Abstract
Bond deterioration between steel bars and concrete in reinforced-concrete beams mostly occurs close to the primary (i.e., bending induced) cracks. To investigate bond-cracking interaction, a novel bond-slip relationship is introduced in this study, where bond parameters are a function of crack-opening displacement. Such a displacement is in turn evaluated based on the highly variable strain profiles in the concrete, through an iterative procedure. The effectiveness of the proposed approach is validated against a set of tests on RC beams well-documented in the literature, which show a clear trend for the local bond stresses to decrease close to the primary cracks. The bond-slip relationships along the bar and the maximum bond stress depend on the applied loads and on the crack pattern, with a mutual interaction that affects both the crack-opening displacement and the bond stresses, causing a nonlinear increase in the steel strains. Nevertheless, the bond-slip relationships display descending branches characterized by remarkably similar slopes within a given region, irrespective of the loads. Consequently, if the descending branch for this region is known under a particular load, the branches under other loads can be obtained by horizontally translating the known branch. The proposed approach may provide a useful tool to describe bond behavior in RC members and to understand the complex interaction among the displacements due to crack opening, bond stresses and their structural effect.
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References
Balazs GL (1993) Cracking analysis based on slip and bond stresses. ACI Materials Journal 90(4):340–348, DOI: https://doi.org/10.14359/3890
Berrocal CG, Fernandez I, Bado MF, Casas JR, Rempling R (2021) Assessment and visualization of performance indicators of reinforced concrete beams by distributed optical fiber sensing. Structural Health Monitoring 20(6):3309–3326, DOI: https://doi.org/10.1177/1475921720984431
Brault A, Hoult NA (2019) Distributed reinforcement strains: Measurement and application. ACI Structural Journal 116(4):115–127, DOI: https://doi.org/10.14359/51714483
Cairns J, Jones K (1996) An evaluation of the bond-splitting action of ribbed bars. ACI Materials Journal 93(1):10–19, DOI: https://doi.org/10.14359/9791
Cantone R, Ruiz MF, Muttoni A (2021) A detailed view on the rebar–to–concrete interaction based on refined measurement techniques. Engineering Structures 226:111332, DOI: https://doi.org/10.1016/j.engstruct.2020.111332
Castel A, Gilbert RI, Ranzi G (2014) Instantaneous stiffness of cracked reinforced concrete including steel-concrete interface damage and long-term effects. Journal of Structural Engineering 140(6):1–9, DOI: https://doi.org/10.1061/(ASCE)ST.1943-541X.0000954
Castel A, Vidal T, François R (2012) Finite-element modeling to calculate the overall stiffness of cracked reinforced concrete beams. Journal of Structural Engineering 138(8):889–898, DOI: https://doi.org/10.1061/(ASCE)ST.1943-541X.0000520
Debernard PG, Guiglia M, Taliano M (2013) Effect of secondary cracks for cracking analysis of reinforced concrete tie. ACI Materials Journal 110(2):209–216, DOI: https://doi.org/10.1007/s13296-013-1019-4
Debernard PG, Taliano M (2016) An improvement to Eurocode 2 and fib Model Code 2010 methods for calculating crack width in RC structures. Structural Concrete 17(3):365–376, DOI: https://doi.org/10.1002/suco.201500033
Fayyad TM, Lees JM (2018) Integrated fracture-based model formulation for RC crack analysis. Journal of Structural Engineering 144(7): 04018083, DOI: https://doi.org/10.1061/(ASCE)ST.1943-541X.0002058
Fib (International Federation for Structural Concrete) (2000) fib Bulletin10. Bond of reinforcement in concrete: State-of-art report. fib, Lausanne, Switzerland
Fib (International Federation for Structural Concrete) (2013) Model Code for Concrete Structures 2010. Ernst & Sohn, Berlin, Germany
Fib (International Federation for Structural Concrete) (2014) fib Bulletin 72. Bond and anchorage of embedded reinforcement: Background to the fib Model Code for Concrete Structures 2010. fib, Lausanne, Switzerland
Fu C, Gao Z, Yan G (2022) Nonlinear steel strains in cracked RC beams based on bond stress profiles. Materials and Structures 55:209, DOI: https://doi.org/10.1617/s11527-022-02048-x
Fu C, Lao Y (2023) Steel–concrete bond deterioration in reinforced concrete tension members due to primary cracks. Structures 56:104895, DOI: https://doi.org/10.1016/j.istruc.2023.104895
Fu C, Zhu Y, Tong D (2021) Stiffness assessment of cracked reinforced concrete beams based on a fictitious crack model. KSCE Journal of Civil Engineering 25(2):516–528, DOI: https://doi.org/10.1007/s12205-020-2056-0
Gambarova PG, Rosati GP (1997) Bond and splitting in bar pull-out: Behavioural laws and concrete cover role. Magazine of Concrete Research 49(179):99–110, DOI: https://doi.org/10.1680/macr.1997.49.179.99
