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In-plane response of masonry infilled RC framed structures: A probabilistic macromodeling approach

  • Received : 2018.06.01
  • Accepted : 2018.09.29
  • Published : 2018.11.25

Abstract

In this paper, masonry infilled reinforced concrete (RC) frames are analyzed through a probabilistic approach. A macro-modeling technique, based on an equivalent diagonal pin-jointed strut, has been resorted to for modelling the stiffening contribution of the masonry panels. Since it is quite difficult to decide which mechanical characteristics to assume for the diagonal struts in such simplified model, the strut width is here considered as a random variable, whose stochastic characterization stems from a wide set of empirical expressions proposed in the literature. The stochastic analysis of the masonry infilled RC frame is conducted via the Probabilistic Transformation Method by employing a set of space transformation laws of random vectors to determine the probability density function (PDF) of the system response in a direct manner. The knowledge of the PDF of a set of response indicators, including displacements, bending moments, shear forces, interstory drifts, opens an interesting discussion about the influence of the uncertainty of the masonry infills and the resulting implications in a design process.

Keywords

Acknowledgement

Supported by : Italian Ministry of Education

References

  1. Al-Chaar, G. (2002), Evaluating Strength and Stiffness of Unreinforced Masonry Infill Structures, No. ERDC/CERL-TR-02-1, Engineer Research and Development Center, Construction Engineering Research Lab, Champaign, IL, U.S.A.
  2. Amanat, K.M. and Hoque, E. (2006), "A rationale for determining the natural period of RC building frames having infill", Eng. Struct., 28(4), 495-502. https://doi.org/10.1016/j.engstruct.2005.09.004
  3. Amato, G., Cavaleri, L., Fossetti, M. and Papia, M. (2008), "Infilled frames: Influence of vertical loads on the equivalent diagonal strut model", Proceedings of the 14th WCEE, Beijing, China.
  4. Angel, R., Abrams, D., Shapiro, D., Uzarski, J. and Webster, M. (1994), Behavior of Reinforced Concrete Frames with Masonry Infills, Civil Engrg. Studies, Structural Research Series No. 589, UILU-ENG-94-2005, Dept. of Civil Engineering, University of Illinois at Urbana Champaign, U.S.A.
  5. Asteris, P.G., Antoniou, S.T., Sophianopoulos, D.S. and Chrysostomou, C.Z. (2011), "Mathematical macro-modeling of infilled frames: state-of-the-art", ASCE J. Struct. Eng., 137(12), 1508-1517. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000384
  6. Asteris, P.G., Cavaleri, L., Di Trapani, F. and Sarhosis, V. (2016a), "A macro-modelling approach for the analysis of infilled frame structures considering the effects of openings and vertical loads", Struct. Infrastruct. Eng., 12(5), 551-566. https://doi.org/10.1080/15732479.2015.1030761
  7. Asteris, P.G., Cavaleri, L., Di Trapani, F. and Tsaris, A.K. (2017b), "Numerical modelling of out-of-plane response of infilled frames: State of the art and future challenges for the equivalent strut macromodels", Eng. Struct., 132, 110-122.
  8. Asteris, P.G., Chrysostomou, C.Z., Giannopoulos, I.P. and Smyrou, E. (2011), "Masonry infilled reinforced concrete frames with openings", Proceedings of the COMPDYN 2011, III ECCOMAS Thematic Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, Corfu, Greece, 26-28 May.
