Skip to main content
SpringerLink
Log in

State-of-the-Art Review of Energy-Based Seismic Design Methods

Archives of Computational Methods in Engineering volume 29, pages 1965–1996 (2022)Cite this article

Abstract

This paper presents a comprehensive state-of-the-art review of the research carried out on the energy-based structural seismic design methods. Since earthquake exerts energy to the structure, it is realistic to use the energy as the main design criteria of the structure. The energy-based seismic design method is based on the concept of energy balance in the structures, which states that the earthquake input energy to the structure must be less than its capacity to dissipate the energy; otherwise, local or global damage will occur. Although the energy-based design method has received increasing attention in recent years, it has not yet become an applicable engineering design procedure. This could be due to the lack of specified and reliable criteria for this method. This paper is intended to provide the reader with a thorough review of energy-based seismic design methods, highlighting the unresolved issues and identifying the gaps that will require attention in future research.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

USD 39.95

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23

Abbreviations

\(a_{rms}\) :

Root-mean-square of acceleration in g

\(AE_{I}\) :

Seismic hazard energy factor

\(A_{pi}\) :

A non-dimensional index of the damage in the i-th story

\(c\) :

Viscous damping coefficient

\(c_{a}\) :

Ratio of spectral elastic response acceleration to PGA in the short (acceleration-controlled) period range

\(c_{v}\) :

Ratio of spectral elastic response velocity to PGV in the medium (velocity-controlled) period range

\(c_{E}\) :

Coefficient that depends on the damping model

\(c_{H}\) :

Coefficient that depends on the hysteretic model

\(CAV\) :

Cumulative absolute velocity

\(d_{n}\) :

Displacement at story n

\(D_{e}\) :

Maximum displacement of the corresponding elastic system

\(D_{y}\) :

Yield displacement

\(D_{max}\) :

Maximum displacement

\(E_{d}\) :

Damping energy

\(E_{D}\) :

The input energy to a single-degree-of-freedom (SDOF) system that will cause structural failure

\(\it {\text{E}}_{{\text{e}}}\) :

Elastic energy

\(E_{ep}\) :

Energy required to push a SDOF system with elasto-perfectly plastic behavior up to the maximum target deformation

\(E_{h}\) :

Hysteretic energy

\(E_{hi}\) :

Energy absorbed in the i-th story

\(E_{h_{r}}\) :

Hysteretic energy in the \(r\)-th mode of the MDOF system

\(E_{h}^{j} \left( {t_{1} } \right)\) :

Hysteretic energy demand in the \(j\)th story of the structure

\(\it \it E_{h\;\;\;\;\;\;_{r}}^{SDOF}\) :

Hysteretic energy in the SDOF system corresponding to \(r\)-th mode

\(E_{h}^{0.1g}\) :

Hysteretic energy corresponding to PGA = 0.1 g

\(E_{I}\) :

Input energy

\(E_{Ia}\) :

Absolute input energy

\(E_{Ir}\) :

Relative input energy

\(E_{I_{r}}\) :

Relative input energy in the \(r\)th mode of MDOF system

\(E_{I\;\;\;\;\;\;_{r}}^{ESDOF}\) :

Relative input energy in the ESDOF system corresponding to \(r\)-th mode of MDOF system

\(E_{I}^{0.1g}\) :

Input energy corresponding to PGA = 0.1 g

\(E_{I}^{*}\) :

Modified input energy

\(E_{k}\) :

Kinetic energy

\(E_{ka}\) :

Absolute kinetic energy

\(E_{kr}\) :

Relative kinetic energy

\(E_{p}\) :

Plastic deformation energy

\(E_{pi}\) :

Plastic deformation energyin i-th story

\(E_{s}\) :

Strain energy

\(E_{se}\) :

Elastic strain energy

\(f_{s}\) :

Damping, restoring force

\(f_{E}\) :

Elastic design input energy spectral shape

\(f_{T}\) :

A period factor

\(\overline{f}\) :

A factor accounting for the ductility and ground motion characteristics

\(F_{i}\) :

Equivalent inertia force at level \(i\)

\(F_{n}\) :

Modal force acting at story n

\(g\) :

Gravitational acceleration

\(h_{i}\) :