Gambarova PG, Rosati GP, Zasso B (1989) Steel-to-concrete bond after concrete splitting: Test results. Materials and Structures 22(1):35–47, DOI: https://doi.org/10.1007/BF02472693
Giuriani E, Plizzari GA (1998) Interrelation of splitting and flexural cracks in RC beams. Journal of Structural Engineering 124(9):1032–1040, DOI: https://doi.org/10.1061/(ASCE)0733-9445(1998)124:9(1032)
Hermawan H, Wiktor V, Gruyaert E, Serna P (2023) Experimental investigation on the bond behaviour of steel reinforcement in self-healing concrete. Construction and Building Materials 383:131378, DOI: https://doi.org/10.1016/j.conbuildmat.2023.131378
Jakubovskis R, Kaklauskas G (2019) Bond–stress and bar–strain profiles in RC tension members modelled via finite elements. Engineering Structures 194:138–146, DOI: https://doi.org/10.1016/j.engstruct.2019.05.069
Jakubovskis R, Kaklauskas G (2021) Damage of bond in reinforced concrete: A detailed finite element analysis. Structural Concrete 22: 3228–3240, DOI: https://doi.org/10.1002/suco.202100229
Kaklauskas G (2017) Crack model for RC members based on compatibility of stress–transfer and mean–strain approaches. Journal of Structural Engineering 143:04017105, DOI: https://doi.org/10.1061/(ASCE)ST.1943-541X.0001842
Marfia S, Rinaldi Z, Sacco E (2004) Softening behaviour of reinforced concrete beams under cyclic loading. International Journal of Solids and Structures 41:3293–3316, DOI: https://doi.org/10.1016/j.ijsolstr.2003.12.015
Mousavi SS, Guizani L, Ouellet-Plamondon CM (2019) On bond-slip response and development length of steel bars in pre-cracked concrete. Construction and Building Materials 199:560–573, DOI: https://doi.org/10.1016/j.conbuildmat.2018.12.039
Muhamad R, Ali MSM, Oehlers DJ, Griffith M (2012) The tension stiffening mechanism in reinforced concrete prisms. Advances in Structural Engineering 15:2053–2069, DOI: https://doi.org/10.1260/1369-4332.15.12.2053
Murray A, Gilbert RI, Castel A (2018) A new approach to modeling tension stiffening in reinforced concrete. ACI Structural Journal 115(1):127–137, DOI: https://doi.org/10.14359/51700952
Parvanova S, Gospodinov G (2008) Development of “event–to–event” nonlinear technique to lightly reinforced concrete beams by simplified constitutive modeling. International Journal of Solids and Structures 45:4676–4686, DOI: https://doi.org/10.1016/j.ijsolstr.2008.04.005
Rabczuk T, Akkermann J, Eibl J (2005) A numerical model for reinforced concrete structures. International Journal of Solids and Structures 42:1327–1354, DOI: https://doi.org/10.1016/j.ijsolstr.2004.07.019
Ruiz G (2001) Propagation of a cohesive crack crossing a reinforcement layer. International Journal of Fracture 111:265–282, DOI: https://doi.org/10.1023/A:1012260410704
Ruiz MF, Muttoni A, Gambarova PG (2007) Analytical modeling of the pre–and postyield behaviour of bond in reinforced concrete. Journal of Structural Engineering 133:1364–1372, DOI: https://doi.org/10.1061/(ASCE)0733-9445(2007)133:10(1364)
Somma G, Vit M, Frappa G, Pauletta M, Pitacco I, Russo G (2021) A new cracking model for concrete ties reinforced with bars having different diameters and bond laws. Engineering Structures 235: 112026, DOI: https://doi.org/10.1016/j.engstruct.2021.112026
Taliano M (2017) Cracking analysis of concrete tie reinforced with two diameter bars accounting for the effect of secondary cracks. Engineering Structures 144:107–119, DOI: https://doi.org/10.1016/j.engstruct.2017.04.045
Tan R, Hendriks MAN, Geiker M, Kanstad T (2020) A numerical investigation of the cracking behaviour of reinforced–concrete tie elements. Magazine of Concrete Research 72(3):109–121, DOI: https://doi.org/10.1680/jmacr.18.00156
Wu HQ, Gilbert RI (2009) Modeling short–term tension stiffening in reinforced concrete prisms using a continuum–based finite element model. Engineering Structures 31(10):2380–2391, DOI: https://doi.org/10.1016/j.engstruct.2009.05.012
Xu T, Zhu L, Castel A, Gilbert RI (2018) Assessing immediate and time-dependent instantaneous stiffness of cracked reinforced concrete beams using residual cracks. Journal of Structural Engineering 144(4):1–12, DOI: https://doi.org/10.1061/(ASCE)ST.1943-541X.0002009
Yankelevsky DZ, Jabareen M, Abutbul AD (2008) One–dimensional analysis of tension stiffening in reinforced concrete with discrete cracks. Engineering Structures 30(1):206–217, DOI: https://doi.org/10.1016/j.engstruct.2007.03.013
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Wang, J., Guo, J. & Fu, C. Steel-Concrete Bond versus Primary Crack Opening in Reinforced Concrete Beams. KSCE J Civ Eng (2024). https://doi.org/10.1007/s12205-024-1566-6
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DOI: https://doi.org/10.1007/s12205-024-1566-6