Bulletin of Earthquake Engineering

, Volume 17, Issue 7, pp 4115–4139 | Cite as

Self-similar interstory drift spectrum and response distribution of flexural-shear beam with nonuniform lateral stiffness

  • Guiqiang Guo
  • Xi Chen
  • Dixiong YangEmail author
  • Yunhe Liu
Original Research


This paper proposes the concept of self-similar interstory drift spectrum based on the dimensional analysis of flexural-shear beam with nonuniform lateral stiffness, and scrutinizes the effects of lateral stiffness reduction on the seismic responses and response distribution. Firstly, the finite element formulation for the combined beam is established, which is convenient for parametric analysis. Subsequently, the intrinsic length scale and time scale are proposed to conduct correctly the dimensional analysis for seismic responses of flexural-shear beam, indicating that the normalized maximum interstory drift ratio and normalized maximum floor acceleration present a complete similarity in the normalized building height and the beauty of order. Hence, the concept of self-similar interstory drift spectrum is suggested to avoid the use of empirical relationship between fundamental period and building height. Moreover, the effects of lateral stiffness reduction on the normalized responses and response distribution of flexural-shear beam are examined under the idealized pulses and near-fault ground motions. With the exception of significant stiffness reduction, the effect of lateral stiffness reduction is generally small. In particular, the vertical distribution of interstory drift mainly depends on the structural type, whereas the floor acceleration generally increases along the building height. Finally, the established regression model can sufficiently fit the mean self-similar interstory drift spectrum and mean self-similar floor acceleration spectrum, and the normalized seismic responses can be well predicted by the fitted curves.


Flexural-shear beam Nonuniform lateral stiffness Dimensional analysis Intrinsic length scale and time scale Self-similar interstory drift spectrum Near-fault ground motions 



The supports of the National Natural Science Foundation of China (Grant Nos. 51478086 and 11772079), and the Open Foundation of State Key Laboratory of Disaster Reduction in Civil Engineering (Grant No. SLDRCE17-03) are much appreciated. Also, the authors thank Dr. Andrés Alonso-Rodríguez for providing us the MATLAB code of the closed-form solution for the flexural-shear beam with nonuniform lateral stiffness along the height.


