10. Younespour, A. and H. Ghaffarzadeh, Structural active vibration control using active mass damper by block pulse functions. Journal of Vibration and Control, 2015. 21(14): p. 2787-2795. [DOI:10.1177/1077546313519285]
11. Gendeshmin, S.R. and D. Davarnia, Using block pulse functions for seismic vibration semi-active control of structures with MR dampers. Results in physics, 2018. 8: p. 914-919. [DOI:10.1016/j.rinp.2018.01.029]
12. Younespour, A., H. Ghaffarzadeh, and B.F. Azar, An equivalent linearization method for nonlinear Van der Pol oscillator subjected to random vibration using orthogonal functions. Control Theory and Technology, 2018. 16(1): p. 49-57. [DOI:10.1007/s11768-018-7038-0]
13. Younespour, A., S. Cheng, and H. Ghaffarzadeh, An equivalent linearization method for nonlinear systems under nonstationary random excitations using orthogonal functions. Structural Engineering and Mechanics, 2018. 66(1): p. 139-149.
14. Ordaz, M., B. Huerta, and E. Reinoso, Exact computation of input‐energy spectra from Fourier amplitude spectra. Earthquake Engineering & Structural Dynamics, 2003. 32(4): p. 597-605. [DOI:10.1002/eqe.240]
15. McGuire, R.K., A simple model for estimating Fourier amplitude spectra of horizontal ground acceleration. Bulletin of the Seismological Society of America, 1978. 68(3): p. 803-822.
16. Cornell, C.A., Engineering seismic risk analysis. Bulletin of the seismological society of America, 1968. 58(5): p. 1583-1606.
17. Yaghmaei-Sabegh, S. and M. Ebrahimi-Aghabagher, Near-field probabilistic seismic hazard analysis with characteristic earthquake effects. Natural Hazards, 2017. 87(3): p. 1607-1633. [DOI:10.1007/s11069-017-2834-2]
18. ASCE, ASCE 7: Minimum design loads for buildings and other structures. 2002.
Numerical Methods in Civil Engineering
Volume 4, Issue 2
December 2019
Pages 36-43

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History

  • Receive Date: 06 September 2019
  • Revise Date: 10 November 2019
  • Accept Date: 01 December 2019

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