The effects of period and nonlinearity on energy demands of MDOF and E-SDOF systems under pulse-type near-fault earthquake records

Document Type : Article


1 Department of Civil Engineering, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran

2 - Department of Civil Engineering, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran. - Department of Civil Engineering, Institute for Higher Education ACECR, Khouzestan, Iran.



The use of the concept of earthquake input energy under far-filed earthquakes and types of internal energy in structures has recently been mentioned to develop the performance-based design method. However, the extension of these studies to near-fault pulse-like earthquakes has been less considered. This paper calculates the applied ratios of energy types in the E-SDOF and MDOF systems and identifies the relationship between them. For this purpose, five steel frames (4, 10, 15, 20, and 30 story steel MRFs with 3-span) were designed, and obtained the E-SDOF structure equivalent to the first mode, using modal pushover analysis (MPA) method. All models were analyzed under 10 near-fault pulse-like earthquake records using nonlinear time history analysis. The results show that the total dissipated energy of the structure (TDE) depends on its nonlinear degree and period. The TDE of the MDOF and E-SDOF systems is equal for long periods, and its size is independent of the design resistance (R) and the degree of nonlinearity. However, in short periods, this ratio is close to the effective modal mass coefficient corresponding to the first mode. The story normalized hysteretic energy ratio is also a function of the height, nonlinear degree and period of the structure.


