DOI QR코드

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Effective stiffness in regular R/C frames subjected to seismic loads

  • 투고 : 2014.09.01
  • 심사 : 2015.05.15
  • 발행 : 2015.09.25

초록

Current design codes and technical recommendations often provide rough indications on how to assess effective stiffness of Reinforced Concrete (R/C) frames subjected to seismic loads, which is a key factor when a linear analysis is performed. The Italian design code (NTC-2008), Eurocode 8 and ACI 318 do not take into account all the structural parameters affecting the effective stiffness and this may not be on the safe side when second-order $P-{\Delta}$ effects may occur. This paper presents a study on the factors influencing the effective stiffness of R/C beams, columns and walls under seismic forces. Five different approaches are adopted and analyzed in order to evaluate the effective stiffness of R/C members, in accordance with the scientific literature and the international design codes. Furthermore, the paper discusses the outcomes of a parametric analysis performed on an actual R/C building and analyses the main variables, namely reinforcement ratio, axial load ratio, concrete compressive strength, and type of shallow beams. The second-order effects are investigated and the resulting displacements related to the Damage Limit State (DLS) under seismic loads are discussed. Although the effective stiffness increases with steel ratio, the analytical results show that the limit of 50% of the initial stiffness turns out to be the upper bound for small values of axial-load ratio, rather than a lower bound as indicated by both Italian NTC-2008 and EC8. As a result, in some cases the current Italian and European provisions tend to underestimate second-order $P-{\Delta}$ effects, when the DLS is investigated under seismic loading.

키워드

참고문헌

  1. ACI Committee 318 (2002), Building code requirements for reinforced concrete, ACI 318-02 and Commentary (318R-02), Farmington Hills, Michigan, USA.
  2. Borzi, B., Vona, M., Masi, A., Pinho, R. and Pola, D. (2013), "Seismic demand estimation of RC frame buildings based on simplified and nonlinear dynamic analyses", Earthq. Struct., 4(2), 157-179. https://doi.org/10.12989/eas.2013.4.2.157
  3. Branson, D.E. (1965), "Instantaneous and time dependent deflections of simple and continuous reinforced-concrete beams", HPR Publications, 7(Part 1), Alabama Highway Department (Alabama, USA), U.S. Bureau of Public Roads.
  4. Canada Standards Association (2005), Design of concrete structures, CSA A23.3-04, Mississauga, Ontario, Canada.
  5. Carvalho, G., Bento, R. and Bhatt, C. (2013), "Nonlinear static and dynamic analyses of reinforced concrete buildings - comparison of different modelling approaches", Earthq. Struct., 4(5), 451-470. https://doi.org/10.12989/eas.2013.4.5.451
  6. Chen, W.F. and Scawthorn, C. (2003), Earthquake engineering handbook, CRC Press, Boca Raton, USA.
  7. Crowley, H. (2003), "Periods of vibration for displacement-based assessment of R/C buildings", MSc. Dissertation, Rose School, University of Pavia, Italy.
  8. EC8 UNI EN 1998-1-2005 (2005), Design of structures for earthquake resistance - Part 1: general rules, Seismic Actions and Rules for Buildings, Comite Europeen de Normalisation, Brussels, Belgium.
  9. Elwood, K.J. and Eberhard, M.O. (2009), "Effective stiffness of reinforced-concrete columns", ACI Struct. J., 106(4), 476-484.
  10. Italian Design Code (2008), Norme tecniche per le costruzioni, Italian Ministry of Public Works and Transportation, Italy.
  11. NZS 3101: Part 2 (2006), Concrete structures standard, Part 2 - Commentary on the design of concrete structures, Standards New Zealand, Wellington, NZ.
  12. FEMA 356 (2000), Prestandard and commentary for the seismic rehabilitation of buildings, FEMA Publications No. 356, prepared by the American Society of Civil Engineers for the Federal Emergency Management Agency, Washington, USA.
  13. Fenwick, R. and MacRae, G. (2009), "Comparison of New Zealand standards used for seismic design of concrete building", Bull. NZ. Soc. Earthq. Eng., 42 (3), 187-203.
  14. Grossman, J.S. (1981), "Simplified computations for effective moment of inertia and minimum thickness to avoid deflection computations", ACI J., 78(6), 423-439.
  15. Khuntia, M. and Ghosh, S.K. (2004), "Flexural stiffness of reinforced-concrete columns and beams: analytical approach", ACI Struct. J., 101(3), 351- 363.
  16. Kumar, R. and Singh, Y. (2010), "Stiffness of reinforced-concrete frame members for seismic analysis", ACI Struct. J., 107(5), 607-615.
  17. Mehanny, S.S.F., Kuramoto, H. and Deierlein, G.G. (2001), "Stiffness modeling of R/C beam-columns for frame analysis", ACI Struct. J., 98(2), 215-225.
  18. Mirza, S.A. (1990), "Flexural stiffness of rectangular reinforced-concrete columns", ACI Struct. J., 7(4), 425-435.
  19. Paulay, T. and Priestley, M.J.N. (1992), Seismic design of reinforced-concrete and masonry buildings, Wiley & Sons, New York, USA.
  20. Petrini, L., Pinho, R. and Calvi, G.M. (2004), Guidelines for seismic design, IUSS Press, Pavia, Italy.
  21. Priestley, M.J.N. (1998), "Brief comments on elastic flexibility of reinforced concrete frames and significance to seismic design", Bull. NZ. Natl. Soc. Earthq. Eng., 31(4), 246-259.
  22. Sugano, S. (1970), "Experimental study on restoring-force characteristics of reinforced-concrete members", Dissertation, University of Tokyo, Japan.
  23. Wallace, J.W. and Orakcal, K. (2002), "ACI 318-99 Provisions for seismic design of structural walls", ACI Struct. J., 99(4), 499-508.
  24. Wang, Q. (2001), "Nonlinear stiffness design optimization of tall reinforced-concrete buildings under service loads", MSc. Dissertation, Hong Kong University of Science and Technology.
  25. Xing, G.H., Wu, T., Niu, D.T. and Liu, X. (2013), "Seismic behavior of reinforced concrete interior beam-column joints with beams of different depths", Earthq. Struct., 4(4), 429-449. https://doi.org/10.12989/eas.2013.4.4.429

피인용 문헌

  1. Stiffness Effects of Structural Elements on the Seismic Response of RC High-Rise Buildings vol.64, pp.1, 2018, https://doi.org/10.2478/ace-2018-0001
  2. A Prediction Model for the Calculation of Effective Stiffness Ratios of Reinforced Concrete Columns vol.14, pp.7, 2015, https://doi.org/10.3390/ma14071792