Height of beam level \(i\) from the ground

\(I_{A}\) :

Arias intensity index

\(I_{c}\) :

Earthquake intensity index

\(I_{e}\) :

Cumulative damage potential

\(k_{i}\) :

Stiffness of the i-th story

\(m\) :

Mass

\(M_{n}^{*}\) :

Effective modal mass of \(n\)-th mode

\(M_{pbi}\) :

Plastic moment of the beam at level \(i\)

\(M_{pc}\) :

Plastic moment of the columns at the base of the structure

\(n_{eq}\) :

Equivalent number of cycles

\(NE\) :

Normalized input energy

\(NE_{I,max,\zeta ,\mu }\) :

Normalized input energy in a structure with desired damping and ductility

\(NE_{I,max,\zeta = 0.02,\mu = 1}\) :

Normalized input energy in an elastic SDOF system with a damping ratio of 2%

\(p_{i}\) :

A parameter that indicates the amount of deviation of the shear of the i-th story from the optimal shear distribution

\(PGV\) :

Peak ground velocity

\(PGA\) :

Peak ground acceleration

\(R_{y}\) :

Yield strength reduction factor

\(S\) :

Soil profile coefficient

\(S_{v}\) :

Spectral pseudo-velocity response

\(S_{v_{max}}\) :

Maximum spectral pseudo-velocity response

\(S_{a}\) :

Spectral pseudo-acceleration response

\(S_{{a@S_{vmax} }}\) :

Spectral pseudo-acceleration response corresponding to \(S_{v_{max}}\)

\(t\) :

Time

\(t_{d}\) :

Duration of the earthquake

\(t_{e}\) :

Effective duration

\(t_{f}\) :

Duration of the earthquake based on the Trifunac–Brady method

\(T\) :

Natural period of the structure

\(T_{c}\) :

Characteristic period of the ground motion

\(T_{eq}\) :

Equivalent period

\(T_{g}\) :

Predominant period of the earthquake

\(u\) :

Relative displacement of system

\(\dot{u}\) :

Relative velocity of system

\(\ddot{u}\) :

Relative acceleration of system

\(u_{g}\) :

Base/ground displacement

\(\ddot{u}_{g}\) :

Base/ground acceleration

\(u_{t}\) :

Absolute (or total) displacement of system

\(V_{by}\) :

Yield base shear

\(V_{e}\) :

Maximum strength of the corresponding elastic system

\(V_{I}\) :

Input energy equivalent velocity

\(V_{Ia}\) :

Absolute input energy equivalent velocity

\(V_{Ir}\) :

Relative input energy equivalent velocity

\(V_{h}\) :

Hysteretic energy equivalent velocity

\(V_{y}\) :

Yield strength

\(w_{i}\) :

Weight of \(i\)th story

\(\alpha\) :

Ratio of damping energy to input energy

\(\alpha_{opt,i}\) :

The optimum yield shear coefficient of the i-th story

\(\overline{{\alpha_{i} }}\) :

The optimum yield-shear coefficient distribution of the i-th story

\(\overline{{{}_{r}^{ } \alpha_{i} }}\) :

Story-shear coefficient distribution

\(\gamma\) :

Energy factor

\(\gamma_{f}\) :

A non-dimensional parameter which controls the low-cycle fatigue effects

\(\zeta\) :

Damping ratio of the structure

\(\zeta_{eq}\) :

Equivalent damping

\(\eta_{p}\) :

Plastic energy modification factor

\(\theta_{p}\) :

The‏ ‏cumulative plastic rotation capacity of the beam

\(\lambda\) :

A parameter that characterizes the spectral shape of the input energy spectrum

\(\lambda_{d}\) :

Modification factor of input energy due to the damping

\(\mu\) :

Displacement ductility factor

\(\mu_{cum}\) :

Cumulative ductility

\(\tau\) :

A measure of the number of cycles of ground motion

\({\varphi }_{n,r}\) :

The i-th story value of the r-th mode shape

\(\psi\) :

Amplification factor of the seismic input energy equivalent velocity

\(\omega\) :

Angular frequency of oscillator

\(\Omega_{v}\) :

Amplification factor of the input energy spectrum

\(\Omega_{v}^{*}\) :

