Structural Engineering and Mechanics

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A simplified method for estimating the fundamental period of masonry infilled reinforced concrete frames

  • Jiang, Rui (School of Civil Engineering, Central South University) ;
  • Jiang, Liqiang (School of Civil Engineering, Central South University) ;
  • Hu, Yi (School of Civil Engineering, Chang'an University) ;
  • Ye, Jihong (Xuzhou Key Laboratory for Fire Safety of Engineering Structures, China University of Mining and Technology) ;
  • Zhou, Lingyu (School of Civil Engineering, Central South University)
  • Received : 2019.08.04
  • Accepted : 2020.01.04
  • Published : 2020.06.25
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Abstract

The fundamental period is an important parameter for seismic design and seismic risk assessment of building structures. In this paper, a simplified theoretical method to predict the fundamental period of masonry infilled reinforced concrete (RC) frame is developed based on the basic theory of engineering mechanics. The different configurations of the RC frame as well as masonry walls were taken into account in the developed method. The fundamental period of the infilled structure is calculated according to the integration of the lateral stiffness of the RC frame and masonry walls along the height. A correction coefficient is considered to control the error for the period estimation, and it is determined according to the multiple linear regression analysis. The corrected formula is verified by shaking table tests on two masonry infilled RC frame models, and the errors between the estimated and test period are 2.3% and 23.2%. Finally, a probability-based method is proposed for the corrected formula, and it allows the structural engineers to select an appropriate fundamental period with a certain safety redundancy. The proposed method can be quickly and flexibly used for prediction, and it can be hand-calculated and easily understood. Thus it would be a good choice in determining the fundamental period of RC frames infilled with masonry wall structures in engineering practice instead of the existing methods.

Keywords

Acknowledgement

This work was sponsored by the Priority Academic Program Development of Jiangsu Higher Education Institutions (CE02-2-32) and the National Natural Science Foundation of China (51578546).

References

  1. Al-Balhawi, A and Zhang, B. (2017), "Investigations of elastic vibration periods of reinforced concrete moment-resisting frame systems with various infill walls", Eng. Struct., 151, 173-187. https://doi.org/10.1016/j.engstruct.2017.08.016.
  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. Aninthaneni, P. K and Dhakal, R. P. (2016), "Prediction of fundamental period of regular frame buildings", Bull. NZ Soc. Earthq. Eng., 49(2). https://doi.org/10.5459/bnzsee.49.2.175-189.
  4. Aninthaneni, P. K and Dhakal, R. P. (2017), "Prediction of lateral stiffness and fundamental period of concentrically braced frame buildings", Bull. Earthq. Eng., 15(7), 3053-3082. https://doi.org/10.1007/s10518-016-0081-7.
  5. Applied Technology Council (ATC) (1978), "Tentative Provision for the development of seismic regulations for buildings", Report No. ATC3-06; Palo Alto, California.
  6. 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.
  7. Asteris, P. G., Repapis, C. C., Repapi, E. V and Cavaleri, L. (2017a), "Fundamental period of infilled reinforced concrete frame structures", Struct. Infrastruct. Eng., 13(7), 929-941. https://doi.org/10.1080/15732479.2016.1227341.
  8. Asteris, P. G. (2003), "Lateral stiffness of brick masonry infilled plane frames", J. Struct. Eng., 129(8), 1071-1079. http://doi.org/10.1061/(ASCE)0733-9445(2003)129:8(1071).
  9. Asteris, P. G., Repapis, C. C., Tsaris, A. K., Di Trapani, F and Cavaleri, L. (2015a), "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.
  10. Asteris, P. G., Repapis, C. C., Cavaleri, L., Sarhosis, V and Athanasopoulou, A. (2015b), "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., Tsaris, A. K., Cavaleri, L., Repapis, C. C., Papalou, A., Di Trapani, F and Karypidis, D. F. (2016a), "Prediction of the fundamental period of infilled RC frame structures using artificial neural networks", Comput. Intel. Neurosc., 2016, 20. https://doi.org/10.1155/2016/5104907.
  12. Asteris, P. G., Repapis, C. C., Foskolos, F., Fotos, A and Tsaris, A. K. (2017b). "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.
