Modelling of Structural Pounding

  • Robert JankowskiEmail author
  • Sayed Mahmoud
Part of the GeoPlanet: Earth and Planetary Sciences book series (GEPS)


Modelling of earthquake-induced pounding between buildings, or bridge segments, requires the use of accurate structural models as well as appropriate models of the effects of collisions. Two different approaches can be found in the literature, which are usually used to simulate structural pounding during ground motions. The first approach considers the classical theory of impact, which is based on the laws of conservation of energy and momentum and does not consider stresses and deformations in the colliding structural elements during impact. Since this is not a force-based approach, the effect of collisions is accounted through updating the velocities of the considered bodies or structural elements. In the second approach, the earthquake-induced structural pounding is simulated using the direct model of impact force during collision.


Root Mean Square Error Ground Motion Force Model Elastic Model Viscoelastic Model 
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  1. Anagnostopoulos, S.A.: Pounding of buildings in series during earthquakes. Earthquake Eng. Struct. Dynam. 16, 443–456 (1988)CrossRefGoogle Scholar
  2. Anagnostopoulos S.A.: Earthquake induced pounding: state of the art. In: Proceedings of 10th European Conference on Earthquake Engineering, Vienna, Austria, 28 Aug–2 Sept 1994. pp. 897–905, Balkema, Rotterdam (1995)Google Scholar
  3. Anagnostopoulos, S.A.: Building pounding re-examined: how serious a problem is it? In: Eleventh World Conference on Earthquake Engineering, Acapulco, Mexico, Paper No. 2108, 23–28 June 1996Google Scholar
  4. Anagnostopoulos, S.A.: Equivalent viscous damping for modeling inelastic impacts in earthquake pounding problems. Earthquake Eng. Struct. Dynam. 33, 897–902 (2004)CrossRefGoogle Scholar
  5. Anagnostopoulos, S.A., Spiliopoulos, K.V.: An investigation of earthquake induced pounding between adjacent buildings. Earthquake Eng. Struct. Dynam. 21, 289–302 (1992)CrossRefGoogle Scholar
  6. Azevedo, J., Bento, R.: Design criteria for buildings subjected to pounding. In: Eleventh World Conference on Earthquake Engineering, Acapulco, Mexico, Paper No. 1063, 23–28 June 1996Google Scholar
  7. Bathe, K.J.: Finite Element Procedures in Engineering Analysis. Prentice-Hall, Englewood Cliffs (1982)Google Scholar
  8. Bendat, J.S., Piersol, A.G.: Random Data: Analysis and Measurement Procedures. Wiley, New York (1971)Google Scholar
  9. Chau, K.T., Wei, X.X.: Pounding of structures modelled as non-linear impacts of two oscillators. Earthquake Eng. Struct. Dynam. 30, 633–651 (2001)CrossRefGoogle Scholar
  10. Chau, K.T., Wei, X.X., Guo, X., Shen, C.Y.: Experimental and theoretical simulations of seismic poundings between two adjacent structures. Earthquake Eng. Struct. Dynam. 32, 537–554 (2003)CrossRefGoogle Scholar
  11. Chopra, A.K.: Dynamics of Structures: Theory and Applications to Earthquake Engineering. Prentice-Hall, Englewood Cliffs (1995)Google Scholar
  12. Crook, A.W.: A study on some impacts between metal bodies by a piezoelectric method. Proc. Roy. Soc. A 212, 377–390 (1952)CrossRefGoogle Scholar
  13. Davis, R.O.: Pounding of buildings modelled by an impact oscillator. Earthquake Eng. Struct. Dynam. 21, 253–274 (1992)CrossRefGoogle Scholar
  14. DesRoches, R., Muthukumar, S.: Effect of pounding and restrainers on seismic response of multiple-frame bridges. J. Struct. Eng. 128, 860–869 (2002)CrossRefGoogle Scholar
  15. Falborski, T., Jankowski, R.: Polymeric bearings—a new base isolation system to reduce structural damage during earthquakes. Key Eng. Mater. 569–570, 143–150 (2013)CrossRefGoogle Scholar
  16. Filiatrault, A., Wagner, P., Cherry, S.: Analytical prediction of experimental building pounding. Earthquake Eng. Struct. Dynam. 24, 1131–1154 (1995)CrossRefGoogle Scholar
  17. Goland, M., Wickersham, P.D., Dengler, M.A.: Propagation of elastic impact in beams in bending. J. Appl. Mech. 22, 1–7 (1955)Google Scholar
  18. Goldsmith, W.: Impact: The Theory and Physical Behaviour of Colliding Solids. Edward Arnold, London (1960)Google Scholar