Peak amplification factor for the input energy spectrum

References

  1. SEAOC (1995) Performance-based seismic engineering of buildings. In: SEAOC, Sacramento, California

  2. BSL (2009) B.S.L., The building standard law of Japan

  3. Hudson D (1956) Response spectrum techniques in engineering seismology. In: Proceedings of the world conference on earthquake engineering. Berkeley

  4. Housner GW (1956) Limit design of structures to resist earthquakes. In: Proc. of 1st WCEE

  5. Housner GW (1959) Behavior of structures during earthquakes. J Eng Mech Div 85(4):109–130

    Article  Google Scholar 

  6. Tanabashi R (1656) Studies on the nonlinear vibrations of structures subjected to destructive earthquakes. In: Proceedings of the first world conference on earthquake engineering, Berkeley

  7. Housner GW (1960) The plastic failure of frame during earthquake. In: Proceedings of 2 WCEE, pp 997–1011

  8. Choi H, Kim J, Chung L (2006) Seismic design of buckling-restrained braced frames based on a modified energy-balance concept. Can J Civ Eng 33(10):1251–1260

    Article  Google Scholar 

  9. Leelataviwat S, Goel SC, Stojadinović B (2002) Energy-based seismic design of structures using yield mechanism and target drift. J Struct Eng 128(8):1046–1054

    Article  Google Scholar 

  10. Goertz C, Mollaioli F, Tesfamariam S (2017) Energy based seismic design of a timber core-wall multi-storey hybrid building. In: Proceedings of 16th world conference on earthquake engineering

  11. McKevitt W, Anderson D, Cherry S (1980) Hysteretic energy spectra in seismic design. In: Proceeding of the seventh world conference on earthquake engineering

  12. Zahrah TF, Hall WJ (1984) Earthquake energy absorption in SDOF structures. J Struct Eng 110(8):1757–1772

    Article  Google Scholar 

  13. Decanini LD, Mollaioli F (1998) Formulation of elastic earthquake input energy spectra. Earthq Eng Struct Dyn 27(12):1503–1522

    Article  Google Scholar 

  14. Khashaee P, Gross JL, Khashaee P, Lew HS, Mohraz B, Sadek F (2003) Distribution of earthquake input energy in structures. 2003: US Department of Commerce, National Institute of Standards and Technology

  15. Ye L, Cheng G, Qu X (2009) Study on energy based seismic design method and the application for steel braced frame structures. In: Sixth international conference on urban earthquake engineering, Tokyo Institute of Technology, pp 417–428

  16. Ucar T, Merter O (2021) Effect of kinematic hardening and ductility ratio on inelastic input energy spectra of near-fault ground motions. Energy-Based Seismic Engineering: Proceedings of IWEBSE 2021, p 117

  17. Uang C-M, Bertero VV (1988) Use of energy as a design criterion in earthquake-resistant design. Vol 88, Earthquake Engineering Research Center, University of California Berkeley

  18. Dasgupta P et al. (2004) Performance-based seismic design and behavior of a composite buckling restrained braced frame. In: Proceedings of the 13th world conference on earthquake engineering, Vancouver

  19. Fajfar P, Vidic T (1994) Consistent inelastic design spectra: hysteretic and input energy. Earthq Eng Struct Dyn 23(5):523–537

    Article  Google Scholar 

  20. Aliakbari F, Garivani S, Aghakouchak AA (2020) An energy based method for seismic design of frame structures equipped with metallic yielding dampers considering uniform inter-story drift concept. Eng Struct 205:110114

    Article  Google Scholar 

  21. Mezgebo MG (2015) Estimation of earthquake input energy, hysteretic energy and its distribution in MDOF structures

  22. Akiyama H (1985) Earthquake-resistant limit-state design for buildings. University of Tokyo Press

  23. Teran-Gilmore A (1996) Performance-based earthquake-resistant design of framed buildings using energy concepts. University of California, Berkeley

  24. Veletsos A, Newmark NM (1960) Effect of inelastic behavior on the response of simple systems to earthquake motions. Department of Civil Engineering, University of Illinois

  25. Veletsos A, Newmark N, Chelapati C (1965) Deformation spectra for elastic and elastoplastic systems subjected to ground shock and earthquake motions. In: Proceedings of the 3rd world conference on earthquake engineering

