Earthquakes and Structures

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

An energy-based approach to determine the yield force coefficient of RC frame structures

  • Merter, Onur (Department of Civil Engineering, Izmir University of Economics) ;
  • Ucar, Taner (Department of Architecture, Dokuz Eylul University)
  • Received : 2020.04.16
  • Accepted : 2021.06.11
  • Published : 2021.07.25
⟨ Previous Next ⟩

Abstract

This paper proposes an energy-based approach for estimating the yield force coefficient of reinforced concrete (RC) frame structures. The procedure is mainly based on the energy balance concept and it considers the nonlinear behavior of structures. First, an energy modification factor is defined to consistently obtain the total energy of the equivalent elastic-plastic single-degree-of-freedom (SDOF) system. Then, plastic energy is formulated as functions of the several structural parameters such as the natural frequency, the strength reduction factor and the yield displacement. Consequently, the plastic energy formulation is derived for multi-degree-of-freedom (MDOF) systems and the yield force coefficient is determined by equating the plastic energy relation to the work needed to push the structure from the yield displacement up to the maximum displacement monotonically. The validity of the energy-based approach is assessed on several RC frame structures by means of nonlinear static pushover analysis considering both material and geometrical nonlinearity. A modification factor is proposed for the yield force coefficient to consider the strain-hardening effects in lateral forces. Moreover, the modified energy-based yield force coefficients are correlated to practical design by using the ductility ratios imposed by Turkey Building Earthquake Code and a quite good agreement is observed.