  9. Asteris, P.G., Cotsovos, D.M., Chrysostomou, C.Z., Mohebkhah, A. and Al-Chaar, G.K. (2013), "Mathematical micromodeling of infilled frames: state of the art", Eng. Struct., 56, 1905-1921. https://doi.org/10.1016/j.engstruct.2013.08.010
  10. Asteris, P.G., Repapis, C.C., Cavaleri, L., Sarhosis, V. and Athanasopoulou, A. (2015a), "On the fundamental period of infilled RC frame buildings", Struct. Eng. Mech., 54(6), 1175-1200. https://doi.org/10.12989/sem.2015.54.6.1175
  11. Asteris, P.G., Repapis, C.C., Tsaris, A.K., Di Trapani, F. and Cavaleri, L. (2015b), "Parameters affecting the fundamental period of infilled RC frame structures", Earthq. Struct., 9(5), 999-1028. https://doi.org/10.12989/eas.2015.9.5.999
  12. Asteris, P.G., Tsaris, A.K., Cavaleri, L., Repapis, C.C., Papalou, A., Di Trapani, F. and Karypidis, D.F. (2016b), "Prediction of the fundamental period of infilled RC frame structures using artificial neural networks", Comput. Intellig. Neurosci., 12.
  13. Asteris, P.G. (2016), The FP4026 Research Database on the Fundamental Period of RC Infilled Frame Structures, Data in Brief, 9, 704-709.
  14. Asteris, P.G., Repapis, C.C., Foskolos, F., Fotos, A. and Tsaris, A.K. (2017a), "Fundamental period of infilled RC frame structures with vertical irregularity", Struct. Eng. Mech., 61(5), 663-674. https://doi.org/10.12989/sem.2017.61.5.663
  15. Avramidis, I., Athanatopoulou, A., Morfidis, K., Sextos, A. and Giaralis, A. (2015), Eurocode ompliant Seismic Analysis and Design of R/C Buildings, Springer.
  16. Bazan, E. and Meli, R. (1980), "Seismic analysis of structures with masonry walls", Proceedings of the 7th WCEE, Istanbul, Turkey.
  17. Benjamin, J.R. and Williams, H.A. (1957), "The behavior of onestorey brick shear walls", J. Struct. Div. ASCE, Proc. Paper 1254, 83, ST3, 1-35.
  18. Benjamin, J.R. and Williams, H.A. (1958), "Behavior of one-storey walls containing opening", J. Am. Concrete Inst., 30(5), 605-618.
  19. Cavaleri, L., Fossetti. and Papia, M. (2005), "Infilled frames: Developments in the evaluation of the cyclic behaviour under lateral loads", ASCE Struct. Eng. Mech., 21, 469-494. https://doi.org/10.12989/sem.2005.21.4.469
  20. Chandrasekaran, A.R. and Chandra, B. (1970), "Experimental Study of Infilled Frames", Proceedings of the 4th Symposium on Earthquake Engineering, Roorkee U.P., India.
  21. Crisafulli, F.J., Carr, A.J. and Park, R. (2000), "Analytical modelling of infilled frame structures-a general review", Bull. New Zeal. Soc. Earth. Eng., 33(1), 30-47.
  22. Crisafulli, F.J. (1997), "Seismic behaviour of reinforced concrete structures with masonry infills", Ph.D. Dissertation, University of Canterbury, New Zealand.
  23. Crowley, H. and Pinho, R. (2004), "Period-height relationship for existing European reinforced concrete buildings", J. Earth. Eng., 8(1), 93-119.
  24. Crowley, H. and Pinho, R. (2006), "Simplified equations for estimating the period of vibration of existing buildings", Proceedings of the First European Conference on Earthquake Engineering and Seismology, Geneva, September.
  25. D.M. LL. PP (2008), Italian Building Code, 14 Gennaio 2008, Nuove norme tecniche per le costruzioni.
  26. Dawe, J.L., Schriver, A.B. and Sofocleous, C. (1989), "Masonry infilled steel frames subjected to dynamic load", Can. J. Civil Eng., 16, 877-885.
  27. De Domenico, D., Falsone, G. and Laudani, R. (2018b), "Probability-based structural response of steel beams and frames with uncertain semi-rigid connections", Struct. Eng. Mech., 67(5), 439-455. https://doi.org/10.12989/sem.2018.67.5.439