  26. Newmark N, Hall W (1982) Earthquake spectrum and design. EERI., Oakland

  27. Lee S-S, Goel S (2002) Performance-based design of steel moment frames using target drift and yield mechanism. Report No. UMCEE, pp 01–17

  28. Choi H, Kim J (2006) Energy-based seismic design of buckling-restrained braced frames using hysteretic energy spectrum. Eng Struct 28(2):304–311

    Article  Google Scholar 

  29. Kharmale SB, Ghosh S (2013) Performance-based plastic design of steel plate shear walls. J Constr Steel Res 90:85–97

    Article  Google Scholar 

  30. Leelataviwat S, Saewon W, Goel SC (2009) Application of energy balance concept in seismic evaluation of structures. J Struct Eng 135(2):113–121

    Article  Google Scholar 

  31. Uang CM, Bertero VV (1990) Evaluation of seismic energy in structures. Earthq Eng Struct Dyn 19(1):77–90

    Article  Google Scholar 

  32. Bruneau M, Wang N (1996) Some aspects of energy methods for the inelastic seismic response of ductile SDOF structures. Eng Struct 18(1):1–12

    Article  Google Scholar 

  33. Chopra AK (1995) Dynamics of structures: theory and applications to earthquake engineering. Prentice Hall

  34. Kalkan E, Kunnath SK (2007) Effective cyclic energy as a measure of seismic demand. J Earthq Eng 11(5):725–751

    Article  Google Scholar 

  35. Gong M-S, Xie L-L (2005) Study on comparison between absolute and relative input energy spectra and effects of ductility factor. Acta Seismol Sin 18(6):717–726

    Article  Google Scholar 

  36. Kalkan E, Kunnath SK (2008) Relevance of absolute and relative energy content in seismic evaluation of structures. Adv Struct Eng 11(1):17–34

    Article  Google Scholar 

  37. Choi H, Kim J (2009) Evaluation of seismic energy demand and its application on design of buckling-restrained braced frames. Struct Eng Mech 31(1):93–112

    Article  Google Scholar 

  38. Berg GV, Thomaides SS (1960) Energy consumption by structures in strong-motion earthquakes. In: Proceedings of the second world conference on earthquake engineering

  39. Goel SC, Berg GV (1968) Inelastic earthquakes response of tall steel frames. J Struct Div 94(8):1907–1934

    Article  Google Scholar 

  40. Teran-Gilmore A (1998) A parametric approach to performance-based numerical seismic design. Earthq Spectra 14(3):501–520

    Article  Google Scholar 

  41. Chapman MC (1999) On the use of elastic input energy for seismic hazard analysis. Earthq Spectra 15(4):607–635

    Article  Google Scholar 

  42. Takewaki I (2004) Bound of earthquake input energy. J Struct Eng 130(9):1289–1297

    Article  Google Scholar 

  43. Mahin SA, Lin J (1983) Construction of inelastic response spectra for single-degree-of-freedom systems. Earthquake Engineering Center, University of California, Berkeley

    Google Scholar 

  44. Kuwamura H, Galambos TV (1989) Earthquake load for structural reliability. J Struct Eng 115(6):1446–1462

    Article  Google Scholar 

  45. Fajfar P, Vidic T, Fischinger M (1992) On energy demand and supply in SDOF systems. In: Nonlinear seismic analysis and design of reinforced concrete buildings. CRC Press, pp 49–70

  46. Sucuoglu H, Nurtug A (1995) Earthquake ground motion characteristics and seismic energy dissipation. Earthq Eng Struct Dyn 24(9):1195–1213

  47. Riddell R, Garcia JE (2001) Hysteretic energy spectrum and damage control. Earthq Eng Struct Dyn 30(12):1791–1816

    Article  Google Scholar 

  48. Akbas B, Shen J (2003) Earthquake resistant design and energy concepts. Techn J Turk Chamber Civ Eng 14(2):2877–2901

  49. Lu S, Li S, Zhai C, Xie L (2013) Effects of hanging wall and footwall on demand of structural input energy during the 2008 Wenchuan earthquake. Earthq Eng Eng Vib 12(1):1–12

