Experimental and theoretical investigation of tension stiffening and curvature in RC beams with extended concrete cover
Abstract
Accurate assessment of tension stiffening is important for predicting deflection and crack width in RC structures. Earlier studies by the authors have shown that an extended cover thickness increases tension stiffening in bending RC members. The current study experimentally and theoretically investigates curvature and tension stiffening in RC beams nominally having a 50 mm cover for 32 mm bars of tensile reinforcement. The four-point bending tests were carried out on square section (400×400 mm) RC beams. Mean experimental curvatures were obtained for the pure bending zone by different approaches, namely, from a mid-point deflection and from strains at several horizontal layers measured either by LVDT or DIC technique. The tension stiffening effect in the test beams was quantified by inversely calculating the resultant internal force of tensile concrete, Nct, using the test moment – curvature diagrams. Tension stiffening is characterized by parameter β0 indicating the ratio of β0 = M / Mcr at which the force Nct reaches zero. The condition Nct = 0 represents the bending stiffness of a fully cracked RC section. Earlier studies by the authors have shown that parameter β0 equals to 3 for the beams with a typical cover thickness (25–35 mm). The current study has demonstrated that for the beams having nominal cover thickness of 50 mm and bar diameter of 32 mm, parameter β0 reached rather high values indicating a little degradation of tension stiffening with increasing load.
Keyword : reinforced concrete, curvature, strain, deflection, test, tension stiffening, inverse analysis
How to Cite
Sokolov, A., Valiukas, D., Praliyeva, M., Kumar, A., Bacinskas, D., & Kaklauskas, G. (2025). Experimental and theoretical investigation of tension stiffening and curvature in RC beams with extended concrete cover. Journal of Civil Engineering and Management, 31(2), 144–152. https://doi.org/10.3846/jcem.2025.23244
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
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Fantilli, A. P., Orfeo, B., & Caldentey, A. P. (2021). The deflection of reinforced concrete beams containing recycled steel fibers. Structural Concrete, 22, 2089–2104. https://doi.org/10.1002/suco.202000729
Gilbert, R. I., & Warner, R. F. (1978). Tension stiffening in reinforced concrete slabs. ASCE Journal of the Structural Division, 104(12), 1885–1900. https://doi.org/10.1061/(ASCE)0733-9445(2007)133:6(899)
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Hung, C. C., Lee, H. S., & Chan, S. N. (2019). Tension-stiffening effect in steel-reinforced UHPC composites: Constitutive model and effects of steel fibers, loading patterns, and rebar sizes. Composites Part B, 158, 269–278. https://doi.org/10.1016/j.compositesb.2018.09.091
Kaklauskas, G. (2004). Flexural layered deformational model of reinforced concrete members. Magazine of Concrete Research, 56(10), 575–584. https://doi.org/10.1680/macr.2004.56.10.575
Kaklauskas, G., & Ghaboussi, J. (2001). Stress-strain relations for cracked tensile concrete from RC beam tests. ASCE Journal of Structural Engineering, 127(1), 64–73. https://doi.org/10.1061/(ASCE)0733-9445(2001)127:1(64)
Kaklauskas, G., & Gribniak, V. (2011). Eliminating shrinkage effect from moment-curvature and tension-stiffening relationships of reinforced concrete members. ASCE Journal of Structural Engineering, 137(12), 1460–1469. https://doi.org/(ASCE)ST.1943-541X.0000395
Kaklauskas, G., & Gribniak, V. (2016). Hybrid tension stiffening approach for decoupling shrinkage effect in cracked reinforced concrete members. ASCE Journal of Engineering Mechanics, 142(11), Article 04016085. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001148
Kaklauskas, G., & Sokolov, A. (2021). A peculiar value of M to Mcr ratio: Reconsidering assumptions of curvature analysis of reinforced concrete beams. Applications in Engineering Science, 7, Article 100053. https://doi.org/10.1016/j.apples.2021.100053
Kaklauskas, G., Gribniak, V., Salys, D., Sokolov, A., & Meskenas, A. (2011). Tension stiffening model attributed to tensile reinforcement for concrete flexural members. Procedia Engineering, 14, 1433–1438. https://doi.org/10.1016/j.proeng.2011.07.180
Kaklauskas, G., Gribniak, V., Jakubovskis, R., Gudonis, E., Salys, D., & Kupliauskas, R. (2012). Serviceability analysis of flexural reinforced concrete members. Journal of Civil Engineering and Management, 18(1), 24–29. https://doi.org/10.3846/13923730.2011.643553
Kaklauskas, G., Sokolov, A., Shakeri, A., Ng, P. L., & Barros J. A. O. (2022). Curvature-based analysis of concrete beams reinforced with steel bars and fibres. Structural Engineering and Mechanics, 81(3), 349–365. https://doi.org/10.12989/sem.2022.81.3.349
Kaklauskas, G., Sokolov, A., & Barros, J. A. O. (2024). A design methodology for fiber reinforced concrete elements in serviceability conditions integrating tension softening and stiffening effects. Engineering Structures, 311, Article 118199. https://doi.org/10.1016/j.engstruct.2024.118199
Kumar, V. S., Indira, P. V., & Ganesan, N. (2019). Tension stiffening and cracking behaviour of hybrid fibre reinforced ternary blend geopolymer concrete. Journal of Structural Engineering, 46(4), 257–266.
