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http://dx.doi.org/10.4334/JKCI.2011.23.1.003

Indeterminate Strut-Tie Model and Load Distribution Ratio of Continuous RC Deep Beams (I) Proposal of Model ＆ Load Distribution Ratio  

Kim, Byung-Hun (Infrastructure Dept., HyunDai Engineering Co. Ltd.)
Chae, Hyun-Soo (School of Architecture & Civil Engineering, Kyungpook National University)
Yun, Young-Mook (School of Architecture & Civil Engineering, Kyungpook National University)
Publication Information
Journal of the Korea Concrete Institute / v.23, no.1, 2011 , pp. 3-12 More about this Journal
Abstract
The structural behavior of continuous reinforced concrete deep beams is mainly controlled by the mechanical relationships associated with the shear span-to-effective depth ratio, flexural reinforcement ratio, load and support conditions, and material properties. In this study, a simple indeterminate strut-tie model which reflects characteristics of the complicated structural behavior of the continuous deep beams is presented. In addition, the reaction and load distribution ratios defined as the fraction of load carried by an exterior support of continuous deep beam and the fraction of load transferred by a vertical truss mechanism, respectively, are proposed to help structural designers for the analysis and design of continuous reinforced concrete deep beams by using the strut-tie model approaches of current design codes. In the determination of the load distribution ratio, a concept of balanced shear reinforcement ratio requiring a simultaneous failure of inclined concrete strut and vertical steel tie is introduced to ensure a ductile shear failure of reinforced concrete deep beams, and the primary design variables including the shear span-to-effective depth ratio, flexural reinforcement ratio, and concrete compressive strength are implemented after thorough parametric numerical analyses. In the companion paper, the validity of the presented model and load distribution ratio was examined by applying them in the evaluation of the ultimate strength of multiple continuous reinforced concrete deep beams, which were tested to failure.
Keywords
continuous reinforced concrete deep beam; indeterminate strut-tie model; reaction distribution ratio; load distribution ratio; ultimate strength;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
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1 Foster, S. J. and Gilbert, R. I., “Experimental Studies on High-Strength Concrete Deep Beams,” ACI Structural Journal, Vol. 95, No. 4, 1998, pp. 382-390.
2 김병헌, 윤영묵, “단순지지 RC 깊은 보 부정정 스트럿-타이 모델의 하중분배율- (I) 하중분배율의 제안,” 대한토목학회 논문집, 28권, 2A호, 2008, pp. 259-267.   과학기술학회마을
3 김병헌, 정찬핵, 윤영묵, “단순지지 RC 깊은 보 부정정스트럿-타이 모델의 하중분배율- (II) 적합성 평가,” 대한토목학회 논문집, 28권, 2A호, 2008, pp. 269-279.   과학기술학회마을
4 Rogowsky, D. M., MacGregor, J. G., and Ong, S. Y., “Tests of Reinforced Concrete Deep Beams,” ACI Structural Journal, Vol. 83, No. 4, 1986, pp. 614-623.
5 Ashour, A. F., “Tests of Reinforced Concrete Continuous Deep Beams,” ACI Structural Journal, Vol. 94, No. 1, 1997, pp. 3-12.
6 Pang, X. B. and Hsu, T. T. C., “Behavior of Reinforced Concrete Membrane Elements in Shear,” ACI Structural Journal, Vol. 92, No. 6, 1995, pp. 665-679.
7 Leonhardt, F., “Reducing the Shear Reinforcement in Reinforced Concrete Beams and Slabs,” Magazine of Concrete Research, Vol. 17, No. 53, 1965, pp. 187-198.   DOI
8 Park, R. and Paulay, T., Reinforced Concrete Structures, John Wiley & Sons, New York, USA, 1970, 769 pp.
9 김우, 정제평, 김대중, “휨과 전단이 작용하는 RC 부재의 해석을 위한 비-베르누이-적합 트러스 모델링 기법 연구(I),” 대한토목학회 논문집, 23권, 6호, 2003, pp. 1247-1256.   과학기술학회마을
10 김우, 정제평, 박대성, “휨과 전단이 작용하는 RC 부재의 해석을 위한 비-베르누이-적합 트러스 모델링 기법 연구(II),” 대한토목학회 논문집, 23권, 6호, 2003, pp. 1257~1266.   과학기술학회마을
11 Zsutty, T. C., “Shear Strenght Prediction for Separate Categories of Simple Beam Tests,” ACI Journal, Vol. 68, No. 2, 1971, pp. 138-143.
12 Okamura, H. and Higai, T, “Proposed Design Equation for Shear Strength of R.C. Beams without Web Reinforcement,” Proceeding of Japan Society of Civil Engineering, 1980, pp. 131-141.