  1. Alavi B, Krawinkler H (2004a) Behavior of moment-resisting frame structures subjected to near-fault ground motions. Earthq Eng Struct Dyn 33(6):687–706CrossRefGoogle Scholar
  2. Alavi B, Krawinkler H (2004b) Strengthening of moment-resisting frame structures against near-fault ground motion effects. Earthq Eng Struct Dyn 33(6):707–722CrossRefGoogle Scholar
  3. Alonso-Rodríguez A, Miranda E (2015) Assessment of building behavior under near-fault pulse-like ground motions through simplified models. Soil Dyn Earthq Eng 79:47–58CrossRefGoogle Scholar
  4. Alonso-Rodríguez A, Miranda E (2016) Dynamic behavior of buildings with non-uniform stiffness along their height assessed through coupled flexural and shear beams. Bull Earthq Eng 14(12):3463–3483CrossRefGoogle Scholar
  5. Barenblatt GI (1996) Scaling, self-similarity, and intermediate asymptotics. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  6. Bertero VV, Mahin SA, Herrera RA (1978) Aseismic design implications of near-fault San Fernando earthquake records. Earthq Eng Struct Dyn 6(1):31–42CrossRefGoogle Scholar
  7. Bray JD, Rodriguez-Marek A (2004) Characterization of forward-directivity ground motions in the near-fault region. Soil Dyn Earthq Eng 24(11):815–828CrossRefGoogle Scholar
  8. Burks LS, Baker JW (2016) A predictive model for fling-step in near-fault ground motions based on recordings and simulations. Soil Dyn Earthq Eng 80:119–126CrossRefGoogle Scholar
  9. Cao YN, Meza-Fajardo KC, Mavroeidis GP, Papageorgiou AS (2016) Effects of wave passage on torsional response of symmetric buildings subjected to near-fault pulse-like ground motions. Soil Dyn Earthq Eng 88:109–123CrossRefGoogle Scholar
  10. Cao YN, Mavroeidis GP, Meza-Fajardo KC, Papageorgiou AS (2017) Accidental eccentricity in symmetric buildings due to wave passage effects arising from near-fault pulse-like ground motions. Earthq Eng Struct Dyn 46(13):2185–2207CrossRefGoogle Scholar
  11. Chopra AK (2012) Dynamics of structures: theory and applications to earthquake engineering, 4th edn. Prentice Hall, Upper Saddle RiverGoogle Scholar
  12. Chopra AK, Chintanapakdee C (2001) Drift spectrum vs modal analysis of structural response to near-fault ground motions. Earthq Spectra 17(2):221–234CrossRefGoogle Scholar
  13. Clough RW, Penzien J (2003) Dynamics of structures, 3rd edn. Computers and Structures Inc., BerkeleyGoogle Scholar
  14. Cork TG, Kim JH, Mavroeidis GP, Kim JK, Halldorsson B, Papageorgiou AS (2016) Effects of tectonic regime and soil conditions on the pulse period of near-fault ground motions. Soil Dyn Earthq Eng 80:102–118CrossRefGoogle Scholar
  15. Crozet V, Politopoulos I, Yang MG, Martinez JM, Erlicher S (2018) Sensitivity analysis of pounding between adjacent structures. Earthq Eng Struct Dyn 47(1):219–235CrossRefGoogle Scholar
  16. Dickinson BW, Gavin HP (2011) Parametric statistical generalization of uniform-hazard earthquake ground motions. J Struct Eng 137(3):410–422CrossRefGoogle Scholar
  17. Dimitrakopoulos EG, Kappos AJ, Makris N (2009) Dimensional analysis of yielding and pounding structures for records without distinct pulses. Soil Dyn Earthq Eng 29(7):1170–1180CrossRefGoogle Scholar
  18. Dimitrakopoulos EG, Makris N, Kappos AJ (2011) Dimensional analysis of the earthquake-induced pounding between inelastic structures. Bull Earthq Eng 9(2):561–579CrossRefGoogle Scholar
  19. Guo GQ, Yang DX, Liu YH (2018) Duration effect of near-fault pulse-like ground motions and identification of most suitable duration measure. Bull Earthq Eng 16(11):5095–5119CrossRefGoogle Scholar
  20. He WL, Agrawal AK (2008) Analytical model of ground motion pulses for the design and assessment of seismic protective systems. J Struct Eng 134(7):229–230CrossRefGoogle Scholar
  21. Iwan WD (1997) Drift spectrum: measure of demand for earthquake ground motions. J Struct Eng 123(4):397–404CrossRefGoogle Scholar
  22. Kalkan E, Kunnath SK (2006) Effects of fling step and forward directivity on seismic response of buildings. Earthq Spectra 22(2):367–390CrossRefGoogle Scholar
  23. Karavasilis TL, Makris N, Bazeos N, Beskos DE (2010) Dimensional response analysis of multistory regular steel MRF subjected to pulselike earthquake ground motions. J Struct Eng 136(8):921–932CrossRefGoogle Scholar
  24. Karavasilis TL, Seo CY, Makris N (2011) Dimensional response analysis of bilinear systems subjected to non-pulselike earthquake ground motions. J Struct Eng 137(5):600–606CrossRefGoogle Scholar
  25. Khaloo AR, Khosravi H (2008) Multi-mode response of shear and flexural buildings to pulse-type ground motions in near-field earthquakes. J Earthq Eng 12(4):616–630CrossRefGoogle Scholar
  26. Liossatou E, Fardis MN (2016) Near-fault effects on residual displacements of RC structures. Earthq Eng Struct Dyn 45(9):1391–1409CrossRefGoogle Scholar
  27. Macrae GA, Kimura Y, Roeder C (2004) Effect of column stiffness on braced frame seismic behavior. J Struct Eng 130(3):381–391CrossRefGoogle Scholar
  28. Makris N, Black CJ (2004a) Dimensional analysis of rigid-plastic and elastoplastic structures under pulse-type excitations. J Eng Mech 130(9):1006–1018CrossRefGoogle Scholar