  50. Vahdani R, Gerami M, Vaseghi-Nia MA (2019) The spectra of relative input energy per unit mass of structure for iranian earthquakes. Int J Civ Eng 17(7):1183–1199

    Article  Google Scholar 

  51. Borekci H, Yalcin C, Yuksel E (2020) Experimental verification of inelastic energy demand spectrum using SDOF steel specimens on shaking table. In: Gulf conference on sustainable built environment. Springer

  52. Minami T, Osawa Y (1988) Elastic-plastic response spectra for different hysteretic rules. Earthq Eng Struct Dyn 16(4):555–568

    Article  Google Scholar 

  53. Akiyama H (1988) Earthquake resistant design based on the energy concept. In: Proceedings of 9th WCEE

  54. Nakashima M, Saburi K, Tsuji B (1996) Energy input and dissipation behaviour of structures with hysteretic dampers. Earthq Eng Struct Dyn 25(5):483–496

    Article  Google Scholar 

  55. Decanini LD, Mollaioli F (2001) An energy-based methodology for the assessment of seismic demand. Soil Dyn Earthq Eng 21(2):113–137

    Article  Google Scholar 

  56. Alici FS, Sucuoglu H (2018) Elastic and inelastic near-fault input energy spectra. Earthq Spectra 34(2):611–637

  57. Amiri GG, Darzi GA (2007) Damping effect on elastic input energy. In: Proceedings of the 4th international conference on earthquake geotechnical engineering. Thessaloniki: Greece

  58. Merter O, Ucar T (2018) An investigation of damping ratio effect on earthquake energy input. Usak Univ J Eng Sci 1(1):8–18

    Google Scholar 

  59. Thomaides SS (1964) Earthquake response of systems with bilinear hysteresis. J Struct Div 90(4):123–144

    Article  Google Scholar 

  60. Murphy M, Bycroft G (1956) The response of a nonlinear oscillator to an earthquake. Bull Seismol Soc Am 46(1):57–65

    Article  Google Scholar 

  61. Kato B, Akiyama H (1977) Earthquake resistant design for steel buildings. In: Proc. of the 6th WCEE

  62. Ucar T (2020) Computing input energy response of MDOF systems to actual ground motions based on modal contributions. Earthq Struct 18:263–273

    Google Scholar 

  63. Iwan W (1980) Estimating inelastic response spectra from elastic spectra. Earthq Eng Struct Dyn 8(4):375–388

    Article  Google Scholar 

  64. Hadjian A (1982) A re-evaluation of equivalent linear models for simple yielding systems. Earthq Eng Struct Dyn 10(6):759–767

    Article  Google Scholar 

  65. Kuwamura H, Galambos T (1988) Earthquake load effect for structural risk assessment. In: Proc. 9th world conference on earthquake Engrg

  66. Arias A (1970) A measure of earthquake intensity: seismic design for nuclear power plants. Massachusetts Institute of Technology

  67. Fajfar P, Vidic T, Fischinger M (1989) Seismic demand in medium-and long-period structures. Earthq Eng Struct Dyn 18(8):1133–1144

    Article  Google Scholar 

  68. Trifunac MD, Brady AG (1975) A study on the duration of strong earthquake ground motion. Bull Seismol Soc Am 65(3):581–626

    Google Scholar 

  69. Kuwamura H, Kirino Y, Akiyama H (1994) Prediction of earthquake energy input from smoothed Fourier amplitude spectrum. Earthq Eng Struct Dyn 23(10):1125–1137

    Article  Google Scholar 

  70. Ordaz M, Huerta B, Reinoso E (2003) Exact computation of input-energy spectra from Fourier amplitude spectra. Earthq Eng Struct Dyn 32(4):597–605

    Article  Google Scholar 

  71. Vidic T, Fajfar P (1994) Behaviour factors taking into account cumulative damage. In: Proceedings of tenth european conference on earthquake engineering. Vienna

  72. Chai Y, Fajfar P, Romstad K (1998) Formulation of duration-dependent inelastic seismic design spectrum. J Struct Eng 124(8):913–921

