Browse > Article
http://dx.doi.org/10.12989/sem.2018.67.5.465

Effective torsional strength of axially restricted RC beams  

Taborda, Catia S.B. (Department of Civil Engineering and Architecture, Centre of Materials and Building Technologies (C-Made), University of Beira Interior)
Bernardo, Luis F.A. (Department of Civil Engineering and Architecture, Centre of Materials and Building Technologies (C-Made), University of Beira Interior)
Gama, Jorge M.R. (Department of Mathematics, Center of Mathematics and Applications, University of Beira Interior)
Publication Information
Structural Engineering and Mechanics / v.67, no.5, 2018 , pp. 465-479 More about this Journal
Abstract
In a previous study, design charts where proposed to help the torsional design of axially restricted reinforced concrete (RC) beams with squared cross section. In this article, new design charts are proposed to cover RC beams with rectangular cross section. The influence of the height to width ratio of the cross section on the behavior of RC beams under torsion is firstly shown by using theoretical and experimental results. Next, the effective torsional strength of a reference RC beam is computed for several values and combinations of the study variables, namely: height to width ratio of the cross section, concrete compressive strength, torsional reinforcement ratio and level of the axial restraint. To compute the torsional strength, the modified Variable Angle Truss Model for axially restricted RC beams is used. Then, an extensive parametric analysis based on multivariable and nonlinear correlation analysis is performed to obtain nonlinear regression equations which allow to build the new design charts. These charts allow to correct the torsional strength in order to consider the favourable influence of the compressive axial stress that arises from the axial restraint.
Keywords
reinforced concrete; beams; torsion; axial restraint; torsional design; charts;
Citations & Related Records
Times Cited By KSCI : 6  (Citation Analysis)
연도 인용수 순위
1 Hsu, T.T.C. and Mo, Y.L. (1985a), "Softening of concrete in torsional members-theory and tests", J. Am. Concrete Inst., 82(3), 290-303.
2 Hsu T.T.C. and Mo, Y.L. (1985b), "Softening of concrete in torsional members-prestressed concrete", J. Am. Concrete Inst., 82(5), 603-615.
3 Jeng, C.H. (2015), "Unified softened membrane model for torsion in hollow and solid reinforced concrete members-modeling the entire pre- and post-cracking behavior", J. Struct. Eng., 141(10).
4 Jeng, C.H., Peng, X. and Wong, Y.L. (2011), "Strain gradient effect in RC elements subjected to torsion", Mag. Concrete Res., 63(5), 343-356.   DOI
5 Jeng, C.H., Chiu, H.J. and Peng, S.F. (2013), "Design formulas for cracking torque and twist in hollow reinforced concrete members", ACI Struct. J., 110(3), 457-468.
6 Koutchoukali, N.E. and Belarbi, A. (2001), "Torsion of highstrength reinforced concrete beams and minimum reinforcement requirement", ACI Struct. J., 98(4), 462-469.
7 Khagehhosseini, A.H., Porhosseini, R., Morshed, R. and Eslami, A. (2013), "An experimental and numerical investigation on the effect of longitudinal reinforcements in torsional resistance of RC beams", Struct. Eng. Mech., 47(2), 247-263.   DOI
8 Lando, M. (1987), "Torsion of closed cross-section thin-walled beams: The influence of shearing strain", Thin-Wall. Struct., 5(4), 277-305.   DOI
9 Lampert, P. and Thurlimann, B. (1969), Torsions-Beige-Versuche an Stanhlbetobalken (Torsion Tests of Reinforced Concrete Beams), Bericht, No. 6506-2, Institute fur Baustatik, ETH, Zurich, Swiss.
10 Leonhardt, F. and Schelling, G. (1974), Torsionsversuche an Stahl Betonbalken, Bulletin No. 239, Dreurscher Ausschuss Fur Stahlbeton, Berlin, Germany.
11 Murín, J. and Kutiš, V. (2008), "An effective finite element for torsion of constant cross-sections including warping with secondary torsion moment deformation effect", Eng. Struct., 30(10), 2716-2723.   DOI
12 Levenberg, K. (1944), "A method for the solution of certain nonlinear problems in least squares", Quarter. Appl. Math., 2, 164-168.   DOI
13 Lou, T., Lopes, A. and Lopes, S. (2011), "Numerical behaviour of axially restricted RC beams", Proceedings of the International Conference on Recent Advances in Nonlinear Models-Structural Concrete Applications.
14 Ali, M.A. and White, R.N. (1999), "Toward a rational approach for design of minimum torsion reinforcement", J. Am. Concrete Inst., 96(1), 40-45.