Lackner, R., & Mang, H. A. (2003). Scale transition in steel-concrete interaction. Part I: Model. ASCE Journal of Engineering Mechanics, 129(4), 393–402. https://doi.org/10.1061/(ASCE)0733-9399(2003)129:4(393)
Lee, J. D. (2022). The effect of tension stiffening in moment-curvature responses of prestressed concrete members. Engineering Structures, 257, Article 114043. https://doi.org/10.1016/j.engstruct.2022.114043
Martin, M. P., Rangel, C. S., Amario, M., Lima, J. M. F., Lima, P. R. L., & Filho, R. D. T. (2020). Modelling of tension stiffening effect in reinforced recycled concrete. Revista IBRACON de Estruturas e Materiais, 13(6), Article e13605. https://doi.org/10.1590/S1983-41952020000600005
Meskenas, A., Ramanauskas, R., Sokolov, A., Bacinskas, D., & Kaklauskas, G. (2021). Residual stress-strain relations inversely derived from experimental moment-curvature response of RC beams with fibres compared to the recommendations of design codes. Structures, 34, 3363–3375. https://doi.org/10.1016/j.istruc.2021.09.070
Ng, P. L., Barros, J. A. O., Kaklauskas, G, & Lam J. Y. K. (2020). Deformation analysis of fiber-reinforced polymer reinforced concrete beams by tension-stiffening approach. Composite Structures, 234, Article 111664. https://doi.org/10.1016/j.compstruct.2019.111664
Pulatsu, B., Erdogmus, E., Lourenco, P. B., Lemos, J.V., & Tuncay, K. (2021). Numerical modeling of the tension stiffening in reinforced concrete members via discontinuum models. Computational Particle Mechanics, 8, 423–436. https://doi.org/10.1007/s40571-020-00342-5
Sakalauskas, K., & Kaklauskas, G. (2023). Pure shear model for crack width analysis of reinforced concrete members. Scientific Reports, 13(1), Article 13883. https://doi.org/10.1038/s41598-023-41080-x
Scanlon, A., & Bischoff, P. H. (2008). Shrinkage restraint and loading history effects on deflection of flexural members. ACI Structural Journal, 105(4), 498–506. https://doi.org/10.14359/19864
Teng, L., Zhang, R., & Khayat, K. H. (2022). Tension-stiffening effect consideration for modeling deflection of cracked reinforced UHPC beams. Sustainability, 14(1), Article 415. https://doi.org/10.3390/su14010415
Torres, L., Lopez-Almansa, F., & Bozzo, L. M. (2004). Tension-stiffening model for cracked flexural concrete members. ASCE Journal of Structural Engineering, 130(8), 1242–1251. https://doi.org/10.1061/(ASCE)0733-9445(2004)130:8(1242)
Torres, L., Barris, C., Kaklauskas, G., & Gribniak, V. (2015). Modelling of tension-stiffening in bending RC elements based on equivalent stiffness of the rebar. Structural Engineering and Mechanics, 53(5), 997–1016. https://doi.org/10.12989/sem.2015.53.5.997
Wu, H. Q., & Gilbert, R. I. (2009). Modeling short-term tension stiffening in reinforced concrete prism using a continuum-based finite element model. Engineering Structures, 31(10), 2380–2391. https://doi.org/10.1016/j.engstruct.2009.05.012
American Concrete Institute. (2019). Building code requirements for structural concrete and commentary (ACI 318-19). https://www.concrete.org/store/productdetail.aspx?ItemID=318U19&Language=English&Units=US_Units
Aryanto, A., & Winata, B. J. (2021). Tension stiffening behavior of polypropylene fiber-reinforced concrete tension members. Journal of Engineering and Technological Sciences, 53(2), Article 210209. https://doi.org/10.5614/j.eng.technol.sci.2021.53.2.9
Bado, M. F., & Casas, J. R. (2021). A review of recent distributed optical fiber sensors applications for civil engineering structural health monitoring. Sensors, 21(5), Article 1818. https://doi.org/10.3390/s21051818
Bado, M. F., Casas, J. R., Dey, A., Berrocal, C. G., Kaklauskas, G., Fernandez, I., & Rempling, R. (2021a). Characterization of concrete shrinkage induced strains in internally-restrained RC structures by distributed optical fiber sensing. Cement and Concrete Composites, 120, Article 104058. https://doi.org/10.1016/j.cemconcomp.2021.104058
Bado, M. F., Casas, J. R., & Kaklauskas, G. (2021b). Distributed sensing (DOFS) in reinforced concrete members for reinforcement strain monitoring, crack detection and bond-slip calculation. Engineering Structures, 226, 24–29. https://doi.org/10.1016/j.engstruct.2020.111385
Bado, M. F., Tonelli, D., Poli, F., Zonta, D., & Casas, J. R. (2022). Digital twin for civil engineering systems: An exploratory review for distributed sensing updating. Sensors, 22(9), Article 3168. https://doi.org/10.3390/s22093168