    Article  Google Scholar 

  73. Vidic T, Fajfar P, Fischinger M (1994) Consistent inelastic design spectra: strength and displacement. Earthq Eng Struct Dyn 23(5):507–521

    Article  Google Scholar 

  74. Manfredi G (2001) Evaluation of seismic energy demand. Earthq Eng Struct Dyn 30(4):485–499

    Article  Google Scholar 

  75. Kunnath S, Chai Y (2004) Cumulative damage-based inelastic cyclic demand spectrum. Earthq Eng Struct Dyn 33(4):499–520

    Article  Google Scholar 

  76. Chai Y, Fajfar P (2000) A procedure for estimating input energy spectra for seismic design. J Earthq Eng 4(04):539–561

    Article  Google Scholar 

  77. Joyner WB, Boore DM (1993) Methods for regression analysis of strong-motion data. Bull Seismol Soc Am 83(2):469–487

    Article  Google Scholar 

  78. Khashaee P (2005) Energy-based seismic design and damage assessment for structures. Southern Methodist University

  79. Park Y-J, Ang AH-S (1985) Mechanistic seismic damage model for reinforced concrete. J Struct Eng 111(4):722–739

    Article  Google Scholar 

  80. Teran-Gilmore A, Jirsa JO (2007) Energy demands for seismic design against low-cycle fatigue. Earthq Eng Struct Dyn 36(3):383–404

    Article  Google Scholar 

  81. Merter O (2019) An investigation on the maximum earthquake input energy for elastic SDOF systems. Earthq Struct 16(4):487–499

    Google Scholar 

  82. Chou CC, Uang CM (2003) A procedure for evaluating seismic energy demand of framed structures. Earthq Eng Struct Dyn 32(2):229–244

    Article  Google Scholar 

  83. Shen J, Akbas B (1999) Seismic energy demand in steel moment frames. J Earthq Eng 3(04):519–559

  84. Fajfar P, Gaspersic P (1996) The N2 method for the seismic damage analysis of RC buildings. Earthq Eng Struct Dyn 25(1):31–46

  85. Akbas B, Shen J, Temiz H (2006) Identifying the hysteretic energy demand and distribution in regular steel frames. Steel Compos Struct 6(6):479

    Article  Google Scholar 

  86. Mezgebo MG, Lui EM (2017) A new methodology for energy-based seismic design of steel moment frames. Earthq Eng Eng Vib 16(1):131–152

    Article  Google Scholar 

  87. Decanini L, Mollaioli F, Mura A (2001) On the characterization of inelastic input energy spectra. Department of Structural and Geotechnical Engineering, University of Rome La Sapienza

  88. Dindar AA, Yalçın C, Yüksel E, Özkaynak H, Büyüköztürk O (2015) Development of earthquake energy demand spectra. Earthq Spectra 31(3):1667–1689

  89. Alici F, Sucuoglu H (2016) Prediction of input energy spectrum: attenuation models and velocity spectrum scaling. Earthq Eng Struct Dyn 45(13):2137–2161

  90. Akkar S, Bommer JJ (2007) Empirical prediction equations for peak ground velocity derived from strong-motion records from Europe and the Middle East. Bull Seismol Soc Am 97(2):511–530

    Article  Google Scholar 

  91. Akkar S, Bommer JJ (2007) Prediction of elastic displacement response spectra in Europe and the Middle East. Earthq Eng Struct Dyn 36(10):1275–1301

    Article  Google Scholar 

  92. Gullu A, Yuksel E, Yalcin C, Anıl Dindar A, Ozkaynak H, Buyukozturk O (2019) An improved input energy spectrum verified by the shake table tests. Earthq Eng Struct Dyn 48(1):27–45

  93. Akiyama H (1999) Earthquake-resistant design method for buildings based on energy balance. Gihodo Shuppan, Tokyo, pp 25–26

    Google Scholar 

  94. López-Almansa F, Yazgan AU, Benavent-Climent A (2013) Design energy input spectra for high seismicity regions based on Turkish registers. Bull Earthq Eng 11(4):885–912

    Article  Google Scholar 

  95. Ghodrati Amiri G, Darzi GA, Vaseghi Amiri J (2008) Design elastic input energy spectra based on Iranian earthquakes. Can J Civ Eng 35(6):635–646

