Browse > Article
http://dx.doi.org/10.12989/cac.2016.18.6.1175

Minimum reinforcement and ductility index of lightly reinforced concrete beams  

Fantilli, Alessandro P. (Department of Structural, Building and Geotechnical Engineering, Politecnico di Torino)
Chiaia, Bernardino (Department of Structural, Building and Geotechnical Engineering, Politecnico di Torino)
Gorino, Andrea (Department of Structural, Building and Geotechnical Engineering, Politecnico di Torino)
Publication Information
Computers and Concrete / v.18, no.6, 2016 , pp. 1175-1194 More about this Journal
Abstract
Nonlinear models, capable of taking into account all the phenomena involved in the cracking and in the failure of lightly reinforced concrete beams, are nowadays available for a rigorous calculation of the minimum reinforcement. To simplify the current approaches, a new procedure is proposed in this paper. Specifically, the ductility index, which is lower than zero for under-reinforced concrete beams in bending, is introduced. The results of a general model, as well as the data measured in several tests, reveal the existence of two linear relationships between ductility index, crack width, and the amount of steel reinforcement. The above relationships can be applied to a wide range of lightly reinforced concrete beams, regardless of the geometrical dimensions and of the mechanical properties of materials. Accordingly, if only a few tests are combined with this linear relationships, a new design-by-testing procedure can be used to calculate the minimum reinforcement, which guarantees both the control of cracking in service and the ductility at failure.
Keywords
lightly reinforced concrete beams; bending moment; minimum reinforcement; ultimate limit state; serviceability limit state; ductility index;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Rizk, E. and Marzouk, H. (2011), "Experimental validation of minimum flexural reinforcement for thick HSC plates", ACI Struct. J., 108(3), 332-340.
2 Ruiz, G., Elices, M. and Planas, J. (1999), "Size effect and bond-slip dependence of lightly reinforced concrete beams", Eur. Struct. Integr. Soc., 24, 67-97.
3 Said, M. and Elrakib, T.M. (2013), "Experimental verification of the minimum flexural reinforcement formulas for HSC beams", IJCIET, 4(5), 152-167.
4 Seguirant, S.J., Brice, R. and Khaleghi, B. (2010), "Making sense of minimum flexural reinforcement requirements for reinforced concrete members", PCI J., 55(3), 64-85.   DOI
5 Yasir Alam, S., Lenormand, T., Loukili, A. and Regoin, J.P. (2010), "Measuring crack width and spacing in reinforced concrete members", Proceedings of the 7th International conference on Fracture Mechanics of Concrete and Concrete Structures (FraMCoS-7), 377-382.
6 Maldague, J.C. (1965), "Etablissement des lois moments-courbures", Annales de l'Institut Technique du Batiment et des Travaux Publics", 213, 1170-1218.
7 Beeby, A.W. (2005), "Discussion-the influence of the parameter $\phi$/${\rho}_{eff}$ on crack widths", Struct. Concrete, 6(4), 155-165.   DOI
8 ACI (2014), ACI 318-14: Building Code Requirements for Structural Concrete and Commentary, American Concrete Institute, Farmington Hills, Michigan, USA.
9 Bazant, Z.P. and Cedolin, L. (1991), Stability of Structures: Elastic, Inelastic, Fracture and Damage Theories, Oxford University Press, New York, U.S.A.
10 Beeby, A.W. (2004), "The influence of the parameter $\phi$/${\rho}_{eff}$ on crack widths", Struct. Concrete., 5(2), 71-83.   DOI
11 Carpinteri, A. (1989), "Minimum reinforcement in reinforced concrete beams", RILEM TC 90-FMA, Code Work, Cardiff, September.
12 Borosnyoi, A. and Balazs, G.L. (2005), "Models for flexural cracking in concrete: the state of the art", Struct. Concrete, 6(2), 53-62.   DOI
13 Bosco, C., Carpinteri, A. and Debernardi, P.G. (1990), "Minimum reinforcement in high-strength concrete", J. Struct. Eng., 116(2), 427-437.   DOI
14 Brincker, R., Henriksen, M.S., Christensen, F.A. and Heshe, G. (1999), "Size effects on the bending behaviour of reinforced concrete beams", Eur. Struct. Integr. Soc., 24, 127-180.
15 Carpinteri, A. (1999), Minimum Reinforcement in Concrete Members, Elsevier, Oxford, U.K.
16 Carpinteri, A., Cadamuro, E. and Corrado, M. (2014), "Minimum flexural reinforcement in rectangular and T-section concrete beams", Struct. Concrete, 15(3), 361-372.   DOI
17 Carpinteri, A., Ferro, G., Bosco, C. and Elkatieb, M. (1999), "Scale effects and transitional failure phenomena of reinforced concrete beams in flexure", Eur. Struct. Integr. Soc., 24, 1-30.
18 CEB (1998), CEB Bulletin 242: Ductility of Reinforced Concrete Structures, European Committee for Concrete, Lausanne, Switzerland.
19 Elrakib, T.M. (2013), "Performance evaluation of HSC beams with low flexural reinforcement", HBRC J., 9(1), 49-59.   DOI
20 CEN. (2004), EN 1992-1-1: Eurocode 2: Design of Concrete Structures - Part 1-1: General Rules and Rules for Buildings, European Committee for Standardization, Brussels, Belgium.
21 Fantilli, A.P. and Chiaia, B. (2013), "Golden ratio in the crack pattern of reinforced concrete structures", J. Eng. Mech., 139(9), 1178-1184.   DOI
22 Fantilli, A.P., Cavallo, A.D. and Pistone, G. (2015), "Fiber-reinforced lightweight concrete slabs for the maintenance of the Soleri Viaduct", Eng. Struct., 99, 184-191.   DOI
23 Fantilli, A.P., Ferretti, D. and Rosati, G. (2005), "Effect of bar diameter on the behavior of lightly reinforced concrete beams", ASCE J. Mater. Civ. Eng., 17(1), 10-18.   DOI
24 Fantilli, A.P., Ferretti, D., Iori, I. and Vallini, P. (1999), "Behaviour of R/C elements in bending and tension: The problem of minimum reinforcement ratio", Eur. Struct. Integr. Soc., 24, 99-125.
25 Fib (2000), Fib Bulletin 10: Bond of Reinforcement in Concrete, International Federation for Structural Concrete, Lausanne, Switzerland.
26 Levi, F. (1985), "On minimum reinforcement in concrete structures", J. Struct. Eng., 111(12), 2791-2796.   DOI
27 Fib (2012), Fib Bulletin 65-66: Model Code 2010-Final Draft, International Federation for Structural Concrete, Lausanne, Switzerland.
28 Giuriani, E. and Plizzari, G.A. (1998), "Interrelation of splitting and flexural cracks in RC beams", J. Struct. Eng., 124(9), 1032-1040.   DOI
29 Lange-Kornbak, D. and Karihaloo, B.L. (1999), "Fracture mechanical prediction of transitional failure and strength of singly-reinforced beams", Eur. Struct. Integr. Soc., 24, 31-66.