  19. Harris, C.M., Piersol, A.G.: Harris’ Shock and Vibration Handbook. McGraw-Hill, New York (2002)Google Scholar
  20. Hertz, H.: Über die Berührung fester elastischer Körper (On the contact of elastic solids). J. für die Reine und Angewandte Mathematik 29, 156–171 (1882). (in German)Google Scholar
  21. Hunt, K.H., Crossley, F.R.E.: Coefficient of restitution interpreted as damping in vibroimpact. J. Appl. Mech. ASME 42, 440–445 (1975)CrossRefGoogle Scholar
  22. Jankowski, R.: Impact force spectrum for damage assessment of earthquake-induced structural pounding. Key Eng. Mater. 293–294, 711–718 (2005a)CrossRefGoogle Scholar
  23. Jankowski, R.: Non-linear viscoelastic modelling of earthquake-induced structural pounding. Earthquake Eng. Struct. Dynam. 34, 595–611 (2005b)CrossRefGoogle Scholar
  24. Jankowski, R.: Analytical expression between the impact damping ratio and the coefficient of restitution in the non-linear viscoelastic model of structural pounding. Earthquake Eng. Struct. Dynam. 35, 517–524 (2006a)CrossRefGoogle Scholar
  25. Jankowski, R.: Pounding force response spectrum under earthquake excitation. Eng. Struct. 28, 1149–1161 (2006b)CrossRefGoogle Scholar
  26. Jankowski, R.: Assessment of damage due to earthquake-induced pounding between the main building and the stairway tower. Key Eng. Mater. 347, 339–344 (2007a)Google Scholar
  27. Jankowski, R.: Non-linear analysis of pounding-involved response of equal height buildings under earthquake excitation. DSc dissertation, Wydawnictwo Politechniki Gdańskiej, Gdańsk, Poland (2007b)Google Scholar
  28. Jankowski, R.: Earthquake-induced pounding between equal height buildings with substantially different dynamic properties. Eng. Struct. 30(10), 2818–2829 (2008)CrossRefGoogle Scholar
  29. Jankowski, R.: Experimental study on earthquake-induced pounding between structural elements made of different building materials. Earthquake Eng. Struct. Dynam. 39, 343–354 (2010)Google Scholar
  30. Jankowski, R., Wilde, K., Fujino, Y.: Pounding of superstructure segments in isolated elevated bridge during earthquakes. Earthquake Eng. Struct. Dynam. 27, 487–502 (1998)CrossRefGoogle Scholar
  31. Jing, H.-S., Young, M.: Impact interactions between two vibration systems under random excitation. Earthquake Eng. Struct. Dynam. 20, 667–681 (1991)CrossRefGoogle Scholar
  32. Karayannis, C.G., Favvata, M.J.: Earthquake-induced interaction between adjacent reinforced concrete structures with non-equal heights. Earthquake Eng. Struct. Dynam. 34, 1–20 (2005)CrossRefGoogle Scholar
  33. Kim, S.-H., Shinozuka, M.: Effects of seismically induced pounding at expansion joints of concrete bridges. J. Eng. Mech. 129, 1225–1234 (2003)CrossRefGoogle Scholar
  34. Komodromos, P., Polycarpou, P.C., Papaloizou, L., Phocas, M.C.: Response of seismically isolated buildings considering poundings. Earthquake Eng. Struct. Dynam. 36, 1605–1622 (2007)CrossRefGoogle Scholar
  35. Lankarani, H.M., Nikravesh, P.E.: A contact force model with hysteresis damping for impact analysis of multibody systems. J. Mech. Design ASME 112, 369–376 (1990)CrossRefGoogle Scholar
  36. Lankarani, H.M., Nikravesh, P.E.: Continuous contact force models for impact analysis in multibody systems. Nonlinear Dyn. 5, 193–207 (1994)Google Scholar
  37. Leibovich, E., Rutenberg, A., Yankelevsky, D.Z.: On eccentric seismic pounding of symmetric buildings. Earthquake Eng. Struct. Dynam. 25, 219–233 (1996)CrossRefGoogle Scholar
  38. Mahmoud, S., Abd-Elhamed, A., Jankowski, R.: Earthquake-induced pounding between equal height multi-storey buildings considering soil-structure interaction. Bull. Earthq. Eng. 11(4), 1021–1048 (2013)CrossRefGoogle Scholar
  39. Mahmoud, S., Austrell, P.-E., Jankowski, R.: Simulation of the response of base-isolated buildings under earthquake excitations considering soil flexibility. Earthq. Eng. Eng. Vibr. 11, 359–374 (2012)CrossRefGoogle Scholar
  40. Mahmoud, S., Chen, X., Jankowski, R.: Structural pounding models with Hertz spring and nonlinear damper. J. Appl. Sci. 8, 1850–1858 (2008)CrossRefGoogle Scholar