Berrocal, C. G., Fernandez, I., Bado, M. F., Casas, J. R., & Rempling, R. (2021). Assessment and visualization of performance indicators of reinforced concrete beams by distributed optical fibre sensing. Structural Health Monitoring, 20(6), 2899–3452. https://doi.org/10.1177/1475921720984431
Bischoff, P. H. (2005). Reevaluation of deflection prediction for concrete beams. reinforced with steel and fiber reinforced polymer bars. ASCE Journal of Structural Engineering, 131(5), 752–767. https://doi.org/10.1061/(ASCE)0733-9445(2005)131:5(752)
CEB-FIP. (2020). CEB-FIP model code 2020: Model code for concrete structures. https://www.fib-international.org/publications/model-codes.html
Daud, R. A., Daud, S. A., & Azzawi, A. A. (2021). Tension stiffening evaluation of steel fiber concrete beams with smooth and deformed reinforcement. Journal of King Saud University – Engineering Sciences, 33, 147–152. https://doi.org/10.1016/j.jksues.2020.03.002
European Committee for Standardization. (2023). Eurocode 2: Design of concrete structures – Part 1-1: General rules and rules for buildings (EN 1992-1-1:2023). https://www.en-standard.eu/bs-en-1992-1-1-2023-eurocode-2-design-of-concrete-structures-general-rules-and-rules-for-buildings-bridges-and-civil-engineering-structures/
Fantilli, A. P., Orfeo, B., & Caldentey, A. P. (2021). The deflection of reinforced concrete beams containing recycled steel fibers. Structural Concrete, 22, 2089–2104. https://doi.org/10.1002/suco.202000729
Gilbert, R. I., & Warner, R. F. (1978). Tension stiffening in reinforced concrete slabs. ASCE Journal of the Structural Division, 104(12), 1885–1900. https://doi.org/10.1061/(ASCE)0733-9445(2007)133:6(899)
Gribniak, V., Perez, C. A., Kaklauskas, G., Rimkus, A., & Sokolov, A. (2016). Effect of arrangement of tensile reinforcement on flexural stiffness and cracking. Engineering Structures, 124, 418–428. https://doi.org/10.1016/j.engstruct.2016.06.026
Hung, C. C., Lee, H. S., & Chan, S. N. (2019). Tension-stiffening effect in steel-reinforced UHPC composites: Constitutive model and effects of steel fibers, loading patterns, and rebar sizes. Composites Part B, 158, 269–278. https://doi.org/10.1016/j.compositesb.2018.09.091
Kaklauskas, G. (2004). Flexural layered deformational model of reinforced concrete members. Magazine of Concrete Research, 56(10), 575–584. https://doi.org/10.1680/macr.2004.56.10.575
Kaklauskas, G., & Ghaboussi, J. (2001). Stress-strain relations for cracked tensile concrete from RC beam tests. ASCE Journal of Structural Engineering, 127(1), 64–73. https://doi.org/10.1061/(ASCE)0733-9445(2001)127:1(64)
Kaklauskas, G., & Gribniak, V. (2011). Eliminating shrinkage effect from moment-curvature and tension-stiffening relationships of reinforced concrete members. ASCE Journal of Structural Engineering, 137(12), 1460–1469. https://doi.org/(ASCE)ST.1943-541X.0000395
Kaklauskas, G., & Gribniak, V. (2016). Hybrid tension stiffening approach for decoupling shrinkage effect in cracked reinforced concrete members. ASCE Journal of Engineering Mechanics, 142(11), Article 04016085. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001148
Kaklauskas, G., & Sokolov, A. (2021). A peculiar value of M to Mcr ratio: Reconsidering assumptions of curvature analysis of reinforced concrete beams. Applications in Engineering Science, 7, Article 100053. https://doi.org/10.1016/j.apples.2021.100053
Kaklauskas, G., Gribniak, V., Salys, D., Sokolov, A., & Meskenas, A. (2011). Tension stiffening model attributed to tensile reinforcement for concrete flexural members. Procedia Engineering, 14, 1433–1438. https://doi.org/10.1016/j.proeng.2011.07.180
Kaklauskas, G., Gribniak, V., Jakubovskis, R., Gudonis, E., Salys, D., & Kupliauskas, R. (2012). Serviceability analysis of flexural reinforced concrete members. Journal of Civil Engineering and Management, 18(1), 24–29. https://doi.org/10.3846/13923730.2011.643553
Kaklauskas, G., Sokolov, A., Shakeri, A., Ng, P. L., & Barros J. A. O. (2022). Curvature-based analysis of concrete beams reinforced with steel bars and fibres. Structural Engineering and Mechanics, 81(3), 349–365. https://doi.org/10.12989/sem.2022.81.3.349
Kaklauskas, G., Sokolov, A., & Barros, J. A. O. (2024). A design methodology for fiber reinforced concrete elements in serviceability conditions integrating tension softening and stiffening effects. Engineering Structures, 311, Article 118199. https://doi.org/10.1016/j.engstruct.2024.118199
Kumar, V. S., Indira, P. V., & Ganesan, N. (2019). Tension stiffening and cracking behaviour of hybrid fibre reinforced ternary blend geopolymer concrete. Journal of Structural Engineering, 46(4), 257–266.