15 Belarbi, A. and Hsu, T.C. (1994), "Constitutive laws of concrete in tension and reinforcing bars stiffened by concrete", Struct. J. Am. Concrete Inst., 91(4), 465-474.
16 Marquardt, D.W. (1963), "An algorithm for least-squares estimation of nonlinear parameters", SIAM J. Appl. Math., 11(2), 431-441.   DOI
17 McMullen, A.E. and Rangan, B.V. (1978), "Pure torsion in rectangular sections: A re-examination", J. Am. Concrete Inst., 75(10), 511-519.
18 Mondal, T.G. and Prakash, S.S. (2015), "Effect of tension stiffening on the behaviour of square RC column under torsion", Struct. Eng. Mech., 54(3), 2131-2134.
19 Nash, J.C. (1990), Compact Numerical Methods for Computers. Linear Algebra and Function Minimisation, 2nd Edition, Adam Hilger, Bristol and New York.
20 NP EN 1992-1-1 (2010), Eurocode 2: Design of Concrete Structures-Part 1: General Rules and Rules for Buildings.
21 Peng, X.N. and Wong, Y.L. (2011), "Behavior of reinforced concrete walls subjected to monotonic pure torsion-an experimental study", Eng. Struct., 33(9), 2495-2508.   DOI
22 Rasmussen, L.J. and Baker, G. (1995), "Torsion in reinforced normal and high-strength concrete beams-part 1: Experimental test series", J. Am. Concrete Inst., 92(1), 56-62.
23 Zhang, L.X. and Hsu, T.C. (1998), "Behavior and analysis of 100 MPa concrete membrane elements", J. Struct. Eng., 124(1), 24-34.   DOI
24 Valipour, H.R. and Foster, S.J. (2010), "Nonlinear analysis of 3D reinforced concrete frames: Effect of section torsion on the global response", Struct. Eng. Mech., 36(4), 421-445.   DOI
25 Waldren, P. (1988), "The significance of warping torsion in the design of straight concrete box girder bridges", Can. J. Civil Eng., 15(5), 879-889.   DOI
26 Wang, Q., Qiu, W. and Zhang, Z. (2015), "Torsion strength of single-box multi-cell concrete box girder subjected to combined action of shear and torsion", Struct. Eng. Mech., 55(5), 953-964.   DOI
27 Bernardo, L.F.A., Taborda, C.S.B. and Andrade, J.M.A. (2015b), "Ultimate torsional behavior of axially restricted RC beams", Comput. Concrete, 16(1), 67-97.   DOI
28 Bernardo L.F.A. and Lopes, S.M.R. (2009), "Torsion in HSC hollow beams: Strength and ductility analysis", ACI Struct. J., 106(1), 39-48.
29 Bernardo, L.F.A., Andrade, J.M.A. and Lopes, S.M.R. (2012), "Softened truss model for reinforced NSC and HSC beams under torsion: A comparative study", Eng. Struct., 42, 278-296.   DOI
30 Bernardo, L.F.A., Taborda, C.S.B. and Gama, J.M.R. (2015a), "Parametric analysis and torsion design charts for axially restricted RC beams", Struct. Eng. Mech., 55(1), 1-27.   DOI
31 Chen, S., Ye, Y., Guo, Q., Cheng, S. and Diao, B. (2016), "Nonlinear model to predict the torsional response of U-shaped thin-walled RC members", Struct. Eng. Mech., 60(6), 1039-1061.   DOI
32 Chiu, H.J., Fang, I.K., Young, W.T. and Shiau J.K. (2007), "Behavior of reinforced concrete beams with minimum torsional reinforcement", Eng. Struct., 29(9), 2193-2205.   DOI
33 Fang, I.K. and Shiau, J.K. (2004), "Torsional behavior of normal and high-stregth concrete beams", ACI Struct. J., 101(3), 304-313.
34 CEB-FIP MODEL CODE (2010), Comite Euro-International du Beton, Suisse.
35 Hsu, T.T.C. (1984), Torsion of Reinforced Concrete, Van Nostrand Reinhold Company.
36 Gomes, D.P. (2011), "Flexural strength of reinforced concrete beams axially restricted", M.Sc. Dissertation, University of Coimbra, Coimbra, Portugal.
37 Hsu, T.T. (1968), Torsion of Structural Concrete-Behavior of Reinforced Concrete Rectangular Members, Torsion of Structural Concrete, SP-18, American Concrete Institute, Detroit, 261-306.