Keywords

References

  1. Akbas, B. and Shen, J. (2003), "Earthquake-resistant design (EQRD) and energy concepts", Tech. J., 14(67), 2877-2901.
  2. Akiyama, H. (1985), Earthquake-Resistant Limit-State Design for Buildings, University of Tokyo Press, Tokyo, Japan.
  3. ASCE (2013), Minimum Design Loads for Buildings and Other Structures (ASCE/SEI 7-10), American Society of Civil Engineers; Reston, Virginia, U.S.A.
  4. ASCE (2014), Seismic Evaluation and Retrofit of Existing Buildings (ASCE/SEI 41-13), American Society of Civil Engineers; Reston, Virginia, U.S.A.
  5. ATC (1996), Seismic Evaluation and Retrofit of Concrete Buildings (ATC-40), Applied Technology Council; Redwood City, C.A., U.S.A.
  6. Ayala, A.G., Castellanos, H. and Lopez, S. (2012), "A displacement-based seismic design method with damage control for RC buildings", Earthq. Struct., 3(3-4), 413-434. http://dx.doi.org/10.12989/eas.2012.3.3.413.
  7. 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. https://doi.org/10.1016/j.soildyn.2011.05.015.
  8. Benavent-Climent, A. and Zahran, R. (2010), "Seismic evaluation of existing RC frames with wide beams using an energy-based approach", Earthq. Struct., 1(1), 93-108. http://dx.doi.org/10.12989/eas.2010.1.1.093.
  9. Benavent-Climent, A., Escobedo, A., Donaire-Avila, J., OliverSaiz, E. and Ramirez-Marquez, A.L. (2014), "Assessment of expected damage on buildings subjected to Lorca earthquake through an energy-based seismic index method and nonlinear dynamic response analyses", Bull. Earthq. Eng., 12(5), 2049-2073. https://doi.org/10.1007/s10518-013-9513-9.
  10. Benavent-Climent, A., Pujades, L.G. and Lopez-Almansa, F. (2002), "Design energy input spectra for moderate seismicity regions", Earthq. Eng. Struct. Dyn., 31(5), 1151-1172. https://doi.org/10.1002/eqe.153.
  11. Bergami, A.V., Forte, A., Lavorato, D. and Nuti, C. (2017), "Proposal of a Incremental Modal Pushover Analysis (IMPA)", Earthq. Struct., 13(6), 539-549. https://doi.org/10.12989/eas.2017.13.6.539.
  12. Bojorquez, E., Reyes-Salazar, A., Teran-Gilmore, A. and Ruiz, S.E. (2010), "Energy-based damage index for steel structures", Steel Compos. Struct., 10(4), 331-348. http://dx.doi.org/10.12989/scs.2010.10.4.331.
  13. Calvi, G.M., Priestley, M.J.N. and Kowalsky, M.J. (2008), "Displacement-based seismic design of structures", 3rd Hellenic Conference on Earthquake Engineering and Engineering Seismology, Athens, Greece, November.
  14. Cheng, Y., Lucchini, A. and Mollaioli, F. (2014), "Proposal of new ground-motion prediction equations for elastic input energy spectra", Earthq. Struct., 7(4), 485-510. http://dx.doi.org/10.12989/eas.2014.7.4.485.
  15. Cheng, Y., Lucchini, A. and Mollaioli, F. (2020), "Ground-motion prediction equations for constant-strength and constant-ductility input energy spectra", Bull. Earthq. Eng., 18(1), 37-55. https://doi.org/10.1007/s10518-019-00725-x.
  16. Choi, H. and 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. http://dx.doi.org/10.12989/sem.2009.31.1.093.
  17. Chopra, A.K. (1995), Dynamics of Structures, Theory and Applications to Earthquake Engineering, Prentice Hall, Upper Saddle River, N.J.
  18. Decanini, L.D. and Mollaioli, F. (1998), "Formulation of elastic earthquake input energy spectra", Earthq. Eng. Struct. Dyn., 27(12), 1503-1522. https://doi.org/10.1002/(SICI)10969845(199812)27:12<1503::AID-EQE797>3.0.CO;2-A.
  19. Dindar, A.A., Yalcin, C., Yuksel, E., Ozkaynak, H. and Buyukozturk, O. (2015), "Development of earthquake energy demand spectra", Earthq. Spectra, 31(3), 1667-1689. https://doi.org/10.1193/011212EQS010M.
  20. Dogru, S., Aksar, B., Akbas, B. and Shen, J. (2017), "Parametric study on energy demands for special steel concentrically braced frames", Steel Compos. Struct., 24(2), 265-276. https://doi.org/10.12989/scs.2017.24.2.265.
  21. Donaire-Avila, J., Lucchini, A., Benavent-Climent, A. and Mollaioli, F. (2018), "New approach for the optimal yield-force coefficient distribution in the seismic design of buildings", 16th European Conference on Earthquake Engineering, Thessaloniki, Greece, June.