  13. Asteris, P. G., Antoniou, S. T., Sophianopoulos, D. S and Chrysostomou, C. Z. (2011), "Mathematical macromodeling of infilled frames: state of the art", J. Struct. Eng., 137(12), 1508-1517. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000384.
  14. Asteris, P. G. (2016b), "The FP4026 Research Database on the fundamental period of RC infilled frame structures", Data Brief, 9, 704-709. https://doi.org/10.1016/j.dib.2016.10.002.
  15. Asteris, P. G., Cavaleri, L., Di Trapani, F and Tsaris, A. K. (2017c), "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. https://doi.org/10.1016/j.engstruct.2016.10.012.
  16. Asteris, P. G., Cavaleri, L., Di Trapani, F and Sarhosis, V. (2016c), "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.
  17. Asteris, P. G and Nikoo, M. (2019), "Artificial bee colony-based neural network for the prediction of the fundamental period of infilled frame structures", Neural Comput Appl, 1-11. https://doi.org/10.1007/s00521-018-03965-1.
  18. Belleri, A., Brunesi, E., Nascimbene, R., Pagani, M and Riva, P. (2014), "Seismic performance of precast industrial facilities following major earthquakes in the Italian territory", J. Perform. Constr. Fac., 29(5), 04014135. https://doi.org/10.1061/(ASCE)CF.1943-5509.0000617.
  19. Blasi, G., Perrone, D and Aiello, M. A. (2018), "Fragility functions and floor spectra of RC masonry infilled frames: influence of mechanical properties of masonry infills", Bull. Earthq. Eng., 16(12), 6105-6130. https://doi.org/10.1007/s10518-018-0435-4.
  20. Cavaleri, L., Di Trapani, F., Asteris, P. G and Sarhosis, V. (2017), "Influence of column shear failure on pushover based assessment of masonry infilled reinforced concrete framed structures: A case study", Soil Dyn Earthq Eng, 100, 98-112. https://doi.org/10.1016/j.soildyn.2017.05.032.
  21. De Domenico, D., Falsone, G and Laudani, R. (2018), "In-plane response of masonry infilled RC framed structures: A probabilistic macromodeling approach", Struct. Eng. Mech., 68(4), 423-442. https://doi.org/10.12989/sem.2018.68.4.423.
  22. Doven, M. S and Kafkas, U. (2017), "Micro modelling of masonry walls by plane bar elements for detecting elastic behavior", Struct. Eng. Mech., 62(5), 643-649. https://doi.org/10.12989/sem.2017.62.5.643.
  23. El-Dakhakhni, W. W., Elgaaly, M and Hamid, A. A. (2003), "Three-strut model for concrete masonry-infilled steel frames", J. Struct. Eng., 129(2), 177-185. https://doi.org/10.1061/(ASCE)0733-9445(2003)129:2(177).
  24. Eurocode 8. (2004), Design of Structures For Earthquake Resistance, Part 1: General Rules, Seismic Actions And Rules For Buildings. European Standard EN 1998-1-1. European Committee for Standardization (CEN), Brussels.
  25. FEMA-274 (1997), NEHRP Commentary on the Guidelines for the Seismic Rehabilitation of Buildings, Federal Emergency Management Agency, Washington, D.C.
  26. FEMA-306 (1998), Evaluation Of Earthquake Damaged Concrete And Masonry Wall Buildings: Basic Procedures Manual, Federal Emergency Management Agency, Washington, D.C.
  27. FEMA-450 (2003), Nehrp Recommended Provisions For Seismic Regulations For New Buildings And Other Structures. Part 1: Provisions, Federal Emergency Management Agency, Washington, D.C.
  28. Fiore, A., Netti, A and Monaco, P. (2012), "The influence of masonry infill on the seismic behaviour of RC frame buildings", Eng. Struct., 44, 133-145. https://doi.org/10.1016/j.engstruct.2012.05.023.
  29. Fiore, A., Spagnoletti, G and Greco, R. (2016), "On the prediction of shear brittle collapse mechanisms due to the infill-frame interaction in RC buildings under pushover analysis", Eng. Struct., 121, 147-159. https://doi.org/10.1016/j.engstruct.2016.04.044.
