Calculation of the Effective Section of Cracked Concrete Beams Based on Gradual Strain Distributions

1. Bischoff, P. H., and Paixao, R., “Tension Stiffening and Cracking of Concrete Reinforced with Glass Fiber Reinforced Polymer (GFRP) Bars,” Canadian Journal of Civil Engineering, V. 31, No. 4, 2004, pp. 579-588. doi: 10.1139/l04-02510.1139/l04-025 ↗

2. Gilbert, R. I., “Tension Stiffening in Lightly Reinforced Concrete Slabs,” Journal of Structural Engineering, ASCE, V. 133, No. 6, 2007, pp. 899-903. doi: 10.1061/(ASCE)0733-9445(2007)133:6(899)10.1061/(ASCE)0733-9445(2007)133:6(899) ↗

3. CEN, “Design of Concrete Structures – Part 1-1: General Rules and Rules for Buildings (Eurocode 2), European Standard BS EN 1992-1-1,” European Committee for Standardization, Brussels, Belgium, 2004.

4. fib, “fib Model Code for Concrete Structures 2010,” International Federation for Structural Concrete, Lausanne, Switzerland, 2013.10.1002/9783433604090 ↗

5. Bischoff, P. H., and Torres, L., “Rational Approach for Computing Long-Term Deflection of Reinforced Concrete,” ACI Structural Journal, V. 118, No. 2, Mar. 2021, pp. 215-224. doi: 10.14359/5172819210.14359/51728192 ↗

6. Sryh, L., and Forth, J., “Long-Term Flexural Behaviour of Cracked Reinforced Concrete Beams with Recycled Aggregate,” International Journal of Concrete Structures and Materials, V. 16, No. 1, 2022, pp. 1-12. doi: 10.1186/s40069-022-00512-010.1186/s40069-022-00512-0 ↗

7. Balakrishnan, S., and Murray, D. W., “Concrete Constitutive Model for NLFE Analysis of Structures,” Journal of Structural Engineering, ASCE, V. 114, No. 7, 1988, pp. 1449-1466. doi: 10.1061/(ASCE)0733-9445(1988)114:7(1449)10.1061/(ASCE)0733-9445(1988)114:7(1449) ↗

8. Massicotte, B.; Elwi, A. E.; and MacGregor, J. G., “Tension-Stiffening Model for Planar Reinforced Concrete Members,” Journal of Structural Engineering, ASCE, V. 116, No. 11, 1990, pp. 3039-3058. doi: 10.1061/(ASCE)0733-9445(1990)116:11(3039)10.1061/(ASCE)0733-9445(1990)116:11(3039) ↗

9. Prakhya, G. K. V., and Morley, C. T., “Tension-Stiffening and Moment-Curvature Relations of Reinforced Concrete Elements,” ACI Structural Journal, V. 87, No. 5, Sept.-Oct. 1990, pp. 597-605.10.14359/2680 ↗

10. Kwak, H. G., and Kim, D. Y., “Material Nonlinear Analysis of RC Shear Walls Subject to Monotonic Loads,” Engineering Structures, V. 26, No. 11, 2004, pp. 1517-1533. doi: 10.1016/j.engstruct.2004.05.01310.1016/j.engstruct.2004.05.013 ↗

11. Stramandinoli, R. S. B., and La Rovere, H. L., “An Efficient Tension Stiffening Model for Nonlinear Analysis of Reinforced Concrete,” Engineering Structures, V. 30, No. 7, 2008, pp. 2069-2080. doi: 10.1016/j.engstruct.2007.12.02210.1016/j.engstruct.2007.12.022 ↗

12. Salvatore, W.; Buratti, G.; Maffei, B.; and Valentini, R., “Dual-Phase Steel Re-Bars for High-Ductile R.C. Structures, Part 2: Rotational Capacity of Beams,” Engineering Structures, V. 29, No. 12, 2007, pp. 3333-3341. doi: 10.1016/j.engstruct.2007.09.00310.1016/j.engstruct.2007.09.003 ↗

13. Morelli, F.; Amico, C.; Salvatore, W.; Squeglia, N.; and Stacul, S., “Influence of Tension Stiffening on the Flexural Stiffness of Reinforced Concrete Circular Sections,” Materials (Basel), V. 10, No. 6, 2017, pp. 669-685. doi: 10.3390/ma1006066910.3390/ma10060669 ↗

14. Lee, J. D., “The Effect of Tension Stiffening in Moment-Curvature Responses of Prestressed Concrete Members,” Engineering Structures, V. 257, 2022, p. 114043 doi: 10.1016/j.engstruct.2022.11404310.1016/j.engstruct.2022.114043 ↗

15. Alam, M. S., and Hussein, A., “Idealized Tension Stiffening Model for Finite Element Analysis of Glass Fiber Reinforced Polymer (GFRP) Reinforced Concrete Members,” Structures, V. 24, 2020, pp. 351-356. doi: 10.1016/j.istruc.2020.01.03310.1016/j.istruc.2020.01.033 ↗

16. Kwak, H. G., and Song, J. Y., “Cracking Analysis of RC Members Using Polynomial Strain Distribution Functions,” Engineering Structures, V. 24, No. 4, 2002, pp. 455-468. doi: 10.1016/S0141-0296(01)00112-210.1016/S0141-0296(01)00112-2 ↗

17. Yankelevsky, D. Z.; Jabareen, M.; and Abutbul, A. D., “One-Dimensional Analysis of Tension Stiffening in Reinforced Concrete with Discrete Cracks,” Engineering Structures, V. 30, No. 1, 2008, pp. 206-217. doi: 10.1016/j.engstruct.2007.03.01310.1016/j.engstruct.2007.03.013 ↗

