Predicting crack spacing of reinforced concrete tension members using strain compliance approach with debonding
Abstract
A novel technique based on strain compliance for investigating the crack spacing of reinforced concrete (RC) tension members has been developed. The new method is based on the mean strain and the partial interaction (stress-transfer) approaches. The strain compliance principle is established by equating together the mean strains of a reinforced concrete block between adjacent primary cracks estimated by the mean strain and the stress-transfer approaches. The distribution of reinforcement strains within the RC block must be known to apply the stress-transfer approach. This technique is intended for the stabilized cracking stage, where formation of new primary cracks has ceased. This work accounts for local effects – fully damaged bond between the concrete and reinforcement near the cracks. Knowledge of a benchmark data point obtained from a reference element is required. The point is defined by the reinforcement ratio, bar diameter and mean crack spacing values. This data point enables the estimation of the mean crack spacing for other RC tension elements. A comparative investigation was carried out, with two different mean strain approaches, following the free-of-shrinkage tension stiffening law and provisions in Eurocode 2. The obtained results provide reasonably accurate estimates of crack spacing compared to experimental values.
Keyword : crack spacing, reinforced concrete tension element, mean strain, partial interaction, strain distribution, strain compliance
How to Cite
Kaklauskas, G., Ramanauskas, R., & Ng, P.-L. (2019). Predicting crack spacing of reinforced concrete tension members using strain compliance approach with debonding. Journal of Civil Engineering and Management, 25(5), 422-430. https://doi.org/10.3846/jcem.2019.9871
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
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Carvalho, E. P., Miranda, M. P., Fernandes, D. S., & Alves, G. V. (2018). Comparison of test methodologies to evaluate steel-concrete bond strength of thin reinforcing bar. Construction and Building Materials, 183, 243-252. https://doi.org/10.1016/j.conbuildmat.2018.06.109
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Houde, J. (1974). Study of force-displacement relationships for the finite-element analysis of reinforced concrete (PhD thesis, McGill University). Montreal, Canada.
Jakubovskis, R., Kaklauskas, G., Gribniak, V., Weber, A., & Juknys, M. (2014). Serviceability analysis of concrete beams with different arrangements of GFRP bars in the tensile zone. Journal of Composites for Construction, 18(5), 04014005. https://doi.org/10.1061/(ASCE)CC.1943-5614.0000465
Kaklauskas, G. (2017). Crack model for RC members based on compatibility of stress-transfer and mean strain approaches. Journal of Structural Engineering, 143(9), 04017105. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001842
Kaklauskas, G., Tamulenas, V., Gribniak, V., Ng, P. L., & Kupliauskas, R. (2015, January). Tension-stiffening behaviour of reinforced concrete ties of various strength classes. In International Conference on Performance-based and Life-cycle Structural Engineering (pp. 582-590). School of Civil Engineering, The University of Queensland. https://doi.org/10.14264/uql.2016.1174
Kaklauskas, G., Ng, P. L., Jakubovskis, R., & Ramanauskas, R. (2016). Numerical modelling of cracked RC tension members using stress-transfer approach. In Mechanics of Structures and Materials XXIV (pp. 166-171). CRC Press.
Kaklauskas, G., Ramanauskas, R., & Jakubovskis, R. (2017). Mean crack spacing modelling for RC tension elements. Engineering Structures, 150, 843-851. https://doi.org/10.1016/j.engstruct.2017.07.090
Kaklauskas, G., Tamulenas, V., Bado, M. F., & Bacinskas, D. (2018). Shrinkage-free tension stiffening law for various concrete grades. Construction and Building Materials, 189, 736-744. https://doi.org/10.1016/j.conbuildmat.2018.08.212
Kaklauskas, G., Sokolov, A., Ramanauskas, R., & Jakubovskis, R. (2019). Reinforcement strains in reinforced concrete tensile members recorded by strain gauges and FBG sensors: experimental and numerical analysis. Sensors, 19(1), 200. https://doi.org/10.3390/s19010200
Kankam, C. K. (1997). Relationship of bond stress, steel stress, and slip in reinforced concrete. Journal of Structural Engineering, 123(1), 79-85. https://doi.org/10.1061/(ASCE)0733-9445(1997)123:1(79)
Lapi, M., Orlando, M., & Spinelli, P. (2018). A review of literature and code formulations for cracking in R/C members. Structural Concrete, 19(5), 1481-1503. https://doi.org/10.1002/suco.201700248
Marti, P., Alvarez, M., Kaufmann, W., & Sigrist, V. (1998). Tension chord model for structural concrete. Structural Engineering International, 8(4), 287-298. https://doi.org/10.2749/101686698780488875
Murray, A., Gilbert, R. I., & Castel, A. (2018). Spacing of cracks in reinforced concrete based on a variable transfer length model. Journal of Structural Engineering, 144(7), 04018090. https://doi.org/10.1061/(ASCE)ST.1943-541X.0002095
Oh, B. H., & Kang, Y. J. (1987). New formulas for maximum crack width and crack spacing in reinforced concrete flexural members. ACI Structural Journal, 84(2), 103-112.