  28. De Domenico, D., Falsone, G. and Settineri, D. (2018a), "Probabilistic buckling analysis of beam-column elements with geometric imperfections and various boundary conditions", Meccan., 53(4-5), 1001-1013. https://doi.org/10.1007/s11012-017-0763-5
  29. De Domenico, D., Fuschi, P., Pardo, S. and Pisano, A.A. (2014a), "Strengthening of steel-reinforced concrete structural elements by externally bonded FRP sheets and evaluation of their load carrying capacity", Compos. Struct., 118(1), 377-384.
  30. De Domenico, D., Pisano, A.A. and Fuschi, P. (2014b), "A FEbased limit analysis approach for concrete elements reinforced with FRP bars", Compos. Struct., 107, 594-603.
  31. De Domenico, D. (2015), "RC members strengthened with externally bonded FRP plates: A FE-based limit analysis approach", Compos. Part B: Eng., 71, 159-174. https://doi.org/10.1016/j.compositesb.2014.11.013
  32. Decanini, L.D. and Fantin, G.E. (1987), "Modelos simplificados de la mamposteria incluida en porticos. Caracteristicas de rigidez y resistencia lateral en astado limite." Proceedings of the Jornadas Argentinas de Ingenieria Estructural.
  33. Dolce, M., Cardone, D., Ponzo, F.C. and Valente, C. (2005), "Shaking table tests on reinforced concrete frames without and with passive control systems", Earth. Eng. Struct. Dyn., 34(14), 1687-1717. https://doi.org/10.1002/eqe.501
  34. Doven, M.S. and Kafkas, U. (2017), "Micro modelling of masonry walls by plane bar elements for detecting elastic behaviour", Struct. Eng. Mech., 62(5), 643-649. https://doi.org/10.12989/SEM.2017.62.5.643
  35. Durrani, A.J. and Luo, Y.H. (1994), "Seismic retrofit of flat-slab buildings with masonry infills", Proceedings of the NCEER Workshop on Seismic Response of Masonry Infills, San Francisco, California, U.S.A.
  36. Erdolen, A. and Doran, B. (2012), "Interval finite element analysis of masonry-infilled walls", Struct. Eng. Mech., 44(1), 73-84. https://doi.org/10.12989/sem.2012.44.1.073
  37. Esteva, L. (1966), "Behavior under alternating loads of masonry diaphragms framed by reinforced concrete members", Proceedings of the International Symposium on the Effects of Repeated Loading of Mat. and Struct., RILEM, Mexico.
  38. Falsone, G. and Impollonia, e . (2002), "A new approach for the stochastic analysis of finite element modelled structures with uncertain parameters", Comput. Meth. Appl. Mech. Eng., 191(44), 5067-5085. https://doi.org/10.1016/S0045-7825(02)00437-1
  39. Falsone, G. and Laudani, R. (2018), "Matching the approximated principal deformation mode method (APDM) with the probability transformation method (PTM) for the analysis of uncertain systems", Prob. Eng. Mech.
  40. Falsone, G. and Settineri, D. (2013a), "Explicit solutions for the response probability density function of linear systems subjected to random static loads", Prob. Eng. Mech., 33, 86-94. https://doi.org/10.1016/j.probengmech.2013.03.001
  41. Falsone, G. and Settineri, D. (2014), "On the application of the probability transformation method for the analysis of discretized structures with uncertain proprieties", Prob. Eng. Mech., 35, 44-51. https://doi.org/10.1016/j.probengmech.2013.10.001
  42. Falsone, G. and Settineri, D. (2013b), "Explicit solutions for the response probability density function of nonlinear transformations of static random inputs", Prob. Eng. Mech., 33, 79-85. https://doi.org/10.1016/j.probengmech.2013.03.003
