# The Spectra of Relative Input Energy per Unit Mass of Structure for Iranian Earthquakes

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## Abstract

Energy criterion is a simple and scalar quantity, so it has been employed by many researchers for the assessment of seismic behavior. Production and presentation of input energy spectra are effective steps for the employment of energy criterion in the seismic design of structures. Ninety-two pairs of horizontal components of Iranian earthquakes were used for this research. These records were divided into near-field and far-field, and in each field, soils categorized to types 1–3. Using nonlinear dynamic analysis, 92 inelastic spectra of relative input energy per unit mass were generated for a damping ratio of 5% and a ductility factor of 3. Then, for each category of records, a combined spectrum was produced at design level corresponding to 10% risk in 50 years. The evaluation of combined spectra led to the conclusion that the average value of combined spectrum in near-field is greater than that in far-field. In addition, the average value of combined spectrum is greater for softer soils. The corresponding period to the peak of combined spectrum in near-field is longer than that in far-field. The effect of soil type in near-field is more than that in far-field. For each field and each type of soil, a relation and its parameters have been proposed for the inelastic spectrum of relative input energy per unit mass.

## Keywords

Inelastic spectrum Soil type Near-field Far-field Seismic design Combined spectrum## List of symbols

*m*Total mass of structure

*C*Viscous damping coefficient of structure

- \({f_{\text{s}}}\)
Restoring force of structure

*T*Fundamental period of structure

*T*_{p}Corresponding period to the peak of combined spectrum

*u*Displacement of mass relative to the ground

*u*_{g}Displacement of the ground during an earthquake

*u*_{t}Total displacement (absolute displacement) of mass

- \({\dot {u}_{\text{g}}}\)
Velocity of mass relative to the ground

- \(\dot {u}\)
Velocity of the ground during an earthquake

- \({\dot {u}_{_{{\text{t}}}}}\)
Total velocity (absolute velocity) of mass

- \(\ddot {u}\)
Acceleration of mass relative to the ground

- \({\ddot {u}_{\text{g}}}\)
Acceleration of the ground during an earthquake

- \({\ddot {u}_{\text{t}}}\)
Total acceleration (absolute acceleration) of mass

- E
_{ri} Relative input energy

*E*_{rk}Relative kinematic energy

*E*_{d}Damping energy

*E*_{a}Strain absorbed energy

*ξ*Damping ratio of structure

*µ*Displacement ductility factor of structure

*u*_{m}Maximum displacement of mass

*u*_{y}Yielding displacement of structure

*γ, β*Coefficients of Newmark method

- \(\frac{{{E_{{\text{ri}}}}}}{m}\)
Relative input energy per unit mass of structure

*E*_{0}Maximum value of \(\frac{{{E_{{\text{ri}}}}}}{m}\) in proposed spectra

*α*_{1},*α*_{2}Coefficients of the proposed spectra of \(\frac{{{E_{{\text{ri}}}}}}{m}\)

*T*_{1}Corresponding period to the

*beginning*of constant segment in the proposed spectra of \(\frac{{{E_{{\text{ri}}}}}}{m}\)*T*_{2}Corresponding period to the

*ending*of constant segment in the proposed spectra of \(\frac{{{E_{{\text{ri}}}}}}{m}\)- SD
Standard deviation

