Analysis of Axial Stress Distribution in Reinforced Concrete Column Considering ACI Guidelines

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Title: Analysis of Axial Stress Distribution in Reinforced Concrete Column Considering ACI Guidelines

Author(s): Alexandre de Macêdo Wahrhaftig, Eduardo Márcio de Oliveira Lopes, and Larysa Neduzha

Publication: Structural Journal

Volume: 123

Issue: 4

Appears on pages(s): 179-190

Keywords: American Concrete Institute; axial stresses; creep; reinforced concrete (RC) column; shrinkage

DOI: 10.14359/51749553

Date: 7/1/2026

Abstract:
Slender reinforced concrete columns have been employed as components of telecommunication and internet infrastructure since the deployment of the system more than 30 years ago. The assessment of these structures must consider the time-dependent behavior of concrete. In this context, a numerical investigation is conducted to determine the critical buckling load and the stress distribution in sections subject to creep and shrinkage of concrete. The guidelines used are those from the American Concrete Institute. It is concluded that the maximum stress induced in the reinforcement is 1.14% of the steel yield stress. Therefore, no yielding of the reinforcement is registered to the examined case, which ensures safety against permanent deformation. During the elapsed time of 7500 days, the modulus of elasticity of concrete decreased by 53% and the critical buckling load by 40%. The results obtained can be applied to similar cases through the slenderness index and the reinforcement ratio.

Related References:

1. Shvets, A.; Murawski, K.; and Fedorov, Y., “Analytical Determination of Critical Forces during Buckling of Systems Consisting of Two Pinned Connected Rods,” Meccanica, V. 60, No. 2, 2025, pp. 441-455. doi: 10.1007/s11012-025-01941-3

2. Pickett, G., “The Effect of Change in Moisture Content on the Creep of Concrete under a Sustained Load,” ACI Journal Proceedings, V. 38, Feb. 1942, pp. 333-355. doi: 10.14359/8607

3. Magalhães, K. M. M.; Brasil, R. M. L. R. F.; Wahrhaftig, A. M.; Siqueira, G. H.; Bondarenko, I.; and Neduzha, L., “Influence of Atmospheric Humidity on the Critical Buckling Load of Reinforced Concrete Columns,” International Journal of Structural Stability and Dynamics, V. 22, No. 1, 2022, p. 2250011. doi: 10.1142/S0219455422500110

4. Havlásek, P.; Šmilauer, V.; Dohnalová, L.; and Sovják, R., “Shrinkage-Induced Deformations and Creep of Structural Concrete: 1-Year Measurements and Numerical Prediction,” Cement and Concrete Research, V. 144, 2021, p. 106402. doi: 10.1016/j.cemconres.2021.106402

5. ACI Committee 318, “Building Code Requirements for Structural Concrete (ACI 318-19) and Commentary (ACI 318R-19) (Reapproved 2022),” American Concrete Institute, Farmington Hills, MI, 2019, 624 pp.

6. Euler, L., “De Curvis Elasticis, Additamentum I to His Methodus Inveniendi Lineas Curvas Maximi Minimive Proprietate Gaudentes,” Lausanne and Geneva, 1744, pp. 245-310.

7. Greenhill, A. G., “Determination of the Greatest Height Consistent with Stability That a Vertical Pole or Mast Can Be Made, and the Greatest Height to Which a Tree of Given Proportions Can Grow,” Proceedings of the Cambridge Philosophy Society, V. 1, No. 1, 1882, pp. 337-338. doi: 10.1051/jphystap:018820010033701

8. Strutt, J. W., (Lord Rayleigh), Theory of Sound, Dover Publications, New York, 1877.

9. Zienkiewicz, O. C., and Cheung, Y. K., The Finite Element Method in Structural and Continuum Mechanics, McGraw-Hill Book Co., Inc., New York, 1967.

10. Eisenberger, M., “Buckling Loads for Variable Cross-Section Members with Variable Axial Forces,” International Journal of Solids and Structures, V. 27, No. 2, 1991, pp. 135-143. doi: 10.1016/0020-7683(91)90224-4

11. Xie, Y.; Han, X.; Chen, B.; Ai, H.; and Wang, Z., “Study of Axial Compressive Stability of Lattice-Type Attached Support,” Journal of Constructional Steel Research, V. 226, 2025, p. 109311. doi: 10.1016/j.jcsr.2024.109311

12. Ergut, A., “Analysis of Transverse Vibration in a Concentrated Mass Rayleigh Pipe,” Symmetry, V. 17, No. 3, 2025, p. 371. doi: 10.3390/sym17030371

13. Abu-Hamd, M.; Abdel-Ghaffar, M. M.; and El-Samman, B. M., “Buckling Strength of Axially Loaded Cold Formed Built-Up I-Sections with and without Stiffened Web,” Ain Shams Engineering Journal, V. 9, No. 4, 2018, pp. 3151-3167. doi: 10.1016/j.asej.2017.11.004