  43. Felice, G.D. and Giannini, R. (2001), "Out-of-plane seismic resistance of masonry walls", J. Earth. Eng., 5(2), 253-271. https://doi.org/10.1080/13632460109350394
  44. FEMA-274 (1997), NEHRP Commentary on the Guidelines for the Seismic Rehabilitation of Buildings. Washington, U.S.A.
  45. FEMA-306 (1998), Evaluation of Earthquake Damaged Concrete and Masonry Wall Buildings: Basic Procedures Manual, Washington, U.S.A.
  46. Flanagan, R.D. and Bennett, R.M. (1999), "Bidirectional behaviour of structural clay tile infilled frames", ASCE J. Struct. Eng., 125(3), 236-244.
  47. Ghanem, R. and Spanos, P. (1991), Stochastic Finite Elements: A Spectral Approach, Springer Verlag, New York, U.S.A.
  48. Ghanem, R.G. and Kruger, R.M. (1996), "eumer ical solution of spectral stochastic finite element systems", Comput. Meth. Appl. Mech. Eng., 129, 289-303. https://doi.org/10.1016/0045-7825(95)00909-4
  49. Graham, A. (1981), Kronecker Products and Matrix Calculus with Applications, Chichester: Ellis Horwood Limited.
  50. Hendry, A.W. (1981), Structural Brickwork, MacMillan Press, Ltd., London, U.K.
  51. Holmes, M. (1961), "Steel frames with brickwork and concrete infilling", Inst. Civil Eng., 19(4), 473-478.
  52. Jones, R.M. (1998), Mechanics of Composite Materials, Tailor and Francis, London, U.K.
  53. Kheirollahi, M. (2013), "Equivalent frame model and shell element for modeling of in-plane behavior of Unreinforced Brick Masonry buildings", Struct. Eng. Mech., 46(2), 213-229. https://doi.org/10.12989/sem.2013.46.2.213
  54. Khoshnoud, H.R. and Marsono, K. (2016), "Experimental study of masonry infill reinforced concrete frames with and without corner openings", Struct. Eng. Mech., 57(4), 641-656. https://doi.org/10.12989/sem.2016.57.4.641
  55. Klinger, R.E. and Bertero, V.V. (1976), Infilled Frames in Earthquake Resistant Construction, Report No. EERC 76-32, University of California, Berkeley, U.S.A.
  56. Liauw, T.C. and Kwan, K.H. (1984), "eonline ar behaviour of nonintegral infilled frames", Comput. Struct., 18, 551-560. https://doi.org/10.1016/0045-7949(84)90070-1
  57. Liu, K.L., Mani, A. and Belytschko, T. (1987), "Finite element methods in probabilistic mechanics", Prob. Eng. Mech., 2(4), 201-213. https://doi.org/10.1016/0266-8920(87)90010-5
  58. Lutes, L.D. and Sarkani, S. (2004), Random Vibration Analysis of Structural and Mechanical System, Burlingthon, U.S.A.
  59. Mainstone, R.J. (1971), "On the stiffness and strengths of infilled frames", Proceedings of the Institution of Civil Engineers, Supplement IV, Garston, U.K.
  60. Mainstone, R.J. (1974), Supplementary Note on the Stiffness and Strengths of Infilled Frames, Current Paper CP 13/74, Garston, Watford, U.K.
  61. Mallick, D.V. and Severn, R.T. (1967), "The behavior of infilled frames under static loading", Proc. Inst. Civil Eng., 38, 639-656.
  62. Matthies, H.G., Brenner, C.E., Bucher, C.G. and Soares, C.G. (1997), "nnce rtainties in probabilistic numerical analysis of structures and solids-stochastic finite elements", Struct. Safety, 19(3), 283-336. https://doi.org/10.1016/S0167-4730(97)00013-1
  63. Mehrabi, A.B., Shing, P.B., Schuller, M.P. and Noland, J.L. (1994), Performance of Masonry-infilled RIC Frames under In-plane Lateral Loads, Rep. CU/SR-94/6 Struct. Engrg. and Struct. Mech. Res. Ser., Dept. of Civ. Envir. and Arch. Engrg., Univ. of Colorado at Boulder.