Maekawa, K., & Qureshi, J. (1996). Computational model for reinforcing bar embedded in concrete under combined axial pullout and transverse displacement. Doboku Gakkai Ronbunshu, 538, 227-239. https://doi.org/10.2208/jscej.1996.538_227
Rehm, G. (1961). Ueber die Grundlagen des Verbundes zwischen Stahl und Beton. Deutscher Ausschuß für Stahlbeton (DAfStb), 138.
Somayaji, S., & Shah, S. P. (1981, May). Bond stress versus slip relationship and cracking response of tension members. ACI Journal Proceedings, 78(3), 217-225.
Torres, L., Sharaky, I. A., Barris, C., & Baena, M. (2016). Experimental study of the influence of adhesive properties and bond length on the bond behaviour of NSM FRP bars in concrete. Journal of Civil Engineering and Management, 22(6), 808-817. https://doi.org/10.3846/13923730.2014.914097
Wang, J. J., Tao, M. X., & Nie, X. (2017). Fracture energy-based model for average crack spacing of reinforced concrete considering size effect and concrete strength variation. Construction and Building Materials, 148, 398-410. https://doi.org/10.1016/j.conbuildmat.2017.05.082
Wu, Y. F., & Zhao, X. M. (2012). Unified bond stress–slip model for reinforced concrete. Journal of Structural Engineering, 139(11), 1951-1962. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000747
Zhang, C. C., Yang, X. H., & Gao, H. (2018). Air-void-affected zone in concrete beam under four-point bending fracture. Journal of Civil Engineering and Management, 24(2), 130-137. https://doi.org/10.3846/jcem.2018.456
Zhou, B., Wu, R., & Feng, J. (2017). Two models for evaluating the bond behavior in pre-and post-yield phases of reinforced concrete. Construction and Building Materials, 147, 847-857. https://doi.org/10.1016/j.conbuildmat.2017.04.067
Balázs, G. L. (1993). Cracking analysis based on slip and bond stresses. ACI Materials Journal, 90, 340-340.
Bažant, Z. P., & Oh, B. H. (1983). Spacing of cracks in reinforced concrete. Journal of Structural Engineering, 109(9), 2066-2085. https://doi.org/10.1061/(ASCE)0733-9445(1983)109:9(2066)
Beeby, A. W. (2004). The influence of the parameter φ/ρeff on crack widths. Structural Concrete, 5(2), 71-83. https://doi.org/10.1680/stco.2004.5.2.71
Borges, J. F. (1965). Cracking and deformability of reinforced concrete beams. Laboratório Nacional de Engenharia Civil.
Borosnyói, A., & Balázs, G. L. (2005). Models for flexural cracking in concrete: the state of the art. Structural Concrete, 6(2), 53-62. https://doi.org/10.1680/stco.2005.6.2.53
Broms, B. B. (1965, October). Crack width and crack spacing in reinforced concrete members. ACI Journal Proceedings, 62(10), 1237-1256.
Carvalho, E. P., Miranda, M. P., Fernandes, D. S., & Alves, G. V. (2018). Comparison of test methodologies to evaluate steel-concrete bond strength of thin reinforcing bar. Construction and Building Materials, 183, 243-252. https://doi.org/10.1016/j.conbuildmat.2018.06.109
Comité Européen de Normalisation. (2004). Eurocode 2: Design of concrete structures – Part 1-1: General rules and rules for buildings. Brussels, Belgium.
Eiras-Lopez, J., Seara-Paz, S., González-Fonteboa, B., & Martinez-Abella, F. (2017). Bond behavior of recycled concrete: analysis and prediction of bond stress–slip curve. Journal of Materials in Civil Engineering, 29(10), 04017156. https://doi.org/10.1061/(ASCE)MT.1943-5533.0002000
Farra, B., & Jaccoud, J. P. (1992, October). Bond behaviour, tension stiffening and crack prediction of high strength concrete. Paper presented at Proceedings of the International Conference of Bond in Concrete, Riga, Latvia.
Fédération Internationale du Béton. (2013). fib model code for concrete structures 2010. Ernst & Sohn. https://doi.org/10.1002/9783433604090
Gergely, P., & Lutz, L. A. (1968). Maximum crack width in reinforced concrete flexural members. ACI Special Publication, 20, 87-117.
Houde, J. (1974). Study of force-displacement relationships for the finite-element analysis of reinforced concrete (PhD thesis, McGill University). Montreal, Canada.