13 Park, J. W. and Kuchma, D. A., “Strut-and-Tie Model Analysis for Strength Prediction of Deep Beams,” ACI Structural Journal, Vol. 104, No. 6, 2007, pp. 657-666.
14 Tjhin, T. N. and Kuchma, D. A., “Integrated Analysis and Design Tool for the Strut-and-Tie Model,” Engineering Structure, Vol. 29, No. 11, 2007, pp. 3042-3052.   DOI   ScienceOn
15 Ashour, F. and Yang, K. H., “Application of Plasticity Theory to Reinforced Concrete Deep Beams: A Review,” Magazine of Concrete Research, Vol. 60, No. 9, 2008, pp. 657-664.   DOI   ScienceOn
16 Canadian Standards Association, Design of Concrete Structures for Buildings, CAN3-A23.3-M84, Rexdale, Ontario, Canada, 1984, 281 pp.
17 Concrete Design Committee, The Design of Concrete (NZS 3101: Part I and II), New Zealand Standard, New Zealand, 1995.
18 British Standards Institution, Code of Practice for Design and Construction (BS8110 Part I), British Standard, UK, 1997, 120 pp.
19 The International Federation for Structural Concrete (fib), Structural Concrete; Textbook on Behavior, Design and Performance Updated Knowledge of the CEB/FIP Model Code 1999 Volume 3, The International Federation for Structural Concrete(fib), Lausanne, Switzerland, 1999, 292 pp.
20 American Association of State Highway and Transportation Officials, AASHTO LRFD Bridge Design Specifications, 4th Edition, Washington, DC, USA, 2007, pp. 5-1-5-264.
21 American Concrete Institute, Building Code Requirements for Structural Concrete (ACI 318M-08) and Commentary, Farmington Hills, Michigan, USA, 2008, 473 pp.
22 Alshegeir, A., Analysis and Design of Disturbed Regions with Strut-Tie Models, Ph.D Dissertation, School of Civil Engineering, Purdue University, West Lafayette, Indiana, USA, 1992. 273 pp.
23 ACI Subcommittee 445-1, Examples for the Design for Structural Concrete with Strut-and-Tie Models; SP-208, Reineck R. H. eds, American Concrete Institute, Michigan, USA, 2002, 242 pp.
24 Quintero-Febres, C. G., Parra-Montesinos, G., and Wight, J. K., “Strength of Struts in Deep Concrete Members Designed Using Strut-and-Tie Method,” ACI Structural Journal, Vol. 103, No. 4, 2006, pp. 577-586.
25 Niwa, J., Yamada, K., Yokozawa, K., and Okamura, M., “Revaluation of the Equation for Shear Strength of R.C.-Beams without Web Reinforcement,” Proceeding of Japan Society of Civil Engineering, 1986, pp. 1986-1988.
26 Eurocode 2, Design of Concrete Structures, Part I: General Rules and Rules for Buildings(DD ENV 1992-1-1), Commission of the European Communities, UK, 1992, 176 pp.
27 Bazant, Z. P., “Fracturing Truss Model: Size Effect in Shear Failure of Reinforced Concrete,” Journal of Engineering Mechanics, ASCE, Vol. 123, No. 12, 1997, pp. 1276-1288.   DOI   ScienceOn
28 American Concrete Institute, Building Code Requirements for Structural Concrete (ACI 318-99) and Commentary (ACI 318R-99), Farmington Hills, Michigan, USA, 1999, 391 pp.
29 Hwang, S. J., Lu, W. Y., and Lee, H. J., “Shear Strength Prediction for Deep Beams,” ACI Structural Journal, Vol. 97, No. 3, 2000, pp. 367-376.
30 MacGregor, J. G., Reinforced Concrete: Mechanics and Design, 3rd Edition, Prentice-Hall, New Jersey, USA, 1997, 938 pp.
31 Foster, S. J. and Malik, A. R., “Evaluation of Efficiency Factor Models Used in Strut-and-Tie Model,” Journal of Structural Engineering, ASCE, Vol. 128, No. 5, 2002, pp. 569-577.   DOI   ScienceOn
32 Hwang, S. J. and Lu, W. Y., “Strength Prediction for Discontinuity Regions by Softened Strut-and-Tie Model,” Journal of Structural Engineering, ASCE, Vol. 128, No. 12, 2002, pp. 1519-1526.   DOI   ScienceOn
33 Matamoros, A. B. and Wong, K. H., “Design of Simply Supported Deep Beams Using Strut-and-Tie Models,” ACI Structural Journal, Vol. 100, No. 6, 2003, pp. 704-712.