Influence of Localized Beam Cracking Representation on Nonlinear Seismic Performance of RC Moment Frames

Document Type : Original Article

Authors

1 Department of Civil Engineering, Se.C., Islamic Azad University, Semnan, Iran

2 Faculty of Civil Engineering, Babol Noshirvani University of Technology, Babol, Iran

Abstract

Cracking in reinforced concrete (RC) members is a key mechanism governing stiffness degradation and seismic response of structural systems. This study examines the influence of different beam-cracking modeling approaches on the nonlinear seismic behavior of RC moment-resisting frames. Three RC frames with 3, 6, and 9 stories are analyzed under three modeling schemes: (1) uncracked elastic model, (2) code-based effective stiffness reduction model, and (3) localized cracking model distributed along beam elements. In the localized formulation, stiffness degradation is defined in a position-dependent manner, allowing non-uniform reduction along the member length to better represent crack concentration in plastic hinge regions and mid-span zones. This overcomes a major limitation of conventional effective stiffness methods, which assume uniform stiffness reduction and cannot capture spatial damage distribution. Nonlinear static (pushover) and nonlinear time-history analyses are performed using Imperial Valley, Duzce, and Northridge ground motions within a nonlinear analysis framework. Results show that cracking representation significantly affects seismic response. Considering cracking reduces initial stiffness, increases fundamental period, and decreases base shear capacity. In the code-based model, base shear capacity decreases by up to 32%, while roof displacement increases by 21%, 26%, and 8% for the 3-, 6-, and 9-story frames, respectively. The localized cracking model yields responses between the uncracked and code-based models and consistently predicts lower displacements than the latter. Crack distribution also significantly influences bending moments, plastic hinge formation, and energy dissipation. Overall, the localized cracking model provides an improved representation of stiffness degradation effects and a practical simplified framework for nonlinear seismic assessment of RC frames.