    Article  Google Scholar 

  96. Benavent-Climent A, Pujades L, López-Almansa F (2002) Design energy input spectra for moderate-seismicity regions. Earthq Eng Struct Dyn 31(5):1151–1172

    Article  Google Scholar 

  97. Benavent-Climent A, López-Almansa F, Bravo-González DA (2010) Design energy input spectra for moderate-to-high seismicity regions based on Colombian earthquakes. Soil Dyn Earthq Eng 30(11):1129–1148

    Article  Google Scholar 

  98. Tselentis G, Danciu L, Sokos E (2010) Probabilistic seismic hazard assessment in Greece-Part 2: acceleration response spectra and elastic input energy spectra. Nat Hazard 10(1):41–49

    Article  Google Scholar 

  99. Quinde P, Reinoso E, Terán-Gilmore A (2016) Inelastic seismic energy spectra for soft soils: application to Mexico City. Soil Dyn Earthq Eng 89:198–207

    Article  Google Scholar 

  100. Mezgebo MG, Lui EM (2016) Hysteresis and soil site dependent input and hysteretic energy spectra for far-source ground motions. Adv Civ Eng 2016

  101. Lawson R, Krawinkler H (1995) Cumulative damage potential of seismic ground motion. In: Proceedings of the 10th European conference on, earthquake engineering

  102. Akbas B (1997) Energy-based earthquake resistant design of steel moment resisting frames. Department of Civil and Architectural Engineering, Illinois Institute of Technology

  103. Arroyo D, Ordaz M (2007) On the estimation of hysteretic energy demands for SDOF systems. Earthq Eng Struct Dyn 36(15):2365–2382

    Article  Google Scholar 

  104. Li HN, Wang F, Lu ZH (2007) Estimation of hysteretic energy of MDOF structures based on equivalent SDOF systems. In: Key engineering materials. Trans Tech Publ

  105. Akbas B (2006) A neural network model to assess the hysteretic energy demand in steel moment resisting frames. Struct Eng Mech 23(2):177–193

    Article  Google Scholar 

  106. Gandomi AH, Alavi AH, Asghari A, Niroomand H, Nazar AM (2014) An innovative approach for modeling of hysteretic energy demand in steel moment resisting frames. Neural Comput Appl 24(6):1285–1291

  107. Benavent-Climent A, Zahran R (2010) An energy-based procedure for the assessment of seismic capacity of existing frames: application to RC wide beam systems in Spain. Soil Dyn Earthq Eng 30(5):354–367

    Article  Google Scholar 

  108. Estes KR, Anderson JC (2004) Earthquake resistant design using hysteretic energy demands for low rise buildings. In: Proceedings of the 13th world conference on earthquake engineering

  109. Erberik MA, Azizi M (2021) Spatial distribution of hysteretic energy in reinforced concrete moment resisting frames. Energy-Based Seismic Engineering: Proceedings of IWEBSE 2021, p 47

  110. Fajfar P, Fischinger M (1988) N2-A method for non-linear seismic analysis of regular buildings. In: Proceedings of the ninth world conference in earthquake engineering

  111. Seneviratna G, Krawinkler H (1997) Evaluation of inelastic MDOF effects for seismic design. The John A. Blume Earthquake Engineering Center. Report

  112. Harada Y, Akiyama H (1998) Seismic design of flexible-stiff mixed frame with energy concentration. Eng Struct 20(12):1039–1044

    Article  Google Scholar 

  113. Akbas B, Shen J, Hao H (2001) Energy appproach in peformance-based seismic design of steel moment resisting frames for basic safety objective. Struct Design Tall Build 10(3):193–217

    Article  Google Scholar 

  114. Estes K, Anderson J (2002) Hysteretic energy demands in multistory buildings. In: Seventh US national conference on earthquake engineering, Boston, Massachusetts

  115. Benavent-Climent A, Zahran R (2010) Seismic evaluation of existing RC frames with wide beams using an energy-based approach. Earthq Struct 1(1):93–108

    Article  Google Scholar 

  116. Wang F, Yi T (2012) A methodology for estimating seismic hysteretic energy of buildings. In: ASCE 2012 international conference on civil engineering and urban planning

