Abstract
The theoretical approaches used for the evaluation of crack width in reinforced concrete (RC) structures, are generally based on the hypothesis of parallel crack surfaces. In this way, crack width measured on the concrete cover should be equal to that on the bar surface. The results of several experimental analyses, developed during the past years in many Research Institutes, do not justify this assumption. On the contrary, even in RC members under tensile actions, crack width appears wider on external surface than on rebar–concrete interface. To better define the effective crack profile of RC structures, a new model, able to analyze the whole structural response of RC ties, is here presented. In the proposed approach, all the physical phenomena involved in the cracking process are taken into account: the bond-slip behavior between steel rebar and tensile concrete, the nonlinear fracture mechanics of concrete in tension, and the mechanism of aggregate interlock. Crack profiles computed with this model seem to be in accordance with those experimentally measured in RC elements in tension. A good agreement between numerical results and experimental data is also found both in case of steel rebar and ordinary fiber reinforced cementitious composites (R/FRCC), and in case of steel rebar and high␣performance fiber reinforced cementitious composites (R/HPFRCC).
Résumé
Les approches théoriques utilisées pour évaluer la largeur des fissures dans les structures en béton armé, sont basés généralement sur l’hypothèse de plans de fracture parallèles. De cette façon, la largeur de la fissure mesurée dans le béton d’enrobage devrait être égale à celle sur la surface des barres d’armature. Les résultats de plusieurs analyses expérimentales, développées pendant les années passées dans beaucoup d’Instituts de Recherche, ne justifient pas cette supposition. Au contraire, aussi dans le cas d’éléments en béton armé soumis à la traction, la largeur de la fissure apparaît plus ample sur la surface du béton que sur l’interface entre les armatures d’acier et le béton. Pour mieux définir l’effectif profil d’ouverture dans les structures en béton armé, on présente ici un nouveau modèle, capable d’analyser la réponse structurale totale des tirants en béton renforcé. L’approche proposée prend en considération tous les phénomènes physiques impliqués dans le procès de formation des fissures: la nature du transfert des efforts entre l’acier et le béton, la mécanique non linéaire de la fissuration du béton soumis à la traction, et le mécanisme d’emboîtement des granulats. Les profils d’ouverture calculés avec ce modèle semblent concorder avec ceux mesurés expérimentalement dans les éléments en béton armé soumis à la traction. Les résultats numériques montrent une bonne concordance avec les données expérimentales, soit dans le cas de barres d’armature et béton renforcé de fibres ordinarire, que de barres d’armature et bétons fibrés à hautes performances.
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References
Broms BB (1965) Crack width and crack spacing in reinforced concrete members. ACI J Proc 62(10):1237–1256
Goto Y (1971) Crack formed in concrete around deformed tension bars. ACI J Proc 68(4):244–251
Watstein D, Mathey RG (1959) Width of cracks in concrete at the surface of reinforcing steel evaluated by means of tensile bond specimens. ACI J Proc 55(7):47–56
Bianchini AC, Kesler CE, Lott JL (1968) Cracking of reinforced concrete under external load. In: ACI-SP 20, Causes, mechanism and control of cracking in concrete, pp 73–85
Lutz LA (1970) Analysis of stresses in concrete near a reinforcing bar due to bond and transverse cracking. ACI J Proc 67(10):778–787
ACI Committee 224 (1986) Cracking of concrete members in direct tension. ACI J 83(1):3–13
Comitè Euro-International du Bèton (CEB) (1993) CEB-FIP Model Code 1990. CEB Bulletin d’Information n. 213/214, Lausanne, Switzerland
Beeby AW (2004) The influence of the parameter ϕ/ρeff on crack widths. Struct Concrete 5(2):71–83
Beeby AW (1972) A study of cracking in reinforced concrete members subjected to pure tension. Cement and Concrete Association, Technical Report n.42.468, London, U.K
Fantilli AP, Ferretti D, Iori I, Vallini P (1998) Behaviour of R/C elements in bending and tension: the problem of minimum reinforcement ratio. In Carpinteri A (ed) Minimum reinforcement in concrete members. ESIS Publication 24, Elsevier, Amsterdam, The Netherland, pp 99–125
Walraven JC, Reinhardt HW (1981) Theory and experiments on the mechanical behaviour of cracks in plain and reinforced concrete subjected to shear loading. Heron 26(1A):1–68
Mihashi H, Kawamata A, Kiyota M, Otsuka K, Suzuki S (2003) Bond crack and tension stiffening effect in high-performance cementitious composite. In: Japan Concrete Institute JCI symposium on ductile fiber reinforced cementitious composites (DFRCC), Tokyo, Japan, pp 1–8