Keywords

Main Subjects

References

  1. Chen, G., Baker, G., Hunt, G. W. Computational approach to localization using global energy minimization. Computers & Structures, 2000; 78: 529–536. doi:10.1016/S0045-7949(00)00043-2.
  2. Degroot, A. K., Kusters, G. M. A., Monnier, T. Concrete mechanics. Part B: Numerical modelling of bond slip behavior. Washington, D.C. (US): NASA; 1981. Report No.: 82.
  3. Eligehausen, R., Popov, E. P., Bertero, V. V. Local bond stress-slip relationships of deformed bars under generalized excitations: experimental results and analytical model. Berkeley (CA): University of California, Berkeley; 1983. Report No.: UCB/EERC-83/23.
  4. Kwak, H.-G., Filippou, F. Finite element analysis of reinforced concrete structures under monotonic loads. Berkeley (CA): University of California, Berkeley; 1990. Report No.: UCB/SEMM-90/14.
  5. Kwak, H.-G., Filippou, F. Finite element analysis of reinforced concrete structures under monotonic and cyclic loads. In: 10th World Conference in Earthquake Engineering; 1992 Jul 19‒24; Madrid, Spain. p. 4227–4232.
  6. Kwak, H.-G., Filippou, F. A New Reinforcing Steel Model With Bond-Slip. Structural Engineering and Mechanics, 1995; 3: 299–312. doi:10.12989/sem.1995.3.4.299.
  7. Monti, G., Filippou, F., Spacone, E. Analysis of hysteretic behavior of anchored reinforcing bars. ACI Structural Journal, 1997; 94: 248–261. doi:10.14359/477
  8. Monti, G., Filippou Filip, C., Spacone, E. Finite Element for Anchored Bars under Cyclic Load Reversals. Journal of Structural Engineering, 1997; 123: 614–623. doi:10.1061/(ASCE)0733-9445(1997)123:5(614).
  9. Monti, G., Spacone, E. Reinforced Concrete Fiber Beam Element with Bond-Slip. Journal of Structural Engineering, 2000; 126: 654–661. doi:10.1061/(ASCE)0733-9445(2000)126:6(654).
  10. Spacone, E., Filippou, F. C., Taucer, F. F. Fibre Beam–Column Model For Non-Linear Analysis of R/C Frames: Part I. Formulation. Earthquake Engineering & Structural Dynamics, 1996; 25: 711–725. doi:10.1002/(SICI)1096-9845(199607)25:7<711::AID-EQE576>3.0.CO;2-9.
  11. Gan, Y. Bond stress and slip modeling in nonlinear finite element analysis of reinforced concrete structures [Master's Thesis]. Toronto (CA): University of Toronto; 2000.
  12. Lowes, L., Moehle, J., Govindjee, S. Concrete-steel bond model for use in finite element modeling of reinforced concrete structures. ACI Structural Journal, 2004; 101: 501–511. doi:10.14359/13336.
  13. Jendele, L., Cervenka, J. Finite element modelling of reinforcement with bond. Computers & Structures, 2006; 84: 1780–1791. doi:10.1016/j.compstruc.2006.04.010.
  14. Kwak, H.-G., Kim, J.-K. Implementation of bond-slip effect in analyses of RC frames under cyclic loads using layered section method. Engineering Structures, 2006; 28: 1715–1727. doi:10.1016/j.engstruct.2006.03.003.
  15. Beconcini, M. L., Croce, P., Formichi, P. Influence of bond-slip on the behaviour of reinforced concrete beam to column joints-Tailor Made Concrete Structures: New Solutions for our Society. In: International FIB Symposium; 2008 May 19‒21; Amsterdam, Netherlands. p. 533–539.
  16. Zhou, Y. D., Cheuk, C. Y., Tham, L. G. An embedded bond-slip model for finite element modelling of soil–nail interaction. Computers and Geotechnics, 2009; 36: 1090–1097. doi:10.1016/j.compgeo.2009.03.002.
  17. Kwak, H.-G., Kim, S.-P. Simplified monotonic moment–curvature relation considering fixed-end rotation and axial force effect. Engineering Structures, 2010; 32: 69–79. doi:10.1016/j.engstruct.2009.08.017.
  18. Murcia-Delso, J., Stavridis, A., Shing, B. Modeling the bond-slip behavior of confined large-diameter reinforcing bars. In: 3rd International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, COMPDYN; 2011 May 25‒28; Corfu, Greece. p. 1–14.
  19. Liang, X. An investigation of bond-slip behavior of reinforcing steel subjected to inelastic strains [Master's Thesis]. Ames (IA): Iowa State University; 2013.
  20. Coccia, S., Di Maggio, E., Rinaldi, Z. Bond slip model in cylindrical reinforced concrete elements confined with stirrups. International Journal of Advanced Structural Engineering (IJASE), 2015; 7: 365–375. doi:10.1007/s40091-015-0104-7.
  21. Shafaie, J., Hosseini, A., Marefat, M. 3D finite element modelling of bond-slip between rebar and concrete in pull-out test. In: 3rd International Conference on Concrete & Development, Iran; 2009 April 27; Tehran, Iran. doi:10.13140/2.1.2012.1605.
  22. Alijani, A., Khomami Abadi, M., Razzaghi, J. A new technique in the modal analysis of cracked reinforced concrete (RC) beams through the finite element method. Journal of Structural and Construction Engineering, 2020; 7: 5–30. doi:10.22065/JSCE.2018.127880.1535.
  23. Khademalrasoul, A. Simulation of the effect of internal heterogeneous linear and curved boundaries on crack propagation path in mixed mode using the level set method. Journal of Structural and Construction Engineering, 2017; 4: 42–54. doi:10.22065/jsce.2017.67302.1001.
  24. Hakimi, A., Moslemi, H. Modeling of Analysis Crack using Adaptive Finite Element Method Via Stress Intensity Factor Error Estimation. Journal of Structural and Construction Engineering, 2015; 2: 57–68.
  25. Dehghan Manshadi, S. M., Nategh, S., Khojasteh, A., Rahimian, M. Fracture Modes of an Annular Crack in a Transversely Isotropic Solid. Amirkabir Journal of Civil Engineering, 2018; 50: 855–864. doi:10.22060/ceej.2017.12713.5255.