  22. EC8 (2004), Eurocode 8: Design of Structures for Earthquake Resistance - Part 1: General Rules, Seismic Actions and Rules for Buildings, European Committee for Standardization; Brussels, Belgium.
  23. FEMA 356 (2000), Prestandard and Commentary for the Seismic Rehabilitation of Buildings, Federal Emergency Management Agency; Washington, D.C., U.S.A.
  24. FEMA 440 (2005), "Improvement of Nonlinear Static Seismic Analysis Procedures", Federal Emergency Management Agency, Washington, D.C., U.S.A.
  25. FEMA P-1050-1 (2015), "NEHRP Recommended Seismic Provisions for New Buildings and Other Structures", Federal Emergency Management Agency; Washington, D.C., U.S.A.
  26. Goel, S.C., Liao, W.C., Bayat, M.R. and Chao, S.H. (2010), "Performance-based plastic design (PBPD) method for earthquake-resistant structures: an overview", Struct. Des. Tall Spec. Build., 19(1-2), 115-137. https://doi.org/10.1002/tal.547.
  27. Housner, G.W. (1956), "Limit design of structures to resist earthquakes", Proceedings of the 1st World Conference on Earthquake Engineering, Oakland, California, U.S.A.
  28. Jafari, M. and Soltani, M. (2017), "A stochastic adaptive pushover procedure for seismic assessment of buildings", Earthq. Struct., 14(5), 477-492. https://doi.org/10.12989/eas.2018.14.5.477.
  29. Khoshnoud, H.R. and Marsono, K. (2012), "Assessment of FEMA356 nonlinear static procedure and modal pushover analysis for seismic evaluation of buildings", Struct. Eng. Mech., 41(2), 243-262. http://dx.doi.org/10.12989/sem.2012.41.2.243.
  30. Kumbhar, O.G. and Kumar, R. (2020), "Performance assessment of RC frame designed using force, displacement & energy based approach", Struct. Eng. Mech., 73(6), 699-714. https://doi.org/10.12989/sem.2020.73.6.699.
  31. Landi, L., Pollio, B. and Diotallevi, P.P. (2014), "Effectiveness of different standard and advanced pushover procedures for regular and irregular RC frames", Struct. Eng. Mech., 51(3), 433-446. http://dx.doi.org/10.12989/sem.2014.51.3.433.
  32. Lestuzzi, P. and Badoux, M. (2003), "An experimental confirmation of the equal displacement rule for RC structural walls", Proceedings of the FIB Symposium 2003: Concrete Structures in Seismic Regions, Athens, Greece, May, Paper No: 127.
  33. Liao, W.C. (2010), "Performance-based plastic design of earthquake resistant reinforced concrete moment frames", Ph.D. Dissertation, University of Michigan, Ann Arbor, U.S.A.
  34. Manfredi, G. (2001), "Evaluation of seismic energy demand", Earthq. Eng. Struct. Dyn., 30(4), 485-499. https://doi.org/10.1002/eqe.17.
  35. Massumi, A. and Monavari, B. (2013), "Energy based procedure to obtain target displacement of reinforced concrete structures", Struct. Eng. Mech., 48(5), 681-695. http://dx.doi.org/10.12989/sem.2013.48.5.681.
  36. Merter, O. (2019), "An investigation on the maximum earthquake input energy for elastic SDOF systems", Earthq. Struct., 16(4), 487-499. https://doi.org/10.12989/eas.2019.16.4.487.
  37. Mezgebo, M.G. and Lui, E.M. (2017), "A new methodology for energy-based seismic design of steel moment frames", Earthq. Eng. Eng. Vib., 16(1), 131-162. https://doi.org/10.1007/s11803-017-0373-1.
  38. Ozsarac, V., Karimzadeh, S., Erberik, M.A. and Askan, A. (2017), "Energy-based response of simple structural systems by using simulated ground motions", Procedia Eng., 199, 236-241. https://doi.org/10.1016/j.proeng.2017.09.009.
  39. Paolacci, F. (2013), "An energy-based design for seismic resistant structures with viscoelastic dampers", Earthq. Struct., 4(2), 219-239. http://dx.doi.org/10.12989/eas.2013.4.2.219.
  40. Priestley M.J.N., Calvi G.M. and Kowalsky M.J. (2007), Displacement-based Seismic Design of Structures, IUSS Press, Pavia, Italy.
  41. Priestley, M.J.N. (2003), Myths and Fallacies in Earthquake Engineering, Revisited (The Mallet-Milne Lecture), IUSS Press, Pavia, Italy.