Otsuka K, Mihashi H, Kiyota M, Mori S, Kawamata A (2003) Observation of multiple cracking in hybrid FRCC at micro and macro levels. J Adv Concrete Technol 1(3):291–298
Tepfers R (1979) Cracking of concrete cover along anchored deformed reinforcing bars. Mag Concrete Res 31(106):3–12
Hillerborg A, Modéer M, Petersson PE (1976) Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cement Concrete Res 6(6):773–782
Bazant ZP, Gambarova P (1980) Rough cracks in reinforced concrete. J Struct Division ASCE 106(4):819–842
Dei Poli S, Gambarova PG, Karakoc C (1986) Aggregate interlock role in R.C. thin-webbed beams in shear. J Struct Eng ASCE 113(1):1–19
Gambarova PG (1980) On aggregate interlock mechanism in reinforced concrete plates with extensive cracking. Studi e Ricerche, Corso di Perfezionamento per le Costruzioni in Cemento Armato F.lli Pesenti, Politecnico di Milano, vol 2, pp 43–102 (in Italian)
Scott RH, Gill PAT (1987) Short-term distributions of strain and bond stress along tension reinforcement. The Struct Eng 65B(2):39–48
Fantilli AP, Mihashi H, Vallini P (2005) Strain compatibility between HPFRCC and steel reinforcement. Mater Struct 38(5):495–503
Bosco C, Carpinteri A, Debernardi PG (1990) Fracture of reinforced concrete: scale effect and snap-back instability. Eng Fract Mech 35(4/5):665–677
Otsuka K (1989) X-ray technique with contrast medium to detect fine cracks in reinforced concrete. In: Mihashi H et al (eds) Fracture toughness and fracture energy. Sendai, Japan, pp 521–534
Li VC (2002) Reflections on the research and development of engineered cementitious composites (ECC). In Proceedings of the JCI international workshop on ductile fiber reinforced cementitious composites (DFRCC 2002) – Application and evaluation, Takayama, Japan, pp 1–21
Mohammed TU, Otsuki N, Hisada M, Shibata T (2001) Effect of crack width and bar types on corrosion of steel in concrete. J Mater Civil Eng ASCE 13(3):194–201
Maalej M, Ahmed SFU, Paramasivam P (2003) Corrosion durability and structural response of functionally-graded concrete beams. J Adv Concrete Technol 1(3):307–316
Acknowledgements
This work has been financially supported by the Government of Italy and the Government of Japan, within the “VII executive program of cooperation in the fields of science and technology” for the period from 2002 to 2006. A part of this work was also financially supported by Kajima Foundation. Special thanks are devoted to Prof. Bernardino Chiaia for providing useful helps.
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Appendix I: Notation
Appendix I: Notation
The following symbols are used in this paper:
A c = Concrete area in a cross-section of a RC member in tension
A c1 = Concrete area within the diffusion zone in a cross-section of a RC member in tension
A s = Reinforcement area
d a = Maximum aggregate size
E c = Young’s modulus of concrete
E s = Young’s modulus of steel rebar
f c = Compressive strength of concrete
f ct = Tensile strength of concrete
G F = Fracture energy of concrete
h a = Rib depth of rebars
K I , K Ic = Mode I stress intensity factor, and its critical value
L = Block length of a RC members in tension (where Eqs. 11–13 are solved)
l c = Distance between main cracks
N = Load applied to the ends of a RC element in tension
p s = Perimeter of rebars
R, ΔR = Distance from the reinforcement axis (radial coordinate), and its increment
R 0 = Distance from the reinforcement axis of steel–concrete interface
R 1 = Distance from the reinforcement axis of concrete surface
R A = Distance from the reinforcement axis of the point where τ changes its sign
R B = Distance of the crack tip from the reinforcement axis
s = Longitudinal slip between steel and concrete
v, Δv = Radial displacement of concrete, and its increment
w, Δw = Crack width, and its increment
w 0 = Crack width at steel–concrete interface
w c = Maximum crack width of the cohesive model with nonzero stress
z = Distance from the cracked cross-section (longitudinal coordinate)
α = Inclination of radial components in the Tepfers’ model
β = Inclination of sliding planes around the ribs in the Tepfers’ model
χ = Coefficient that reproduces the stress evolution in tensile concrete
εct = Tensile concrete strain
εs = Tensile steel strain
Φ = Bar diameter
γ = Function introduced in Eq. 4
σcc = Compressive stress in concrete
σct = Tensile stress in concrete
σct,0 = Tensile stress in concrete on the bar surface (Fig. 7)
σct,1 = Tensile stress in concrete outside the diffusion circle (Fig. 7)
σs = Tensile stress in steel rebars
τ = Shear stress in concrete
τ0 = Bond stresses on bar surface
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Fantilli, A.P., Mihashi, H. & Vallini, P. Crack profile in RC, R/FRCC and R/HPFRCC members in tension. Mater Struct 40, 1099–1114 (2007). https://doi.org/10.1617/s11527-006-9208-7
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DOI: https://doi.org/10.1617/s11527-006-9208-7