DOI QR코드

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New strut-and-tie-models for shear strength prediction and design of RC deep beams

  • 투고 : 2013.07.17
  • 심사 : 2014.05.18
  • 발행 : 2014.07.25

초록

Reinforced concrete deep beams are structural beams with low shear span-to-depth ratio, and hence in which the strain distribution is significantly nonlinear and the conventional beam theory is not applicable. A strut-and-tie model is considered one of the most rational and simplest methods available for shear strength prediction and design of deep beams. The strut-and-tie model approach describes the shear failure of a deep beam using diagonal strut and truss mechanism: The diagonal strut mechanism represents compression stress fields that develop in the concrete web between diagonal cracks of the concrete while the truss mechanism accounts for the contributions of the horizontal and vertical web reinforcements. Based on a database of 406 experimental observations, this paper proposes a new strut-and-tie-model for accurate prediction of shear strength of reinforced concrete deep beams, and further improves the model by correcting the bias and quantifying the scatter using a Bayesian parameter estimation method. Seven existing deterministic models from design codes and the literature are compared with the proposed method. Finally, a limit-state design formula and the corresponding reduction factor are developed for the proposed strut-andtie model.

키워드

참고문헌

  1. AASHTO (2008), AASHTO LRFD Bridge design specifications. 4th Edition-2008 Interim Revisions. Washington, DC.
  2. ACI Committee 318 (2008), Building code requirements for structural concrete (ACI 318-08) and commentary. Detroit.
  3. Aguilar, G., Matamoros, A.B., Parra-Montesinos, G.J., Ramirez, J.A. and Wight, J.K. (2002), "Experimental evaluation of design procedures for shear strength of deep reinforced concrete beams", ACI Struct. J., 99(4), 539-548.
  4. Amornpinyo, P. (2010), "Influence of horizontal to vertical reinforcement ratio on behavior of reinforced concrete deep beams designed by strut-and-tie method", Master Thesis in Civil Eng., Khon Kaen University, Khon Kaen, Thailand.
  5. Ang, A.H-S. and Tang, W.H. (2006), Probabilistic concepts in engineering: Emphasis on applications to civil and environmental engineering, John Wiley & Sons, NJ, USA.
  6. Arabzadeh, A., Aghayari, R. and Rahai, A.R. (2011), "Investigation of experimental and analytical shear strength of reinforced concrete deep beams", Int. J. Civil Eng., 9(3),207-214.
  7. Ashour, A.F. (2000), "Shear capacity of reinforced concrete deep beams", J. Struct. Eng., ASCE, 126(9), 1045-1052. https://doi.org/10.1061/(ASCE)0733-9445(2000)126:9(1045)
  8. Box, G.E.P. and Tiao, G.C. (1992), Bayesian inference in statistic analysis, Addison-Wesley, MA, USA.
  9. Clark, A.P. (1951), "Diagonal tension in reinforced concrete beams", ACI J., 48(10), 145-156.
  10. Fang, I., Chen, J. and Hong, L. (1995), "Shear behavior of high strength concrete deep beams", Proc., 5th East Asia-Pacific Conf. on Structural Engineering and Construction, Gold Coast, Qld., July.
  11. Foster, S.J. and Gilbert, R.I. (1996), "The design of nonflexural members with normal and high-strength concrete", ACI Struct. J., 93(1), 3-10.
  12. Foster, S.J. and Gilbert, R.I. (1998), "Experimental studies on high-strength concrete deep beams", ACI Struct. J., 95(4), 382-390.
  13. Foster, S.J. and Malik, A.R. (2002), "Evaluation of efficiency factor models used in strut-and-tie modeling of nonflexural members", J. Struct. Eng., ASCE, 128, (5), 569-577. https://doi.org/10.1061/(ASCE)0733-9445(2002)128:5(569)
  14. Ferguson, P.M., Breen, J.E., and Jirsa, J.O. (1988), Reinforced concrete fundamentals, 5th Edition, John Wiley and Sons ,New York, USA.