  30. Gallipoli, M. R., Mucciarelli, M., Sket-Motnikar, B., Zupancic, P., Gosar, A., Prevolnik, S et al. (2010), "Empirical estimates of dynamic parameters on a large set of European buildings", Bull. Earthq. Eng., 8(3), 593-607. https://doi.org/10.1007/s10518-009-9133-6.
  31. Guler, K., Yuksel, E and Kocak, A. (2008), "Estimation of the fundamental vibration period of existing RC buildings in Turkey utilizing ambient vibration records", J. Earthq. Eng., 12(S2), 140-150. https://doi.org/10.1080/13632460802013909.
  32. Hatzigeorgiou, G. D and Kanapitsas, G. (2013), "Evaluation of fundamental period of low-rise and mid-rise reinforced concrete buildings", Earthq. Eng. Struct. D., 42(11), 1599-1616. https://doi.org/10.1002/eqe.2289.
  33. Holmes, M. (1961), "Steel frames with brickwork and concrete infilling", Proceedings Institution Civil Eng., 19(4), 473-478. https://doi.org/10.1680/iicep.1961.11305.
  34. Jiang, L., Hong, Z and Hu, Y. (2018), "Effects of various uncertainties on seismic risk of steel frame equipped with steel panel wall", Bull. Earthq. Eng., 16(12), 5995-6012. https://doi.org/10.1007/s10518-018-0423-8.
  35. Jiang, L and Ye, J. (2019). "Redundancy of a mid-rise CFS composite shear wall building based on seismic response sensitivity analysis". Eng. Struct., 200, 109647. https://doi.org/10.1016/j.engstruct.2019.109647.
  36. Jiang, L and Ye, J. (2020). Quantifying the effects of various uncertainties on seismic risk assessment of CFS structures. Bull. Earthq. Eng., 1-32. https://doi.org/10.1007/s10518-019-00726-w.
  37. Kose, M. M. (2009), "Parameters affecting the fundamental period of RC buildings with infill walls", Eng. Struct., 31(1), 93-102. https://doi.org/10.1016/j.engstruct.2008.07.017.
  38. Koutas, L., Bousias, S. N and Triantafillou, T. C. (2014), "Seismic strengthening of masonry-infilled RC frames with TRM: Experimental study", J. Compos. Constr., 19(2), 04014048. https://doi.org/10.1061/(ASCE)CC.1943-5614.0000507.
  39. Koutromanos, I., Stavridis, A., Shing, P. B and Willam, K. (2011), "Numerical modeling of masonry-infilled RC frames subjected to seismic loads", Comput. Struct., 89(11-12), 1026-1037. https://doi.org/10.1016/j.compstruc.2011.01.006.
  40. Lee, L. H., Chang, K. K and Chun, Y. S. (2000), "Experimental formula for the fundamental period of RC buildings with shear-wall dominant systems", Struct. Des. Tall. Spec., 9(4), 295-307. https://doi.org/10.1002/1099-1794(200009)9:4<295::AID-TAL153>3.0.CO;2-9.
  41. Lemonis, M. E., Asteris, P. G., Zitouniatis, D. G and Ntasis, G. D. (2019), "Modeling of the lateral stiffness of masonry infilled steel moment-resisting frames", Struct. Eng. Mech., 70(4), 421-429. https://doi.org/10.12989/sem.2019.70.4.421.
  42. Mainstone, R. J and Weeks, G. A. (1970), "The influence of bounding frame on the racking stiffness and strength of brick walls", Proceedings of the 2nd International Brick Masonry Conference, Building Research Establishment, Watford, United Kingdom, 165-171.
  43. Mainstone, R.J. (1974), "Supplementary note on the stiffness and strengths of infilled frames", Current Paper CP 13/74, Garston, Watford, United Kingdom.
  44. Marques, R. and Lourenco, P. B. (2019), "Structural behaviour and design rules of confined masonry walls: Review and proposals", Constr. Build. Mater., 217, 137-155. https://doi.org/10.1016/j.conbuildmat.2019.04.266.