- MS
Mean spectrum

- Index
*x* Related to

*x*-direction- Index
*y* Related to

*y*-direction

## References

- 1.Akiyama H (1985) Earthquake-resistant limit-state design for buildings. University of Tokyo press, Tokyo. ISBN: 0-86008-377-2Google Scholar
- 2.Fakhri-Niasar M (1998) The energy spectrum of the Iranian earthquakes. Dissertation, Science and Research Branch of Islamic Azad University, Tehran (
**In Persian**)Google Scholar - 3.Vahdani R, Gerami M, Vaseghi-Nia MA (2017) Structural damping and displacement ductility effects on input energy spectrum of earthquake. J Struct Constr Eng. https://doi.org/10.22065/JSCE.2017.80788.1138 (
**In Persian**)CrossRefGoogle Scholar - 4.Ruzi A (2003) Energy concept in earthquake-resistant design. Dissertation, Istanbul Technical University. http://hdl.handle.net/11527/10837. Accessed 3 June 2018
- 5.Haddad-Shargh F, Hosseini M (2011) An optimal distribution of stiffness over the height of shear buildings to minimize the seismic input energy. J Seismol Earthq Eng 13:25–32Google Scholar
- 6.Housner GW (1956) Limit design of structures to resist earthquakes. In: Proceedings of the 1st World conference on earthquake engineering, California 5:1–13. http://www.iitk.ac.in/nicee/wcee/article/1_5-1.pdf. Accessed 2 June 2018
- 7.Housner GW (1959) Behavior of structures during earthquakes. J Eng Mech Div 85:109–130Google Scholar
- 8.Uang CM, Bertero VV (1988) Use of energy as a design criterion in earthquake resistant design. Report No. UCB/EERC-88/18, Earthquake Engineering Research Center, University of California, California. https://nehrpsearch.nist.gov/static/files/NSF/PB91210906.pdf. Accessed 11 June 2018
- 9.Ghafory-Ashtiany M, Maleki H (2000) Study on the energy of earthquakes in reinforced concrete moment frames. J Seismol Earthq Eng 3:33–43Google Scholar
- 10.Ghodrati-Amiri G, Abdollahzadeh-Darzi G, Khanzadi M (2007) Earthquake duration and damping effects on input energy. Int J Civ Eng 5:14–29Google Scholar
- 11.Ghodrati-Amiri G, Abdollahzadeh-Darzi G, Vaseghi-Amiri J (2008) Design elastic input energy spectra based on Iranian earthquakes. Can J Civ Eng 35:635–646. https://doi.org/10.1139/L08-013 CrossRefGoogle Scholar
- 12.Decanini L, Mollaioli F (2001) An energy-based methodology for the assessment of seismic demand. Soil Dyn Earthq Eng 21:113–137. https://doi.org/10.1016/S0267-7261(00)00102-0 CrossRefGoogle Scholar
- 13.Ye L, Cheng G, Qu Z (2009) Study on energy-based seismic design method and the application for steel braced frame structures. In: 6th International conference on urban earthquake engineering, Tokyo, Tokyo Institute of Technology. file:///C:/Users/USER1/Downloads/2009_Ye.pdf. Accessed 2 June 2018Google Scholar
- 14.Siahpolo N (2015) The effect of near-field earthquake on seismic demands of SMRFs with MDOFʼs and higher modes considerations. Dissertation, Semnan University, Semnan, Iran. http://diglib.semnan.ac.ir/diglib/WebUI/WebPageViewer.aspx. Accessed 2 June 2018 (
**In Persian**) - 15.Bagheri B, oh SH (2018) Seismic design of coupled shear wall building linked by hysteretic dampers using energy based seismic design. Int J Steel Struct 18:225–253. https://doi.org/10.1007/s13296-018-0318-1 CrossRefGoogle Scholar
- 16.Ucar T, Merter O (2018) Derivation of energy-based base shear force coefficient considering hysteretic behavior and P-delta effects. Earthq Eng Eng Vib 17:149–163. https://doi.org/10.1007/s11803-018-0431-3 CrossRefGoogle Scholar
- 17.Zahrah TF, Hall WJ (1984) Earthquake energy absorption in SDOF structures. J Struct Eng 110:1757–1772. https://doi.org/10.1061/(ASCE)0733-9445(1984)110:8(1757) CrossRefGoogle Scholar
- 18.Manfredi G (2001) Evaluation of seismic energy demand. Earthq Eng Struct Dyn 30:485–499CrossRefGoogle Scholar
- 19.Khashaee P, Mohraz B, Sadek F, Lew HS, Gross JL (2003) Distribution of earthquake input energy in structures. National Institute of Standards and Technology, Report No. NISTIR 6903. https://ws680.nist.gov/publication/get_pdf.cfm?pub_id=860444. Accessed 6 July 2018
- 20.Akbas B, Shen J, Hao H (2001) Energy approach in performance-based seismic design of steel moment resisting frames for basic safety objective. Struct Des Tall Build 10:193–217. https://doi.org/10.1002/tal.172 CrossRefGoogle Scholar
- 21.Benavent-Climent A, Pujades LG, Lopez-Almansa F (2002) Design energy input spectra for moderate-seismicity regions. Earthq Eng Struct Dyn 31:1151–1172CrossRefGoogle Scholar
- 22.Chopra AK (2012) Dynamics of structures—theory and applications to earthquake engineering, 4th edn. Prentice Hall, New York. ISBN 13: 978-0-13-285803-8$4Google Scholar
- 23.Pacific Earthquake Engineering Research Center (2017) OpenSees. http://opensees.berkeley.edu. Accessed 15 July 2017
- 24.Road, Housing and Urban Development Research Center (2017) Iran strong motion network. http://ismn.bhrc.ac.ir. Accessed 21 July 2017
- 25.Pacific Earthquake Engineering Research Center (2017) PEER ground motion database. https://ngawest2.berkeley.edu. Accessed 1 July 2017
- 26.Earthquake Engineering Software Solutions (2017) Seismosignal 2016. http://www.seismosoft.com/seismosignal. Accessed 6 July 2018
- 27.BHRC (2014) Iranian code of practice for seismic resistant design of buildings, Standard No. 2800, 4th edn. Road, Housing and Urban Development Research Center, Tehran. ISBN: 978-600-113-128-8 (
**In Persian**)Google Scholar - 28.Yaghmaei-Sabegh S, Mohammad-Alizadeh H (2012) Improvement of Iranian seismic design code considering the near-fault effects. Int J Eng 25:147–158CrossRefGoogle Scholar
- 29.Mohraz B (1992) Recent studies of earthquake ground motion and amplification. In: Proceedings of the 10th world conference on earthquake engineering, Madri, XI:6695–6704. http://www.iitk.ac.in/nicee/wcee/article/10_vol11_6695.pdf. Accessed 6 July 2018
- 30.Javan-emrooz HR, Eskandari-Ghadi M, Mirzaei N (2014) Magnitude and distance dependent design spectra for rock sites based on Iranian acceleration time-histories and comparison with regional design spectra. J Earth Space Phys 40:1–16Google Scholar
- 31.Nasiri P (2006) Statistics and probabilities for engineers. Payame Noor University, Tehran. ISBN: 964-387-177-0 (
**In Persian**)Google Scholar