Lackner, R., & Mang, H. A. (2003). Scale transition in steel-concrete interaction. Part I: Model. ASCE Journal of Engineering Mechanics, 129(4), 393–402. https://doi.org/10.1061/(ASCE)0733-9399(2003)129:4(393)
Lee, J. D. (2022). The effect of tension stiffening in moment-curvature responses of prestressed concrete members. Engineering Structures, 257, Article 114043. https://doi.org/10.1016/j.engstruct.2022.114043
Martin, M. P., Rangel, C. S., Amario, M., Lima, J. M. F., Lima, P. R. L., & Filho, R. D. T. (2020). Modelling of tension stiffening effect in reinforced recycled concrete. Revista IBRACON de Estruturas e Materiais, 13(6), Article e13605. https://doi.org/10.1590/S1983-41952020000600005
Meskenas, A., Ramanauskas, R., Sokolov, A., Bacinskas, D., & Kaklauskas, G. (2021). Residual stress-strain relations inversely derived from experimental moment-curvature response of RC beams with fibres compared to the recommendations of design codes. Structures, 34, 3363–3375. https://doi.org/10.1016/j.istruc.2021.09.070
Ng, P. L., Barros, J. A. O., Kaklauskas, G, & Lam J. Y. K. (2020). Deformation analysis of fiber-reinforced polymer reinforced concrete beams by tension-stiffening approach. Composite Structures, 234, Article 111664. https://doi.org/10.1016/j.compstruct.2019.111664
Pulatsu, B., Erdogmus, E., Lourenco, P. B., Lemos, J.V., & Tuncay, K. (2021). Numerical modeling of the tension stiffening in reinforced concrete members via discontinuum models. Computational Particle Mechanics, 8, 423–436. https://doi.org/10.1007/s40571-020-00342-5
Sakalauskas, K., & Kaklauskas, G. (2023). Pure shear model for crack width analysis of reinforced concrete members. Scientific Reports, 13(1), Article 13883. https://doi.org/10.1038/s41598-023-41080-x
Scanlon, A., & Bischoff, P. H. (2008). Shrinkage restraint and loading history effects on deflection of flexural members. ACI Structural Journal, 105(4), 498–506. https://doi.org/10.14359/19864
Teng, L., Zhang, R., & Khayat, K. H. (2022). Tension-stiffening effect consideration for modeling deflection of cracked reinforced UHPC beams. Sustainability, 14(1), Article 415. https://doi.org/10.3390/su14010415
Torres, L., Lopez-Almansa, F., & Bozzo, L. M. (2004). Tension-stiffening model for cracked flexural concrete members. ASCE Journal of Structural Engineering, 130(8), 1242–1251. https://doi.org/10.1061/(ASCE)0733-9445(2004)130:8(1242)
Torres, L., Barris, C., Kaklauskas, G., & Gribniak, V. (2015). Modelling of tension-stiffening in bending RC elements based on equivalent stiffness of the rebar. Structural Engineering and Mechanics, 53(5), 997–1016. https://doi.org/10.12989/sem.2015.53.5.997
Wu, H. Q., & Gilbert, R. I. (2009). Modeling short-term tension stiffening in reinforced concrete prism using a continuum-based finite element model. Engineering Structures, 31(10), 2380–2391. https://doi.org/10.1016/j.engstruct.2009.05.012