  45. Masi, A and Vona, M. (2009), "Estimation of the period of vibration of existing RC building types based on experimental data and numerical results", Increasing Seismic Safety by Combining Engineering Technologies and Seismological Data, Dordrecht, Springer. 207-225. https://doi.org/10.1007/978-1-4020-9196-4_15.
  46. MATLAB (2016a), Mathworks, Natick, MA, USA.
  47. Mouzakis, C., Adami, C.E., Karapitta, L. and Vintzileou, E. (2018), "Seismic behaviour of timber-laced stone masonry buildings before and after interventions: shaking table tests on a two-storey masonry model", Bull. Earthq. Eng., 16(2), 803-829. https://doi.org/10.1007/s10518-017-0220-9.
  48. NBCC (1995), Canadian Commission on Building and Fire Code, National Building Code of Canada, National Research Council; Ottawa, Canada.
  49. Newmark, N. M and Hall, W. J. (1982), Earthquake Spectra and Design, Earthquake Engineering Research Institute, Berkeley, Calif, USA.
  50. Nikoo, M., Hadzima-Nyarko, M., Khademi, F and Mohasseb, S. (2017), "Estimation of fundamental period of reinforced concrete shear wall buildings using self organization feature map", Struct. Eng. Mech., 63(2), 237-249. https://doi.org/10.12989/sem.2017.63.2.237.
  51. Oliveira, C. S and Navarro, M. (2010), "Fundamental periods of vibration of RC buildings in Portugal from in-situ experimental and numerical techniques", Bull. Earthq. Eng., 8(3), 609-642. https://doi.org/10.1007/s10518-009-9162-1.
  52. Parghi, A and Alam, M.S. (2018), "A review on the application of sprayed-FRP composites for strengthening of concrete and masonry structures in the construction sector", Compos. Struct., 187, 518-534. https://doi.org/10.1016/j.compstruct.2017.11.085.
  53. Penava, D., Sarhosis, V., Kozar, I and Guljas, I. (2018), "Contribution of RC columns and masonry wall to the shear resistance of masonry infilled RC frames containing different in size window and door openings", Eng. Struct., 172, 105-130. https://doi.org/10.1016/j.engstruct.2018.06.007.
  54. Penava, D., Sigmund, V and Kozar, I. (2016), "Validation of a simplified micromodel for analysis of infilled RC frames exposed to cyclic lateral loads", Bull. Earthq. Eng., 14(10), 2779-2804. https://doi.org/10.1007/s10518-016-9929-0.
  55. Peng, Q., Zhou, X and Yang, C. (2018), "Influence of connection and constructional details on masonry-infilled RC frames under cyclic loading", Soil. Dyn. Earthq. Eng., 108, 96-110. https://doi.org/10.1016/j.soildyn.2018.02.009.
  56. Penna, A., Morandi, P., Rota, M., Manzini, C. F., Da Porto, F and Magenes, G. (2014), "Performance of masonry buildings during the Emilia 2012 earthquake", Bull. Earthq. Eng., 12(5), 2255-2273. https://doi.org/10.1007/s10518-013-9496-6.
  57. Perrone, D., Leone, M and Aiello, M. A. (2016), "Evaluation of the infill influence on the elastic period of existing RC frames", Eng. Struct., 123, 419-433. https://doi.org/10.1016/j.engstruct.2016.05.050.
  58. Perrone, D., Leone, M and Aiello, M. A. (2017), "Non-linear behaviour of masonry infilled RC frames: Influence of masonry mechanical properties", Eng. Struct., 150, 875-891. https://doi.org/10.1016/j.engstruct.2017.08.001.
  59. Petry, S and Beyer, K. (2014), "Scaling unreinforced masonry for reduced-scale seismic testing", Bull. Earthq. Eng., 12(6), 2557-2581. https://doi.org/10.1007/s10518-014-9605-1.
  60. Polyakov, S. V. (1960), "On the interaction between masonry filler walls and enclosing frame when loaded in the plane of the wall", Translations in Earthquake Engineering, Earthquake engineering Research Institute, Oakland, California, 36-42.