  64. Milani, G. and Benasciutti, D. (2010), "Homogenized limit analysis of masonry structures with random input properties: Polynomial response surface approximation and Monte Carlo simulations", Struct. Eng. Mech., 34(4), 417-447. https://doi.org/10.12989/sem.2010.34.4.417
  65. Papoulis, A. and Pillai, S.U. (2002), Probability, Random Variables, and Stochastic Processes, 4th Edition. McGraw-Hill.
  66. Pasca, M., Liberatore, L. and Masiani, R. (2017), "Reliability of analytical models for the prediction of out-of-plane capacity of masonry infills", Struct. Eng. Mech., 64(6), 765-781. https://doi.org/10.12989/SEM.2017.64.6.765
  67. Paulay, T. and Priestley, M.J.N. (1992), Seismic Design of Reinforced Concrete and Masonry Buildings, John Wiley, New York, U.S.A.
  68. Pisano, A.A., Fuschi, P. and De Domenico, D. (2013a), "A kinematic approach for peak load evaluation of concrete elements", Comput. Struct., 119, 125-139. https://doi.org/10.1016/j.compstruc.2012.12.030
  69. Pisano, A.A., Fuschi, P. and De Domenico, D. (2013b), "Peak loads and failure modes of steel-reinforced concrete beams: Predictions by limit analysis", Eng. Struct., 56, 477-488. https://doi.org/10.1016/j.engstruct.2013.05.030
  70. Pisano, A.A., Fuschi, P. and De Domenico, D. (2014), "Limit state evaluation of steel-reinforced concrete elements by von Mises and Menetrey-Willam-type yield criteria", Int. J. Appl. Mech., 6(5), 1450058. https://doi.org/10.1142/S1758825114500586
  71. Pisano, A.A., Fuschi, P. and De Domenico, D. (2015), "eum erical limit analysis of steel-reinforced concrete walls and slabs", Comput. Struct., 160, 42-55. https://doi.org/10.1016/j.compstruc.2015.08.004
  72. Polyakov, S.V. (1960), On the Interaction between Masonry Filler Walls and Enclosing Frame When Loading in the Plane of the Wall, Translations in Earthquake Engineering, EERI, Oakland, CA, 36-42.
  73. Roberts, J.B. and Spanos, P.D. (1990), Random Vibration and Statistical Linearization, Wiley, New York, U.S.A.
  74. Schueller, G.I., Bucher, C.G., Bourgund, U. and Ouyporpraset, W. (1987), On Efficient Computational Schemes to Calculate Structural failure Probabilities, In: Stochastic Structural Mechanics (Y.K. Lin, G.I. Schueller eds.), Springer-Verlag, Berlin, Germany.
  75. Schueller, G.I. and Pradlwarter, H.J. (2009), "nnce rtain linear systems in dynamics: Retrospective and recent developments by stochastic approaches", Eng. Struct., 31(11), 2507-2517. https://doi.org/10.1016/j.engstruct.2009.07.005
  76. Stafford Smith, B. (1967), "Methods for predicting the lateral stiffness and strength of multi-storey infilled frames", Build. Sci., 2(3), 247-257. https://doi.org/10.1016/0007-3628(67)90027-8
  77. Tarque, N., Candido, L., Camata, G. and Spacone, E. (2015), "Masonry infilled frame structures: State-of-the-art review of numerical modelling", Earth. Struct., 8(3), 731-757.
  78. Tassios, T.P. (1984), "Masonry infill and R/C walls under cyclic actions, (An invited state-of-the-art report)", Proceedings of the 3rd International Symposium on Wall Structures, Warsaw, Poland.
  79. Valiasis, T. and Stylianidis, K. (1989), "Masonry infilled R/C frames under horizontal loading: Experimental results", Eur. Earthq. Eng., 3, 10-20.
  80. Zarnic, R. and Tomazevic, M. (1985), Study of the Behavior of Masonry Infilled Reinforced Concrete Frames Subjected to Seismic Loading-Part Two, Report ZRMK/IKPI-85/02, Institute for Testing and Research in Materials and Structures, Ljubljana, Yugoslavia.

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