  15. Garay-Moran, J.S. and Lubell, A.S. (2008), "Behavior of concrete deep beams with high strength reinforcement", Structural Engineering Report 277, Department of Civil and Env. Eng., Univ. of Alberta, Canada.
  16. Gardoni, P. (2002), "Probabilistic models and fragility estimates for structural components and systems" Ph.D. Thesis, Univ. of California, Berkeley, Calif.
  17. Gardoni, P., Der Kiureghian, A. and Mosalam, K.M. (2002), "Probabilistic capacity models and fragility estimates for reinforced concrete columns based on experimental observations", J. Eng. Mech., ASCE, 128(10), 1024-1038. https://doi.org/10.1061/(ASCE)0733-9399(2002)128:10(1024)
  18. Hsu, T.T.C. (2000), Unified theory of reinforced concrete.CRC Press, Inc., Florida, USA.
  19. Hwang, S. J., Lu, W. Y., and Lee, H. J.(2000a), "Shear strength prediction for deep beams", ACI Struct. J., 97(3), 367-376.
  20. Hwang, S.J., Lu, W.Y. and Lee, H.J. (2000b), "Shear strength prediction for reinforced concrete corbels", ACI Struct. J., 97(4), 543-552.
  21. Kim, J., LaFave, J.M. and Song, J. (2007), "A new statistical approach for joint shear strength determination of RC beam-column connections subjected to lateral earthquake loading", Struct. Eng. Mech., 27(4), 439-456. https://doi.org/10.12989/sem.2007.27.4.439
  22. Kim, J., LaFave, J.M. and Song, J. (2009), "Joint shear behavior of RC beam-column connections", Mag Concr Res., 61(2), 119-132. https://doi.org/10.1680/macr.2008.00068
  23. Kong, F.K., Robins, P.J. and Cole, D.F. (1970), "Web reinforcement effects on deep beams", ACI J., 67(12), 1010-1016.
  24. Kong, F.K., Robins, P.J., Singh, A. and Sharp, G.R. (1972), "Shear analysis and design of reinforced concrete deep beams", The Struct. Eng., 50(10), 405-409.
  25. Kotsovos, M.D. (1988), "Design of reinforced concrete deep beams", The Struct. Eng., 62(2), 28-32.
  26. Kunopas, S. (2008), "Influence of horizontal to vertical reinforcement ratio on behavior of reinforced concrete deep beams designed by strut-and-tie method", Master Thesis in Civil Eng., Khon Kaen University, Khon Kaen, Thailand.
  27. Li, L., He, Z., Ma, Z.J. and Yao, L. (2013), "Development of strut-and-tie model and design guidelines for improved joint in decked bulb-tee bridge", Struct. Eng. Mech., 48(2), 221-239. https://doi.org/10.12989/sem.2013.48.2.221
  28. Lin, I.J., Hwang, S.J., Lu, W.Y. and Tsai, J.T. (2003), "Shear strength of reinforced concrete dapped-end beams", Struct. Eng. Mech., 16(3), 275-294. https://doi.org/10.12989/sem.2003.16.3.275
  29. Lu, W.Y. and Lin, I. J. (2009), "Behavior of reinforced concrete corbels", Struct. Eng. Mech., 33(3), 357-371. https://doi.org/10.12989/sem.2009.33.3.357
  30. Matamoros, A.B. and Wong, K.H. (2003), "Design of simply supported deep beams using strut-and-tie models", ACI Struct. J., 100(6), 704-712.
  31. Nowak, A.S. and Collins, K.R. (2000), Reliability of structures, McGraw-Hill, New York, USA.
  32. Nowak, A.S. and Szerszen, M.M. (2003), "Calibration of design code for buildings (ACI 318): Part 1-statistical models for resistance", ACI Struct. J., 100(3), 377-382.
  33. Nowak, A.S., Rakoczy, A.M. and Szeliga, E. (2011), "Revised statistical resistance models for R/C structural components", ACI Special Publication, Honoring Andy Scanlon.
  34. Oh, J.K. and Shin, S.W. (2001), "Shear strength of reinforced high-strength concrete deep beams", ACIStruct. J., 98(2), 164-173.
  35. Park, J.W. and Kuchma, D. (2007), "Strut-and-tie model analysis for strength prediction ofdeep beams", ACI Struct. J., 104(6), 657-666.
  36. Roy, N.C. and Brena, S.F. (2008), "Behavior of deep beams with short longitudinal bar anchorages", ACI Struct. J., 105(4), 460-470.
