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On the rocking complex response of ancient multispondyle columns: a genious and challenging structural system requiring reliable solution

  • Experimental Solid Mechanics
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Abstract

The dynamic analysis of the heighly complex problem of rocking instablity of free-standing statues on the top of ancient multispondyle columns under ground motion is thoroughly discussed. As shown an exact analysis of this problem is impossible due to insuperable computational difficulties for evaluating the loss of energy between spondyles in connection with the extremely large number of differential equations of motion. Thus, a viscoelastic monolithic column with loss of energy equivalent to that of the multispondyle column is proposed. The solution of such a monolithic column together with its uniqueness is properly established. This work based on an analytic approach supplemented by experimental data gives the best approximate solution which can be obtained for this yet unsolved problem.

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References

  1. Kounadis AN (2012) Rocking οf slender cantilever consisting οf rigid blocks freely supported οn each other under seismic excitation, issue 87 A. In: Proceedings, Academy of Athens, pp 225–251

  2. Housner GW (1963) The behavior of inverted pendulum structure during earthquakes. Bull Seismol Soc Am 53(2):403–417

    Google Scholar 

  3. Psycharis IN, Jennings PC (1983) Rocking of slender rigid bodies allowed to uplift. Earthq Eng Struct Dyn 11:57–76

    Article  Google Scholar 

  4. Spanos PD, Koh A-S (1984) Rocking of rigid blocks due to harmonic shaking. J Eng Mech ASCE 110(11):1627–1642

    Article  Google Scholar 

  5. Hogan SJ (1990) Many steady state responses of a rigid block under harmonic forcing. Earthq Eng Struct Dyn 19(7):1057–1071

    Article  Google Scholar 

  6. Shenton HW (1996) Criteria for initiation of slide, rock, and slide-rock rigid-body modes. J Eng Mech ASCE 122(7):690–693

    Article  Google Scholar 

  7. Makris N, Roussos YS (2000) Rocking response of rigid blocks under near-source ground motions. Geotechnique 50(3):243–262

    Article  Google Scholar 

  8. Makris N, Konstantinidis D (2003) The rocking spectrum and the limitations of practical design methodologies. Earthq Eng Struct Dyn 32(12):265–289

    Article  Google Scholar 

  9. Zhang J, Makris N (2001) Rocking response of free-standing blocks under cycloid pulses. J Eng Mech ASCE 127:473–483

    Article  Google Scholar 

  10. Kounadis AN (2010) On the overturning instability of a rectangular rigid block under ground excitation. Open Mech J 4:43–57

    Article  Google Scholar 

  11. Kounadis AN, Makris N (2012) Restoration-preservation in an urban environment and seismic stability of the statues of Athena and Apollo on the forefront of the Academy of Athens. Special Issue: sustainable environment design in architecture, impacts on health. In: Rassia S Th, Pardalos PM (eds) Springer optimization and its applications, vol 56. Springer, Berlin, p 277

  12. Kounadis AN (2013a) Parametric study in rocking instability of a rigid block under harmonic ground pulse: a unified approach. Soil Dyn Earthq Eng 45:125–143

    Article  Google Scholar 

  13. Kounadis AN (2014a) Rocking instability of free-standing statues atop slender viscoelastic columns under ground motion. Soil Dyn Earthq Eng 63:83–91

  14. Allen RH, Oppenheim IJ, Parker AR, Bielak J (1986) On the dynamic response of rigid body assemblies. Earthq Eng Struct Dyn 14:861–876

    Article  Google Scholar 

  15. Psycharis ΙΝ (1990) Dynamic behaviour of rocking two-block assemblies. Earthq Eng Struct Dyn 19(4):555–575

    Article  Google Scholar 

  16. Spanos PD, Panayiotis CR, Politis NPA (2001) Dynamic analysis of stacked rigid blocks. Soil Dyn Earthq Eng 21:559–578

    Article  Google Scholar 

  17. Kounadis AN, Papadopoulos GJ, Cotsovos DM (2012) Overturning instability of a two-rigid-block system under ground excitation. J Appl Math Mech 92(7):536–557

  18. Yim C-S, Chopra AK, Penzien J (1980) Rocking response of rigid blocks to earthquakes. Earthq Eng Struct Dyn 8:565–587

    Article  Google Scholar 

  19. Koh A-S, Spanos PD (1986) Analysis of block random rocking. Soil Dyn Earthq Eng 5(3):178–183

    Article  Google Scholar 

  20. Kounadis AN (2013b) Rocking instability of free- standing statues atop slender cantilevers under ground motion. Soil Dyn Earthq Eng 48:294–305

    Article  Google Scholar 

  21. Kounadis AN (2014b) Rocking instability under ground motion of large statues freely standing atop elastically supported cantilevers. Arch Appl Mech (to appear)

  22. Drosos V, Anastasopoulos I, Gazetas G (2012) Seismic behaviour of classical columns: an experimental study. Laboratory of Soil Mechanics Research Report: LSM. NTUA.-12-01

  23. Kounadis AN, Papadopoulos GJ, Cotsovos DM (2014) On the rocking instability of a three-rigid block system under ground excitation (to be submitted)

  24. Tuma JJ (1970) Engineering mathematics handbook. McGraw-Hill Book Co., New York, p 7

    Google Scholar 

  25. Rogers LG (1959) Dynamics of framed structures. Wiley, New York

    Google Scholar 

  26. Kounadis AN (1989) Dynamics of continuous elastic systems, vol 1, 2nd edn. Symeon, Athens, pp 246–249

    Google Scholar 

  27. Kounadis AN (1975) Dynamic response of cantilevers with attached masses. J Eng Mech ASCE 101(5):695–706

    Google Scholar 

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Acknowledgments

The author is indebted to Dr. DM Cotsovos for the computation of the numerical results and their presentation in graphical form.

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Authors and Affiliations

  1. Οffice of Theoretical & Applied Mechanics Foundation for Biomedical Research of the Academy of Athens, Soranou Efessiou 4, 115,27, Athens, Greece

    Anthony N. Kounadis

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  1. Anthony N. Kounadis
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Correspondence to Anthony N. Kounadis.

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In Honour of Professor Emmanuel Gdoutos

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Kounadis, A.N. On the rocking complex response of ancient multispondyle columns: a genious and challenging structural system requiring reliable solution. Meccanica 50, 261–292 (2015). https://doi.org/10.1007/s11012-014-9928-7

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