1. Haddad-Shargh, F. and Hosseini, M. An optimal distributionof sti ness over the height of shear buildingsto minimize the seismic input energy", Journal ofSeismology and Earthquake Engineering, 13(1), pp.25{32 (2011).2. Uang, C.M. and Bertero, V.V. Evaluation of seismicenergy in structures", Earthquake Engineering: StructuralDynamics, 19(1), pp. 77{90 (1990).3. Housner, G.W. Limit design of structures to resistearthquakes", In: Proceedings of 1st World Conferenceon Earthquake Engineering, 5, Oakland, Calif, USA,pp. 1{13 (1956).4. Leelataviwat, S., Goel, S.C., and Stojadinovic, B.Toward performance-based seismic design of structures",Earthquake Spectra, 15(3), pp. 435{461 (1999).1210 S.A. Razavi et al./Scientia Iranica, Transactions A: Civil Engineering 28 (2021) 1195{12115. Khashaee, P., Mohraz, B., Sadek, F., et al. Distributionof earthquake input energy in structures",Tech. Rep. NISTIR 6905, United States Departmentof Commerce Technology Administration, NationalInstitute of Standards and Technology,  ormance-based plastic design (PBPD) method forearthquake-resistant structures: an overview", StructDes Tall Spec, 19(1{2), pp. 115{37 (2010).7. Banihashemi, M.R., Mirzagoltabar, A.R., andTavakoli, H.R. Development of the performance based-plastic design for steel moment resistant frame", Int JSteel Struct, 15(1), pp. 51{62 (2015).8. Sahoo, D.R. and Chao, S. Performance-based plasticdesign method for buckling-restrained braced frames",Eng Struct, 32(9), pp. 2950{2958 (2013).9. Wongpakdee, N., Leelataviwat. S., Goel. S.C., et al.Performance-based design and collapse evaluation ofbuckling restrained knee braced truss moment frames",Eng Struct, 60, pp. 23{31 (2014).10. Heidari, A. and Gharehbaghi, S. Seismic performanceimprovement of special truss moment frames usingdamage and energy concepts", Earthq Eng Struct Dyn,44(7), pp. 1055{1073 (2015).11. Kharmale, S.B. and Ghosh, S. Performance-basedplastic design of steel plate shear walls", J Constr SteelRes, 90, pp. 85{97 (2013).12. Connor, J.J., Wada, A., and I - al.Damage-controlled structures. I. Preliminary designmethodology for seismically active regions", J Struct-Eng, 123(4), pp. 423{431 (1997).13. Vargas, R. and Bruneau, M. Analytical response anddesign of buildings with metallic structural fuses. I", JStruct Eng, 135(4), pp. 386{393 (2009).14. Ke, K., Yam, MCH., and Ke, S. A dualenergy-demand-indices-based evaluation procedure ofdamage-control frame structures with energy dissipationfuses", Soil Dyn Earthq Eng, 95, pp. 61{82 (2017).15. Du, B., He, Z., Wu, Y., and Pan, F. A compatibleenergy demand estimate considering code-speci eddesign spectra", Soil Dynamics and Earthquake Engineering,137, p. 106273 (2020).16. Yang, T.Y., Neitsch, J., Al-Janabi, M.A.Q., and Tung,D.P. Seismic performance of eccentrically bracedframes designed by the conventional and equivalentenergy procedures", Soil Dynamics and EarthquakeEngineering, 139, p. 106322 (2020).17. Guo, W., Du, Q., Huang, Z., et al. An improvedequivalent energy-based design procedure for seismicisolation  23, pp. 124{143 (2019).19. Zhou, Y., Song, G., Huang, S. et al. Input energyspectra for self-centering SDOF systems", Soil Dynamics
and Earthquake Engineering, 121, pp. 293{305(2019).20. Zhou, Y., Song, G., and Tan, P. Hysteretic energydemand for self-centering SDOF systems", Soil Dynamicsand Earthquake Engineering, 125, p. 105703(2019). 21. Yang, T.Y., Tung, D.P., and Li, Y. Equivalentenergy design procedure for earthquake resilient fusedstructures", Earthquake Spectra, 34(2), pp. 795{815 (2018).22. Vahdani, R., Gerami, M., and Vaseghinia, M.A.Structural damping and displacement ductility e ectson input energy spectrum of earthquake", Journal of
Structural and Construction Engineering, 5(2), pp. 5{21 (2017) (in Persian).23. Benio , H. Mechanism and strain characteristics of the white wolf fault as indicated by the aftershocksequence", Calif. Div. Mines Bull, 171, pp. 199{202(1955).
24. Mahin, S.A., Bertero, V.V., Chopra, A.K., et al.Response of the olive view hospital main building
during the San Fernando earthquake", EarthquakeEngineering Research Center, University of California,
Berkeley, Technical Report, 1976-10 (1976).25. Bertero, V.V., Mahin, S.A., and Herrera, R.A. A
seismic design implications of near-fault San Fernandoearthquake records", Earthquake Engineering
and Structural Dynamics, 6(1), pp. 31{42 (1978).26. Hall, J.F., Heaton, T.H., Halling, M.W., et al. Nearsource
ground motion and its e ects on
exible buildings",Earthquake Spectra, 11(4), pp. 569{605 (1995).
27. Krawinkler, H., Anderson, J., Bertero, V., and Theil,Jr. C. Steel buildings", Earthquake Spectra, 12(S1),
pp. 25{47 (1996).28. Makris, N. and Black, C.J. Dimensional analysisof bilinear oscillators under pulse-type excitations",
Journal of Engineering Mechanics, 130(9), pp. 1019{1031 (2004).29. DHUD-Part6: Applied loads on buildings", Department
of Housing and Urban Development, IranianNational Building Code-Part 6, third edition (2014)(in Persian).
30. BHRC-PN 253: Iranian code of practice for seismicresistant design of building", Iranian Building Codes
and Standards, forth revision (2014) (in Persian).31. ASCE/SEI 7: Minimum Design Loads for Buildings
and Other Structures, American Society of Civil Engineers,USA (2016).32. Computers and Structures, Inc Etabs 2016-extended
3D analysis of building systems, nonlinear", Berkeley,California 94704, USA.33. ANSI/AISC 360-10: Speci cation for Structural Steel
Buildings, American Institute of Steel Construction,Chicago (2010).S.A. Razavi et al./Scientia Iranica, Transactions A: Civil Engineering 28 (2021) 1195{1211 1211
34. McKenna, F. OpenSees: a framework for earthquakeengineering simulation", Computing in Science: Engineering,13(4), pp. 58{66 (2011).35. Baker, J. Quantitative classi cation of near- eldground motion using wavelet analysis", Bulletin of theSeismological Society of America, 97(5), pp. 1486{1501(2007).36. Chopra, A.K. and Goel, R.K. A modal pushoveranalysis procedure for estimating seismic demandsfor buildings", Earthquake Engineering: StructuralDynamics, 31(3), pp. 561{582 (2002).37. Seneviratna, G. and Krawinkler, H., Evaluation ofInelastic MDOF E ects for Seismic Design, John A. Blume Earthquake Engineering Center (1997).38. Fajfar, P. and Vidic, T. Consistent inelastic designspectra hysteretic and input energy", Earthquake Engineering:Structural Dynamics, 23(5), pp. 523{537(1994).
39. Gerami, M. and Abdollahzadeh, D. Estimation of forward directivity e ect on design spectra in near eld of fault", Journal of Basic and Applied Scienti cResearch, 2(9), pp. 8670{8678 (2012).40. Gerami, M. and Abdollahzadeh, D. Numerical studyon energy dissipation of steel moment resisting framesunder e ect of earthquake vibrations", Advances inAcoustics and Vibration, 2014, pp. 1{13 (2014).