Jakubovskis, R., Kaklauskas, G., Gribniak, V., Weber, A., & Juknys, M. (2014). Serviceability analysis of concrete beams with different arrangements of GFRP bars in the tensile zone. Journal of Composites for Construction, 18(5), 04014005. https://doi.org/10.1061/(ASCE)CC.1943-5614.0000465
Kaklauskas, G. (2017). Crack model for RC members based on compatibility of stress-transfer and mean strain approaches. Journal of Structural Engineering, 143(9), 04017105. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001842
Kaklauskas, G., Tamulenas, V., Gribniak, V., Ng, P. L., & Kupliauskas, R. (2015, January). Tension-stiffening behaviour of reinforced concrete ties of various strength classes. In International Conference on Performance-based and Life-cycle Structural Engineering (pp. 582-590). School of Civil Engineering, The University of Queensland. https://doi.org/10.14264/uql.2016.1174
Kaklauskas, G., Ng, P. L., Jakubovskis, R., & Ramanauskas, R. (2016). Numerical modelling of cracked RC tension members using stress-transfer approach. In Mechanics of Structures and Materials XXIV (pp. 166-171). CRC Press.
Kaklauskas, G., Ramanauskas, R., & Jakubovskis, R. (2017). Mean crack spacing modelling for RC tension elements. Engineering Structures, 150, 843-851. https://doi.org/10.1016/j.engstruct.2017.07.090
Kaklauskas, G., Tamulenas, V., Bado, M. F., & Bacinskas, D. (2018). Shrinkage-free tension stiffening law for various concrete grades. Construction and Building Materials, 189, 736-744. https://doi.org/10.1016/j.conbuildmat.2018.08.212
Kaklauskas, G., Sokolov, A., Ramanauskas, R., & Jakubovskis, R. (2019). Reinforcement strains in reinforced concrete tensile members recorded by strain gauges and FBG sensors: experimental and numerical analysis. Sensors, 19(1), 200. https://doi.org/10.3390/s19010200
Kankam, C. K. (1997). Relationship of bond stress, steel stress, and slip in reinforced concrete. Journal of Structural Engineering, 123(1), 79-85. https://doi.org/10.1061/(ASCE)0733-9445(1997)123:1(79)
Lapi, M., Orlando, M., & Spinelli, P. (2018). A review of literature and code formulations for cracking in R/C members. Structural Concrete, 19(5), 1481-1503. https://doi.org/10.1002/suco.201700248
Marti, P., Alvarez, M., Kaufmann, W., & Sigrist, V. (1998). Tension chord model for structural concrete. Structural Engineering International, 8(4), 287-298. https://doi.org/10.2749/101686698780488875
Murray, A., Gilbert, R. I., & Castel, A. (2018). Spacing of cracks in reinforced concrete based on a variable transfer length model. Journal of Structural Engineering, 144(7), 04018090. https://doi.org/10.1061/(ASCE)ST.1943-541X.0002095
Oh, B. H., & Kang, Y. J. (1987). New formulas for maximum crack width and crack spacing in reinforced concrete flexural members. ACI Structural Journal, 84(2), 103-112.
Maekawa, K., & Qureshi, J. (1996). Computational model for reinforcing bar embedded in concrete under combined axial pullout and transverse displacement. Doboku Gakkai Ronbunshu, 538, 227-239. https://doi.org/10.2208/jscej.1996.538_227
Rehm, G. (1961). Ueber die Grundlagen des Verbundes zwischen Stahl und Beton. Deutscher Ausschuß für Stahlbeton (DAfStb), 138.
Somayaji, S., & Shah, S. P. (1981, May). Bond stress versus slip relationship and cracking response of tension members. ACI Journal Proceedings, 78(3), 217-225.
Torres, L., Sharaky, I. A., Barris, C., & Baena, M. (2016). Experimental study of the influence of adhesive properties and bond length on the bond behaviour of NSM FRP bars in concrete. Journal of Civil Engineering and Management, 22(6), 808-817. https://doi.org/10.3846/13923730.2014.914097
Wang, J. J., Tao, M. X., & Nie, X. (2017). Fracture energy-based model for average crack spacing of reinforced concrete considering size effect and concrete strength variation. Construction and Building Materials, 148, 398-410. https://doi.org/10.1016/j.conbuildmat.2017.05.082
Wu, Y. F., & Zhao, X. M. (2012). Unified bond stress–slip model for reinforced concrete. Journal of Structural Engineering, 139(11), 1951-1962. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000747
Zhang, C. C., Yang, X. H., & Gao, H. (2018). Air-void-affected zone in concrete beam under four-point bending fracture. Journal of Civil Engineering and Management, 24(2), 130-137. https://doi.org/10.3846/jcem.2018.456
Zhou, B., Wu, R., & Feng, J. (2017). Two models for evaluating the bond behavior in pre-and post-yield phases of reinforced concrete. Construction and Building Materials, 147, 847-857. https://doi.org/10.1016/j.conbuildmat.2017.04.067