  37. Russo, G., Venir, R. and Pauletta, M. (2005), "Reinforced concrete deep beams-shear strength model and design formula", ACI Struct. J., 102(3), 429-437.
  38. Sagaseta, J. and Vollum, R. L. (2010), "Shear design of short-span beams", Mag Concr Res., 62(4), 267-282. https://doi.org/10.1680/macr.2010.62.4.267
  39. Salamy, M., Kobayashi, H., Unjoh, S., Kosa, K. and Nishioka, T. (2005), "A comparative study on RC deep beams behavior with shear span to depth ratio between 0.5 and 1.5", 8th Symposium on Ductility Design Method for Bridges,Tokyo, Japan, February.
  40. Sarsam, K.F. and Al-Musawi, J.M. (1992), "Shear design of high-and normal strength concrete beams with web reinforcement", ACI Struct. J., 89(6), 658-664.
  41. Siao, W.B. (1993), "Strut-and-tie model for shear behavior in deep beams and pile caps failing in diagonal splitting", ACI Struct. J., 90(4), 356-363.
  42. Smith, K.N. and Vantsiotis, A.S. (1982), "Shear strength of deep beams", ACI J., 79(3), 201-213.
  43. Song, J., Kang, W.-H., Kim, K.S. and Jung, S. (2010), "Probabilistic shear strength models for reinforced concrete beams without shear reinforcement", Struct. Eng. Mech., 34(1), 15-38. https://doi.org/10.12989/sem.2010.34.1.015
  44. Subedi, N.K., Vardy, A.E. and Kubota, N. (1986), "Reinforced concrete deep beams - some test results", Mag Concr Res., 38(137), 206-219. https://doi.org/10.1680/macr.1986.38.137.206
  45. Szerszen, M.M. and Nowak, A.S. (2003), "Calibration of design code for buildings (ACI 318), part 2-reliability analysis and resistance factors", ACI Struct. J., 100(3), 383-391.
  46. Tan, K.H., Kong, F.K., Teng, S. and Guan, L. (1995), "High-strength concrete deep beams with effective span and shear span variations", ACI Struct. J., 92(4), 1-11.
  47. Tan, K.H., Kong, F.K., Teng, S. and Weng, L. (1997), "Effect of web reinforcement on high-strength concrete deep beams", ACI Struct. J., 94(5), 572-582.
  48. Tan, K.H., Teng, S., Kong, F.K. and Lu, H. (1997), "Main tension steel in high-strength concrete deep and short beams", ACI Struct. J., 94(6), 752-768.
  49. Tan, K.H. and Lu, H.Y. (1999), "Shear behavior of large reinforced concrete deep beams and code comparisons", ACI Struct. J., 96(5), 836-845.
  50. Tang, C.Y. and Tan, K.H. (2004), "Interactive mechanical model for shear strength of deep beams", J. Struct. Eng., ASCE, 130(10), 1534-1544. https://doi.org/10.1061/(ASCE)0733-9445(2004)130:10(1534)
  51. Tanimura, Y. and Sato, T. (2005), "Evaluation of shear strength of deep beams with stirrups" Quarterly Report of the Railway Technical Research Institute, 46(1), 53-58.
  52. Wight, J.K. and Mac Gregor, J.G. (2012), Reinforced concrete: mechanics and design. 6th Edition, Pearson Education, Inc., New Jersey, USA.
  53. Yang, K.H., Chung, H.S., Lee, E.T. and Eun, H.C. (2003), "Shear characteristics of high-strength concrete deep beams without shear reinforcements", Eng. Struct., 25, 1343-1352. https://doi.org/10.1016/S0141-0296(03)00110-X
  54. Zhang, L.X., and Hsu, T.T.C. (1998), "Behavior and analysis of 100 MPa concrete membrane elements", J. Struct. Eng., ASCE, 124(1), 24-34. https://doi.org/10.1061/(ASCE)0733-9445(1998)124:1(24)
  55. Zhang, N. and Tan K.H. (2007), "Direct strut-and-tie model for single and continuous deep beams", Eng. Struct., 29(3), 2987-3001. https://doi.org/10.1016/j.engstruct.2007.02.004
  56. Zhang, N. and Tan K.H. (2007), "Size effect in RC deep beams: experimental investigation and STM verification", Eng. Struct., 29(11), 3241-3254. https://doi.org/10.1016/j.engstruct.2007.10.005
  57. Zwicky, D. and Thomas Vogel, T. (2006), "Critical inclination of compression struts in concrete beams", J. Struct. Eng., ASCE, 132(5), 686-693. https://doi.org/10.1061/(ASCE)0733-9445(2006)132:5(686)

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