  61. Puglisi, M., Uzcategui, M and Florez-Lopez, J. (2009), "Modeling of masonry of infilled frames, Part I: The plastic concentrator", Eng. Struct., 31(1), 113-118. https://doi.org/10.1016/j.engstruct.2008.07.012.
  62. Pujol, S and Fick, D. (2010), "The test of a full-scale three-story RC structure with masonry infill walls", Eng. Struct., 32(10), 3112-3121. https://doi.org/10.1016/j.engstruct.2010.05.030.
  63. Ricci, P., Verderame, G.M and Manfredi, G. (2011), "Analytical investigation of elastic period of infilled RC MRF buildings", Eng. Struct., 33(2), 308-319. https://doi.org/10.1016/j.engstruct.2010.10.009.
  64. Schultz, A. E. (1992), "Approximating lateral stiffness of stories in elastic frames", J. Struct. Eng., 118(1), 243-263. https://doi.org/10.1061/(ASCE)0733-9445(1992)118:1(243).
  65. Smith, B. S. (1966), "Behavior of square infilled frames", J. Struct. Division., 92(1), 381-404. https://doi.org/10.1061/JSDEAG.0001387
  66. Smith, B., S and Carter, C. (1969), "A method of analysis for infilled frames", Proceedings Institution Civil Eng., 44(1), 31-48. https://doi.org/10.1680/iicep.1969.7290.
  67. Smyrou, E., Blandon, C., Antoniou, S., Pinho, R and Crisafulli, F. (2011), "Implementation and verification of a masonry panel model for nonlinear dynamic analysis of infilled RC frames", Bull. Earthq. Eng., 9(5), 1519-1534. https://doi.org/10.1007/s10518-011-9262-6
  68. Stavridis, A and Shing, P.B. (2010), "Finite-element modeling of nonlinear behavior of masonry-infilled RC frames", J. Struct. Eng., 136(3), 285-296. https://doi.org/10.1061/(ASCE)ST.1943-541X.116.
  69. Surana, M., Pisode, M., Singh, Y and Lang, D. H. (2018), "Effect of URM infills on inelastic floor response of RC frame buildings", Eng. Struct., 175, 861-878. https://doi.org/10.1016/j.engstruct.2018.08.078.
  70. Tzamtzis, A. D and Asteris, P. G. (2003), "Finite Element Analysis of Masonry Structures: Part II-Proposed 3-D Nonlinear Microscopic Model", Proceedings, Ninth North American Masonry Conference, Clemson, South Carolina, USA, June.
  71. Verderame, G. M., Ricci, P and Di Domenico, M. (2019), "Experimental vs. theoretical out-of-plane seismic response of URM infill walls in RC frames", Struct. Eng. Mech., 69(6), 677-691. https://doi.org/10.12989/sem.2019.69.6.677.
  72. Verderame, G. M., De Luca, F., Ricci, P and Manfredi, G. (2011), "Preliminary analysis of a soft-story mechanism after the 2009 L'Aquila earthquake", Earthq. Eng. Struct. D., 40(8), 925-944. https://doi.org/10.1002/eqe.1069.
  73. Xin, R., Yao, J and Zhao, Y. (2017), "Experimental research on masonry mechanics and failure under biaxial compression", Struct. Eng. Mech., 61(1), 161-169. https://doi.org/10.12989/sem.2017.61.1.161.
  74. Zarnic, R., Gostic, S., Crewe, A. J and Taylor, C. A. (2001), "Shaking table tests of 1: 4 reduced-scale models of masonry infilled reinforced concrete frame buildings", Earthq. Eng. Struct. D., 30(6), 819-834. https://doi.org/10.1002/eqe.39.
  75. Zengin, B., Toydemir, B., Ulukaya, S., Oktay, D., Yuzer, N and Kocak, A. (2018), "The effect of mortar type and joint thickness on mechanical properties of conventional masonry walls", Struct. Eng. Mech., 67(6), 579-585. https://doi.org/10.12989/sem.2018.67.6.579.
  76. Zhao, B., Taucer, F and Rossetto, T. (2009), "Field investigation on the performance of building structures during the 12 May 2008 Wenchuan earthquake in China", Eng. Struct., 31(8), 1707-1723. https://doi.org/10.1016/j.engstruct.2009.02.039.