  42. Priestley, M.J.N. and Kowalsky, M.J. (2000), "Direct displacement-based design of concrete buildings", Bull. N. Z. Soc. Earthq. Eng., 33(4).
  43. Qiang, X. and Chen, C.C. (2003), "Performance-based seismic design of structures: a direct displacement-based approach", Eng. Struct., 25(14), 1803-1813. https://doi.org/10.1016/j.engstruct.2003.08.003.
  44. Qiu, C., Qi, J. and Chen, C. (2020), "Energy-based seismic design methodology of SMABFs using hysteretic energy spectrum", J. Struct. Eng., 146(2), 04019207. https://doi.org/10.1061/(ASCE)ST.1943-541X.0002515.
  45. Quinde, P., Reinoso, E., Teran-Gilmore, A. and Ramos, S. (2019), "Expected damage for SDOF systems in soft soil sites: an energy-based approach", Earthq. Struct., 17(6), 577-590. https://doi.org/10.12989/eas.2019.17.6.577.
  46. Rubinstein, M. and Moller, O. (2001), "Inelastic displacementbased design approach of R/C building structures in seismic regions", Struct. Eng. Mech., 12(6), 573-594. http://dx.doi.org/10.12989/sem.2001.12.6.573.
  47. Santarsiero, M., Bedon, C. and Moupagitsoglou, K. (2019), "Energy-based considerations for the seismic design of ductile and dissipative glass frames", Soil Dyn. Earthq. Eng., 125, 105710. https://doi.org/10.1016/j.soildyn.2019.105710.
  48. SAP2000 Ultimate (2018), Integrated Solution for Structural Analysis and Design, Computers and Structures Inc. (CSI), Berkeley, California, U.S.A.
  49. Sarkar, P., Prasad, A.M. and Menon, D. (2016), "Seismic evaluation of RC stepped building frames using improved pushover analysis", Earthq. Struct., 10(4), 913-938. http://dx.doi.org/10.12989/eas.2016.10.4.913.
  50. SEAOC Vision 2000 Committee (1995), "Performance-Based Seismic Engineering", Report prepared by Structural Engineers Association of California; Sacramento, California, U.S.A.
  51. Segovia, V.A. and Ruiz, S.E. (2017), "Direct displacement-based design for buildings with hysteretic dampers, using best combinations of stiffness and strength ratios", J. Earthq. Eng., 21(5), 752-775. https://doi.org/10.1080/13632469.2016.1185054.
  52. Sharma, A., Reddy, G.R., Eligehausen, R. and Vaze, K.K. (2011), "Experimental and analytical investigation on seismic behavior of RC framed structure by pushover method", Struct. Eng. Mech., 39(1), 125-145. http://dx.doi.org/10.12989/sem.2011.39.1.125.
  53. Sucuoglu, H. and Akkar, S. (2014), Basic Earthquake Engineering from Seismology to Analysis and Design, Springer International Publishing, Switzerland.
  54. Sucuoglu, H. and Erberik, A. (2004), "Energy-based hysteresis and damage models for deteriorating systems", Earthq. Eng. Struct. Dyn., 33(1), 69-88. https://doi.org/10.1002/eqe.338.
  55. TBEC (2018), Turkish Building Earthquake Code, Ministry of Public Works and Settlement; Ankara, Turkey.
  56. Tehranizadeh, M., Amirmojahedi, M. and Moshref, A. (2016), "Simplified methods for seismic assessment of existing buildings", Earthq. Struct., 10(6), 1405-1428. http://dx.doi.org/10.12989/eas.2016.10.6.1405.
  57. Ucar, T. (2020), "Computing input energy response of MDOF systems to actual ground motions based on modal contributions", Earthq. Struct., 18(2), 263-273. https://doi.org/10.12989/eas.2020.18.2.263.
  58. Ucar, T. and Merter, O. (2018), "Derivation of energy-based base shear force coefficient considering hysteretic behavior and Pdelta effects", Earthq. Eng. Eng. Vib., 17(1), 149-163. https://doi.org/10.1007/s11803-018-0431-3.
  59. Wang, F., Zhang, N. and Huang, Z. (2016), "Estimation of earthquake induced story hysteretic energy of multi-Story buildings", Earthq. Struct., 11(1), 165-178. http://dx.doi.org/10.12989/eas.2016.11.1.165.
  60. Yu, X., Lu, D. and Li, B. (2016), "Estimating uncertainty in limit state capacities for reinforced concrete frame structures through pushover analysis", Earthq. Struct., 10(1), 141-161. http://dx.doi.org/10.12989/eas.2016.10.1.141.
  61. Zhou, Y., Song, G., Huang, S. and Wu, H. (2019), "Input energy spectra for self-centering SDOF systems", Soil Dyn. Earthq. Eng., 121, 293-305. https://doi.org/10.1016/j.soildyn.2019.03.017.