  117. Wang F, Zhang N, Huang Z (2016) Estimation of earthquake induced story hysteretic energy of multi-Story buildings. Earthq Struct 11(1):165–178

    Article  Google Scholar 

  118. Benavent-Climent A, Donaire-Ávila J, Mollaioli F (2021) Key Points and Pending Issues in the Energy-Based Seismic Design Approach. Energy-Based Seismic Engineering: Proceedings of IWEBSE 2021, p 151

  119. Kato B, Akiyama H (1982) Seismic design of steel buildings. J Struct Div 108(8):1709–1721

    Article  Google Scholar 

  120. Leelataviwat S, Goel S, Stojadinovic B (1988) Drift and yield mechanism based seismic design and upgrading of steel moment frames, vol 98. University of Michigan

  121. Leelataviwat S, Goel SC, Stojadinovic BI (1999) Toward performance-based seismic design of structures. Earthq Spectra 15(3):435–461

    Article  Google Scholar 

  122. Kim J, Choi H, Chung L (2004) Energy-based seismic design of structures with buckling-restrained braces. Steel Compos Struct 4(6):437–452

    Article  Google Scholar 

  123. Benavent-Climent A (2011) An energy-based method for seismic retrofit of existing frames using hysteretic dampers. Soil Dyn Earthq Eng 31(10):1385–1396

    Article  Google Scholar 

  124. Ye L, Cheng G, Qu Z, Lu X (2012) Study on energy-based seismic design method and application on steel braced frame structures. Jianzhu Jiegou Xuebao J Build Struct 33(11):36–45

  125. Liao W-C, Goel SC (2012) Performance-based plastic design and energy-based evaluation of seismic resistant RC moment frame. J Mar Sci Technol 20(3):304–310

    Article  Google Scholar 

  126. Lee S, Goel S, Chao S (2004) Performance-based seismic design of steel moment frame using target drift and yield mechanism. In: Proceedings of 13th World Conference on Earthquake Engneering. Vancouver, Canada

  127. Terapathana S (2012) An energy method for earthquake resistant design of RC structures. University of Southern California Los Angeles

  128. Merter O, Ucar T (2014) Design of RC frames for pre-selected collapse mechanism and target displacement using energy–balance. Sadhana 39(3):637–657

    Article  Google Scholar 

  129. Goertz C (2016) Energy based seismic design of a multi-storey hybrid building: timber-steel core walls. University of British Columbia

  130. Benavent-Climent A, Mota-Páez S (2017) Earthquake retrofitting of R/C frames with soft first story using hysteretic dampers: energy-based design method and evaluation. Eng Struct 137:19–32

    Article  Google Scholar 

  131. Merter O, Ucar T (2017) Energy-based design base shear for RC frames considering global failure mechanism and reduced hysteretic behavior. Struct Eng Mech 63(1):23–35

    Google Scholar 

  132. Guo W, Du Q, Huang Z, Gou H, Xie X, Li Y (2020) An improved equivalent energy-based design procedure for seismic isolation system of simply supported bridge in China’s high-speed railway. Soil Dyn Earthq Eng 134:106161

  133. Rezazadeh F, Talatahari S (2020) Seismic energy-based design of BRB frames using multi-objective vibrating particles system optimization. Structures 24:227–239

    Article  Google Scholar 

  134. Nabid N, Hajirasouliha I, Margarit DE, Petkovski M (2020) Optimum energy based seismic design of friction dampers in RC structures. Structures 27:2550–2562

Download references

Funding

Not applicable.

Author information

Authors and Affiliations

  1. Faculty of Engineering, University of Bojnord, Bojnord, 94531-55111, Iran

    Narges Gholami, Sadegh Garivani & Seyed Saeed Askariani

Authors
  1. Narges Gholami
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sadegh Garivani
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Seyed Saeed Askariani
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sadegh Garivani.

Ethics declarations

Conflict of interest

The authors have no relevant financial or non-financial interests to disclose.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gholami, N., Garivani, S. & Askariani, S.S. State-of-the-Art Review of Energy-Based Seismic Design Methods. Arch Computat Methods Eng 29, 1965–1996 (2022). https://doi.org/10.1007/s11831-021-09645-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11831-021-09645-z

search

Navigation