18. Wu, H. Q., and Gilbert, R. I., “Modeling Short-Term Tension Stiffening in Reinforced Concrete Prisms Using a Continuum-Based Finite Element Model,” Engineering Structures, V. 31, No. 10, 2009, pp. 2380-2391. doi: 10.1016/j.engstruct.2009.05.01210.1016/j.engstruct.2009.05.012 ↗

19. Yang, S. Y.; Liu, X. L.; and Leng, Y. B., “Prediction of Flexural Deformation of a Corroded RC Beam with a Polynomial Tension-Stiffening Model,” Journal of Structural Engineering, ASCE, V. 139, No. 6, 2013, pp. 940-948. doi: 10.1061/(ASCE)ST.1943-541X.000070410.1061/(ASCE)ST.1943-541X.0000704 ↗

20. Sturm, A. B.; Visintin, P.; and Oehlers, D. J., “Time-Dependent Serviceability Behavior of Reinforced Concrete Beams: Partial Interaction Tension Stiffening Mechanics,” Structural Concrete, V. 19, No. 2, 2018, pp. 508-523. doi: 10.1002/suco.20170002110.1002/suco.201700021 ↗

21. Manfredi, G., and Pecce, M., “A Refined RC Beam Element Including Bond–Slip Relationship for the Analysis of Continuous Beams,” Computers & Structures, V. 69, No. 1, 1998, pp. 53-62. doi: 10.1016/S0045-7949(98)00078-910.1016/S0045-7949(98)00078-9 ↗

22. Gilbert, R. I., and Ranzi, G., Time-Dependent Behaviour of Concrete Structures, Spon Press, London, UK, 2011.10.1201/9781482288711 ↗

23. Castel, A.; Vidal, T.; and François, R., “Effective Tension Active Cross-Section of Reinforced Concrete Beams after Cracking,” Materials and Structures, V. 39, No. 1, 2006, pp. 115-126. doi: 10.1617/s11527-005-9038-z10.1617/s11527-005-9038-z ↗

24. Galkovski, T.; Mata-Falcón, J.; and Kaufmann, W., “Effective Reinforcement Ratio of RC Beams: Validation of Modelling Assumptions with High-Resolution Strain Data,” Structural Concrete, V. 23, No. 3, 2022, pp. 1353-1369. doi: 10.1002/suco.20210073910.1002/suco.202100739 ↗

25. Carbonell-Màrquez, J. F.; Gil-Martìn, L. M.; Fernàndez-Ruìz, M. A.; and Hernàndez-ontes, E., “Effective Area in Tension Stiffening of Reinforced Concrete Piles Subjected to Flexure According to Eurocode 2,” Engineering Structures, V. 76, No. 1, 2014, pp. 62-74. doi: 10.1016/j.engstruct.2014.06.04110.1016/j.engstruct.2014.06.041 ↗

26. Behzad, M.; Meghdari, A.; and Ebrahimi, A., “A Linear Theory for Bending Stress–Strain Analysis of a Beam with an Edge Crack,” Engineering Fracture Mechanics, V. 75, No. 16, 2008, pp. 4695-4705. doi: 10.1016/j.engfracmech.2008.06.02810.1016/j.engfracmech.2008.06.028 ↗

27. Murray, A.; Gilbert, R. I.; and Castel, A., “A New Approach to Modeling Tension Stiffening in Reinforced Concrete,” ACI Structural Journal, V. 115, No. 1, Jan. 2018, pp. 127-137. doi: 10.14359/5170095210.14359/51700952 ↗

28. Castel, A.; Vidal, T.; and François, R., “Finite-Element Modeling to Calculate the Overall Stiffness of Cracked Reinforced Concrete Beams,” Journal of Structural Engineering, ASCE, V. 138, No. 7, 2012, pp. 889-898. doi: 10.1061/(ASCE)ST.1943-541X.000052010.1061/(ASCE)ST.1943-541X.0000520 ↗

29. Fu, C.; Zhu, Y.; and Wang, Y., “Stiffness Assessment of Cracked Post-Tensioned Concrete Beams with Unbonded Tendons Based on the Cracking Pattern,” Engineering Structures, V. 214, 2020, p. 110599. doi: 10.1016/j.engstruct.2020.11059910.1016/j.engstruct.2020.110599 ↗

30. ACI Committee 318, “Building Code Requirements for Structural Concrete (ACI 318-19) and Commentary (ACI 318R-19),” American Concrete Institute, Farmington Hills, MI, 2019, 623 pp.

31. Castel, A.; Gilbert, R. I.; and Ranzi, G., “Instantaneous Stiffness of Cracked Reinforced Concrete Including Steel-Concrete Interface Damage and Long-Term Effects,” Journal of Structural Engineering, ASCE, V. 140, No. 6, 2014, pp. 1-9. doi: 10.1061/(ASCE)ST.1943-541X.000095410.1061/(ASCE)ST.1943-541X.0000954 ↗

32. Xu, T.; Zhu, L.; Castel, A.; and Gilbert, R. I., “Assessing Immediate and Time-Dependent Instantaneous Stiffness of Cracked Reinforced Concrete Beams Using Residual Cracks,” Journal of Structural Engineering, ASCE, V. 144, No. 4, 2018, pp. 1-12. doi: 10.1061/(ASCE)ST.1943-541X.000200910.1061/(ASCE)ST.1943-541X.0002009 ↗