Civil and Project journal

Nonlinear finite element modeling of reinforced concrete beams

https://doi.org/10.22034/cpj.2026.573959.1429
Volume 8, Issue 3 - Serial Number 85
June 2026
Pages 11-26
Civil and Project journal

Document Type : Research Article

Authors

Morteza Amooie 1
Mahdieh Sabbaghian 2
Ali kheyroddin 3
Mohammadreza Sabbaghian 4

1 Faculty of Civil Engineering, University of Guilan, Guilan, Iran.

2 PhD Student in Civil Engineering, Faculty of Civil Engineering and Environment, Amirkabir University of Technology, Tehran, Iran

3 3. Distinguished Professor, Faculty of Civil Engineering, University of Semnan, Semnan

4 MSc in Civil Engineering, Faculty of Civil, Water and Environmental Engineering, Shahid Beheshti University, Tehran, Iran.

Abstract
Nonlinear behavior of reinforced concrete beams is complex due to the formation of multiple cracks and the interaction of various internal forces. Therefore, accurate prediction of this behavior requires experimental investigations and numerical modeling based on nonlinear finite element analysis. The objective of this study is to present effective and reliable approaches for modeling reinforced concrete beams in the software Vector2, as one of the widely used tools for concrete structural analysis. For this purpose, four rectangular reinforced concrete beams selected from existing experimental studies are simulated using Vector2. The influence of key modeling parameters on the accuracy of numerical results is investigated and their optimal values are identified. The analysis results indicate that the finite element model employed in Vector2 is capable of predicting load–displacement curves and cracking patterns with satisfactory accuracy. Moreover, the proposed approach is able to simulate beam behavior governed by both flexural and shear failure mechanisms.

Keywords

Reinforced concrete beams
Modified Compression Field Theory
Distributed Stress Field
Nonlinear finite element analysis
Vector2
Subjects
ع
[1] P. Bernardi, R. Cerioni, and E. Michelini, “A nonlinear procedure for the analysis of RC
beams,” Procedia Structural Integrity, vol. 2, pp. 2873–2880, Jan. 2016, doi:
10.1016/J.PROSTR.2016.06.359.
[2] M. F. Giberson, “Two Nonlinear Beams With Definitions of Ductility,” Journal of the
Structural Division, vol. 95, no. 2, pp. 137–157, Feb. 1969, doi: 10.1061/JSDEAG.0002184.
[3] A. Calabrese, J. P. Almeida, and R. Pinho, “Numerical Issues in Distributed Inelasticity
Modeling of RC Frame Elements for Seismic Analysis,” Journal of Earthquake
Engineering, vol. 14, no. SUPPL. 1, pp. 38–68, 2010, doi: 10.1080/13632461003651869.
[4] F. J. Vecchio, “Disturbed Stress Field Model for Reinforced Concrete: Formulation,”
Journal of Structural Engineering, vol. 126, no. 9, pp. 1070–1077, Sep. 2000, doi:
10.1061/(ASCE)0733-9445(2000)126:9(1070).
[5] F. J. Vecchio and M. P. Collins, “Compression Response of Cracked Reinforced Concrete,”
Journal of Structural Engineering, vol. 119, no. 12, pp. 3590–3610, Dec. 1993, doi:
10.1061/(ASCE)0733-9445(1993)119:12(3590).
[6] E. Hognestad, “A study of combined bending axial load in reinforced concrete members,”
in Bulletin Series No. 399, Engineering Experimental Station: The University of Illinois,
1951.
[7] D. C. Kent and R. Park, “Flexural Members with Confined Concrete,” Journal of the
Structural Division, vol. 97, no. 7, pp. 1969–1990, Jul. 1971, doi:
10.1061/JSDEAG.0002957.
[8] H. B. Kupfer and K. H. Gerstle, “Behavior of Concrete under Biaxial Stresses,” Journal of
the Engineering Mechanics Division, vol. 99, no. 4, pp. 853–866, Aug. 1973, doi:
10.1061/JMCEA3.0001789.
[9] F. E. Richart, A. Brandtzaeg, and R. L. Brown, “The failure of plain and spirally reinforced
concrete in compression,” Urbana: University of Illinois., 1929.
[10] W. Ramberg and W. R. Osgood, “Description of stress–strain curves by three parameters,”
in National Advisory Committee For Aeronautics, Washington, 1943, p. Technical Note
No. 902.
[11] F. Vecchio, “Towards Cyclic Load Modeling of Reinforced Concrete,” ACI Struct J, vol.
96, no. 2, pp. 193–202, 1999.
[12] E. C. Bentz, “Explaining the Riddle of Tension Stiffening Models for Shear Panel
Experiments,” Journal of Structural Engineering, vol. 131, no. 9, pp. 1422–1425, Sep. 2005,
doi: 10.1061/(ASCE)0733-9445(2005)131:9(1422).
Civil and Project Journal, 2026, 8(3), 11-26
https://doi.org/10.22034/cpj.2026.573959.1429
26
[13] M. Seckin, “Hysteretic Behavior of Cast in-place Exterior Beam Column-slab
Subassemblies,” University of Toronto, 1981.
[14] F. J. Vecchio and W. Shim, “Experimental and Analytical Reexamination of Classic
Concrete Beam Tests,” Journal of Structural Engineering, vol. 130, no. 3, pp. 460–469, Mar.
2004, doi: 10.1061/(ASCE)0733-9445(2004)130:3(460).
  • Receive Date 06 December 2025
  • Revise Date 25 December 2025
  • Accept Date 08 January 2026
  • First Publish Date 07 February 2026
  • Publish Date 22 May 2026

Home

Submit

Contact Us

Forthcoming Articles