  41. Mahmoud, S., Jankowski, R.: Elastic and inelastic multi-storey buildings under earthquake excitation with the effect of pounding. J. Appl. Sci. 9(18), 3250–3262 (2009)CrossRefGoogle Scholar
  42. Mahmoud, S., Jankowski, R.: Pounding-involved response of isolated and non-isolated buildings under earthquake excitation. Earthq. Struct. 1(3), 231–252 (2010)CrossRefGoogle Scholar
  43. Mahmoud, S., Jankowski, R.: Modified linear viscoelastic model of earthquake-induced structural pounding. Iran. J. Sci. Technol. 35(C1), 51–62 (2011)Google Scholar
  44. Maison, B.F., Kasai, K.: Analysis for type of structural pounding. J. Struct. Eng. 116, 957–977 (1990)CrossRefGoogle Scholar
  45. Maison, B.F., Kasai, K.: Dynamics of pounding when two buildings collide. Earthquake Eng. Struct. Dynam. 21, 771–786 (1992)CrossRefGoogle Scholar
  46. Marhefka, D.W., Orin, D.E.: A compliant contact model with nonlinear damping for simulation of robotic systems. IEEE Trans. Syst. Man Cyber. Part A Syst. Hum. 29, 566–572 (1999)CrossRefGoogle Scholar
  47. Muthukumar, S., DesRoches, R.: A Hertz contact model with nonlinear damping for pounding simulation. Earthquake Eng. Struct. Dynam. 35, 811–828 (2006)CrossRefGoogle Scholar
  48. Newmark, N.: A method of computation for structural dynamics. J. Eng. Mech. Div. ASCE 85, 67–94 (1959)Google Scholar
  49. Pantelides, C.P., Ma, X.: Linear and nonlinear pounding of structural systems. Comput. Struct. 66, 79–92 (1998)CrossRefGoogle Scholar
  50. Papadrakakis, M., Mouzakis, H., Plevris, N., Bitzarakis, S.A.: Lagrange multiplier solution method for pounding of buildings during earthquakes. Earthquake Eng. Struct. Dynam. 20, 981–998 (1991)CrossRefGoogle Scholar
  51. Pekau, O.A., Zhu, X.: Seismic behaviour of cracked concrete gravity dams. Earthquake Eng. Struct. Dynam. 35, 477–495 (2006)CrossRefGoogle Scholar
  52. Polycarpou, P.C., Komodromos, P.: On poundings of a seismically isolated building with adjacent structures during strong earthquakes. Earthquake Eng. Struct. Dynam. 39, 933–940 (2010)Google Scholar
  53. Ruangrassamee, A., Kawashima, K.: Relative displacement response spectra with pounding effect. Earthquake Eng. Struct. Dynam. 30, 1511–1538 (2001)CrossRefGoogle Scholar
  54. Sołtysik, B., Jankowski, R.: Non-linear strain rate analysis of earthquake-induced pounding between steel buildings. Int. J. Earth Sci. Eng. 6, 429–433 (2013)Google Scholar
  55. Van Mier, J.G.M., Pruijssers, A.F., Reinhardt, H.W., Monnier, T.: Load-time response of colliding concrete bodies. J. Struct. Eng. 117, 354–374 (1991)CrossRefGoogle Scholar
  56. Valles, R.E., Reinhorn, A.M.: Evaluation, prevention and mitigation of pounding effects in building structures. In Eleventh World Conference on Earthquake Engineering, Acapulco, Mexico, Paper No. 26. 23–28 June 1996Google Scholar
  57. Valles, R.E., Reinhorn, A.M.: Evaluation, prevention and mitigation of pounding effects in building structures. Technical Report NCEER-97-0001. National Center for Earthquake Engineering Research, State University of New York, Buffalo, USA (1997)Google Scholar
  58. Wolf, J.P., Skrikerud, P.E.: Mutual pounding of adjacent structures during earthquakes. Nucl. Eng. Des. 57, 253–275 (1980)CrossRefGoogle Scholar
  59. Ye, K., Li, L., Zhu, H.: A note on the Hertz contact model with nonlinear damping for pounding simulation. Earthquake Eng. Struct. Dynam. 38, 1135–1142 (2009)CrossRefGoogle Scholar
  60. Zanardo, G., Hao, H., Modena, C.: Seismic response of multi-span simply supported bridges to a spatially varying earthquake ground motion. Earthquake Eng. Struct. Dynam. 31, 1325–1345 (2002)CrossRefGoogle Scholar
  61. Zhu, P., Abe, M., Fujino, Y.: Modelling three-dimensional non-linear seismic performance of elevated bridges with emphasis on pounding of girders. Earthquake Eng. Struct. Dynam. 31, 1891–1913 (2002)CrossRefGoogle Scholar

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© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Faculty of Civil and Environmental EngineeringGdansk University of TechnologyGdanskPoland
  2. 2.Department of Construction Engineering, College of EngineeringUniversity of DammamDammamKingdom of Saudi Arabia

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