  26. Miri, M., Rakhshanimehr, M., Miri, F. The effect of Cover, Pressure Strength, and bars corrosion on Cracking of Reinforced Concrete Structures. Amirkabir Journal of Civil Engineering, 2017; 49: 251–262. doi:10.22060/ceej.2016.693.
  27. Hajighasemali, S., Ramezanianpour, A. A., Kashefizadeh, M. Analytical Modeling of Load-Deflection Curve in Reinforced Concrete Beams. Amirkabir Journal of Civil Engineering, 2016; 47: 63–70. doi:10.22060/ceej.2016.614.
  28. Broujerdian, V., Sherafati, A., Karimpour, H. Effect of Crack Cohesive Stresses on the Load-Deformation Response of Reinforced Concrete Beams. Amirkabir Journal of Civil Engineering, 2018; 50: 89–96. doi:10.22060/ceej.2017.11366.5012.
  29. Okamura, H., Maekawa, K. Nonlinear Analysis and Constitutive Models of Reinforced Concrete. 1st ed. Tokyo (JP): Giho-do Press; 1991.
  30. Shima, H., Chou, L., Okamura, H. Micro and Macro Models for Bond Behavior in Reinforced Concrete. Journal of the Faculty of Engineering, Univ. of Tokyo, 1987; 39: 133–194.
  31. Maekawa, K., Okamura, H., Pimanmas, A. Non-Linear Mechanics of Reinforced Concrete. 1st ed. London (UK): CRC Press; 2003. doi:10.1201/9781482288087.
  32. Soltani, M., Maekawa, K. Path-dependent mechanical model for deformed reinforcing bars at RC interface under coupled cyclic shear and pullout tension. Engineering Structures, 2008; 30: 1079–1091. doi:10.1016/j.engstruct.2007.06.013.
  33. Birely, A. C., Lowes, L. N., Lehman, D. E. A model for the practical nonlinear analysis of reinforced-concrete frames including joint flexibility. Engineering Structures, 2012; 34: 455–465. doi:10.1016/j.engstruct.2011.09.003.
  34. Vandecruys, E., Hendriks, M. A. N., van de Velde, M., Lombaert, G., Verstrynge, E. Dynamic stiffness parameter assessment of cracked reinforced concrete beams: A numerical and experimental study. Engineering Structures, 2024; 318: 118758. doi:10.1016/j.engstruct.2024.118758.
  35. Kordtabar, B., Dehestani, M., Yazdanpanah, O., Hasanzadeh, A. Time-dependent seismic fragility and serviceability assessment of reinforced concrete frames under chloride-induced corrosion. Scientific Reports, 2025; 15: 40575. doi:10.1038/s41598-025-24197-z.
  36. Zhang, H. Y., Li, Q. Y., Kodur, V., Lv, H. R. Effect of cracking and residual deformation on behavior of concrete beams with different scales under fire exposure. Engineering Structures, 2021; 245: 112886. doi:10.1016/j.engstruct.2021.112886.
  37. Dancygier, A. N., Karinski, Y. S. Effect of cracking localization on the structural ductility of normal strength and high strength reinforced concrete beams with steel fibers. International Journal of Protective Structures, 2019; 10: 457–469. doi:10.1177/2041419618824609.
  38. Namdar, A., Darvishi, E., Feng, X., Zakaria, I., Mat Yahaya, F. Effect of flexural crack on plain concrete beam failure mechanism: A numerical simulation. Fracture and Structural Integrity, 2016; 10: 168–181. doi:10.3221/IGF-ESIS.36.17.
  39. Karinski, Y. S., Dancygier, A. N., Gebreyesus, Y. Y. Probabilistic model for cracking localization in reinforced fibrous concrete beams. Journal of Engineering Mathematics, 2024; 144: 23. doi:10.1007/s10665-023-10330-2.
  40. Fu, C., Zhu, Y., Tong, D. Stiffness Assessment of Cracked Reinforced Concrete Beams Based on a Fictitious Crack Model. KSCE Journal of Civil Engineering, 2021; 25: 516–528. doi:10.1007/s12205-020-2056-0.
  41. Forouzan, S. Effect of bond-slip on the ductility of reinforced concrete beams [Thesis]. Babol (IR): Babol Noshirvani University of Technology; 2016.
  42. Ayoub, A., Filippou Filip, C. Mixed Formulation of Bond-Slip Problems under Cyclic Loads. Journal of Structural Engineering, 1999; 125: 661–671. doi:10.1061/(ASCE)0733-9445(1999)125:6(661).
  43. Gergely, P., Lutz, L. A. Maximum Crack Width in Reinforced Concrete Flexural Members. 318Reference, 2005; 10: 87–117. doi:10.14359/17348.
  44. Bayrak, O., Sheikh, S. High-strength concrete columns under simulated earthquake loading. 1997; 94: 708–722.
  45. PEER ground motion database. Pacific Earthquake Engineering Research Center. 2010. Available online: https://ngawest2.berkeley.edu/. (Accessed December 2010).
  46. Shayanfar, J., Akbarzadeh Bengar, H. Nonlinear analysis of RC frames considering shear behaviour of members under varying axial load. Bulletin of Earthquake Engineering, 2017; 15: 2055–2078. doi:10.1007/s10518-016-0060-z.
  47. Sadeghpour Haji, M., Niknam, R., Shayanfar, J. ANN-Based Modeling of Shear Behavior of Reinforced Concrete Columns under Constant Axial Loads. Civil Engineering and Applied Solutions, 2026; 2: 28–48. doi:10.22080/ceas.2025.30228.1050.
  48. Shayanfar, S., Ghasemi Naghibdehi, M., Shayanfar, J. Data-Driven Prediction of FRP Confinement Efficiency in Concrete Columns: Incorporating Corner Radius and Aspect Ratio Effects. Civil Engineering and Applied Solutions, 2026; 2: 1–15. doi:10.22080/ceas.2026.30750.1059.
  49. Shayanfar, S., Ghasemi Naghibdehi, M., Shayanfar, J. Data-Driven Predictive Formulation for FRP-Confined Circular Concrete Columns. Civil Engineering and Applied Solutions, 2027; 3: 25–36. doi:10.22080/ceas.2026.30751.1060.
  50. Javad, S., Meysam, O., Mahdi, N. Analysis-oriented model for seismic assessment of RC jacket retrofitted columns. Steel and Composite Structures, An International Journal, 2020; 37: 371–390. doi:10.12989/scs.2020.37.3.371.
Civil Engineering and Applied Solutions
Volume 3, Issue 2
April 2027
Pages 102-121

Files

History

  • Receive Date: 06 June 2026
  • Revise Date: 28 June 2026
  • Accept Date: 01 August 2026
  • First Publish Date: 01 August 2026

Share

How to cite

Statistics