  29. Makris N, Black CJ (2004b) Dimensional analysis of bilinear oscillators under pulse-type excitations. J Eng Mech 130(9):1019–1031CrossRefGoogle Scholar
  30. Makris N, Psychogios T (2006) Dimensional response analysis of yielding structures with first-mode dominated response. Earthq Eng Struct Dyn 35(10):1203–1224CrossRefGoogle Scholar
  31. Makris N, Vassiliou MF (2011) The existence of ‘complete similarities’ in the response of seismic isolated structures subjected to pulse-like ground motions and their implications in analysis. Earthq Eng Struct Dyn 40(10):1103–1121CrossRefGoogle Scholar
  32. Mavroeidis GP, Papageorgiou AS (2003) A mathematical representation of near-fault ground motions. Bull Seismol Soc Am 93(3):1099–1131CrossRefGoogle Scholar
  33. Mavroeidis GP, Dong G, Papageorgiou AS (2004) Near-fault ground motions and the response of elastic and inelastic single-degree-of-freedom (SDOF) systems. Earthq Eng Struct Dyn 33(9):1023–1049CrossRefGoogle Scholar
  34. Meza-Fajardo KC, Papageorgiou AS (2017) Residual slip of sliding blocks induced by near-fault ground motions. Earthq Eng Struct Dyn 46(7):1043–1220CrossRefGoogle Scholar
  35. Miranda E (1999) Approximate seismic lateral deformation demands in multistory buildings. J Struct Eng 125(4):417–425CrossRefGoogle Scholar
  36. Miranda E, Akkar SD (2006) Generalized interstory drift spectrum. J Struct Eng 132(6):840–852CrossRefGoogle Scholar
  37. Miranda E, Reyes CJ (2002) Approximate lateral drift demands in multistory buildings with nonuniform stiffness. J Struct Eng 128(7):840–849CrossRefGoogle Scholar
  38. Miranda E, Taghavi S (2005) Approximate floor acceleration demands in multistory buildings. I: formulation. J Struct Eng 131(2):203–211CrossRefGoogle Scholar
  39. Neam AS, Taghikhany T (2016) Prediction equations for generalized interstory drift spectrum considering near-fault ground motions. Nat Hazards 80(3):1443–1473CrossRefGoogle Scholar
  40. Nikfar F, Konstantinidis D (2017) Effect of the stick-slip phenomenon on the sliding response of objects subjected to pulse excitation. J Eng Mech 143(4):04016122CrossRefGoogle Scholar
  41. Pan P, Wu SJ, Nie X (2015) A distributed parameter model of a frame pin-supported wall structure. Earthq Eng Struct Dyn 44(10):1643–1659CrossRefGoogle Scholar
  42. Pitilakis D, Makris N (2010) A study on the effects of the foundation compliance on the response of yielding structures using dimensional analysis. Bull Earthq Eng 8(6):1497–1514CrossRefGoogle Scholar
  43. Shu Z, Ma RL, He MJ (2016) Dimensional analysis of the slotted bolted connections against impulsive earthquake ground motions. J Constr Steel Res 125:128–141CrossRefGoogle Scholar
  44. Sun TS, Kurama YC, Zhang PZ, Ou JP (2018) Linear-elastic lateral load analysis and seismic design of pin-supported wall-frame structures with yielding dampers. Earthq Eng Struct Dyn 47(4):988–1013CrossRefGoogle Scholar
  45. Tang YC, Zhang J (2011) Response spectrum-oriented pulse identification and magnitude scaling of forward directivity pulses in near-fault ground motions. Soil Dyn Earthq Eng 31(1):59–76CrossRefGoogle Scholar
  46. Tothong P, Cornell CA (2008) Structural performance assessment under near-source pulse-like ground motions using advanced ground motion intensity measures. Earthq Eng Struct Dyn 37(37):1013–1037CrossRefGoogle Scholar
  47. Vafaei D, Eskandari R (2015) Seismic response of mega buckling-restrained braces subjected to fling-step and forward-directivity near-fault ground motions. Struct Des Tall Spec 24(9):672–686CrossRefGoogle Scholar
  48. Vassiliou MF, Makris N (2011) Estimating time scales and length scales in pulselike earthquake acceleration records with wavelet analysis. Bull Seismol Soc Am 101(2):596–618CrossRefGoogle Scholar
  49. Wu DY, Zhao B, Lu XL (2018) Dynamic behavior of upgraded rocking wall-moment frames using an extended coupled-two-beam model. Soil Dyn Earthq Eng 115:365–377CrossRefGoogle Scholar
  50. Xie YZ, Zhang J, Xi W (2018) Effectiveness evaluation and optimal design of nonlinear viscous dampers for inelastic structures under pulse-type ground motions. Earthq Eng Struct Dyn 47(14):2802–2820CrossRefGoogle Scholar
  51. Yang DX, Pan JW, Li G (2010) Interstory drift ratio of building structures subjected to near-fault ground motions based on generalized drift spectral analysis. Soil Dyn Earthq Eng 30(11):1182–1197CrossRefGoogle Scholar
  52. Yang DX, Guo GQ, Liu YH, Zhang JF (2019) Dimensional response analysis of bilinear SDOF systems under near-fault ground motions with intrinsic length scale. Soil Dyn Earthq Eng 116:397–408CrossRefGoogle Scholar
  53. Yazdani Y, Alembagheri M (2017) Nonlinear seismic response of a gravity dam under near-fault ground motions and equivalent pulses. Soil Dyn Earthq Eng 92:621–632CrossRefGoogle Scholar
  54. Zhai CH, Jiang S, Chen ZQ (2015) Dimensional analysis of the pounding response of an oscillator considering contact duration. J Eng Mech 141(4):04014138CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering MechanicsDalian University of TechnologyDalianChina
  2. 2.State Key Laboratory of Eco-Hydraulics in Northwest Arid Region of China, School of Civil Engineering and ArchitectureXi’an University of TechnologyXi’anChina

Personalised recommendations