14. Pinto-Cruz, M. C., “Analytical Solutions for Global Buckling Analysis of Regular Buildings: Inclusion of Local Shear Deformation of Walls,” Structures, V. 69, 2024, p. 107370. doi: 10.1016/j.istruc.2024.107370

15. Zeng, J.-J.; Chen, S.-P.; Zhuge, Y.; Gao, W.-Y.; Duan, Z.-J.; and Guo, Y.-C., “Three-Dimensional Finite Element Modeling and Theoretical Analysis of Concrete Confined with FRP Rings,” Engineering Structures, V. 234, 2021, p. 111966. doi: 10.1016/j.engstruct.2021.111966

16. Zeng, J.; Guo, Y.; Li, L.; and Chen, W., “Behavior and Three-Dimensional Finite Element Modeling of Circular Concrete Columns Partially Wrapped with FRP Strips,” Polymers, V. 10, No. 3, 2018, p. 253. doi: 10.3390/polym10030253

17. Wahrhaftig, A. M., “Time-Dependent Analysis of Slender, Tapered Reinforced Concrete Columns,” Steel and Composite Structures, V. 36, No. 2, 2020, pp. 229-247. doi: 10.12989/scs.2020.36.2.229

18. ACI Committee 209, “Prediction of Creep, Shrinkage, and Temperature Effects in Concrete Structures (ACI 209R-92) (Reapproved 2008),” American Concrete Institute, Farmington Hills, MI, 1992, 47 pp.

19. Behan, J. E., and O’Connor, C., “Creep Buckling of Reinforced Concrete Columns,” Journal of the Structural Division, ASCE,V. 108, No. 12, 1982, pp. 2799-2818. doi: 10.1061/JSDEAG.0006106

20. Mickleborough, N. C., and Gilbert, R. I., “Creep Buckling of Uniaxially Loaded Reinforced Concrete Columns,” Computer Analysis of Effects of Creep, Shrinkage, and Temperature Changes on Concrete Structures, SP-129, C. C. Fu and M. D. Daye, eds., American Concrete Institute, Farmington Hills, MI, 1991, pp. 39-55. doi: 10.14359/1254

21. Ma, W.; Tian, Y.; Zhao, H.; and Orton, S. L., “Time-Dependent Behavior of Reinforced Concrete Columns Subjected to High Sustained Loads,” Journal of Structural Engineering, V. 148, No. 10, 2022, p. 04022161. doi: 10.1061/(ASCE)ST.1943-541X.0003462

22. Bradford, M. A., and Gilbert, R. I., “Analysis of Circular RC Columns for short‐ and long‐term deformations,” Journal of Structural Engineering, ASCE, V. 118, No. 3, 1992, pp. 669-682. doi: 10.1061/(ASCE)0733-9445(1992)118:3(669)

23. Qu, Z.; Si, R.; Jia, P.; and Zhang, Y., “Creep and Relaxation Responses of Fly Ash Concrete: Linear and Nonlinear Cases,” Case Studies in Construction Materials, V. 17, 2022, p. e01562. doi: 10.1016/j.cscm.2022.e01562

24. Biscaia, H. C., “Experimental and Numerical Evaluations of the Bond Behaviour between Ribbed Steel Rebars and Concrete,” Archives of Civil and Mechanical Engineering, V. 23, No. 3, 2023, p. 159. doi: 10.1007/s43452-023-00704-9

25. Dezi, L.; Gara, F.; and Leoni, G., “Construction Sequence Modelling of Continuous Steel-Concrete Composite Bridge Decks,” Steel and Composite Structures, V. 6, No. 2, 2006, pp. 123-138. doi: 10.12989/scs.2006.6.2.123

26. Burlayenko, V. N.; Kouhia, R.; and Dimitrova, S. D., “One-Dimensional vs. Three-Dimensional Models in Free Vibration Analysis of Axially Functionally Graded Beams with Non-Uniform Cross-Sections,” Mechanics of Composite Materials, V. 60, No. 1, 2024, pp. 83-102. doi: 10.1007/s11029-024-10176-4

27. Bradford, M. A., “Shrinkage and Creep Response of Slender Reinforced Concrete Columns under Moment Gradient: Theory and Test Results,” Magazine of Concrete Research, V. 57, No. 4, 2005, pp. 235-246. doi: 10.1680/macr.2005.57.4.235

28. Kwak, H. G., and Kim, J. K., “Time-Dependent Analysis of RC Frame Structures Considering Construction Sequences,” Building and Environment, V. 41, No. 10, 2006, pp. 1423-1434. doi: 10.1016/j.buildenv.2005.05.013

29. Gilbert, R. I., and Ranzi, G., Time-Dependent Behaviour of Concrete Structures, CRC Press, Boca Raton, FL, 2010.

30. Murray, V., and Gilbert, R. I., “Effects of Creep on the Strength of Eccentrically-Loaded Slender Reinforced Concrete Columns,” Australian Journal of Structural Engineering, V. 16, No. 2, 2015, pp. 129-136. doi: 10.1080/13287982.2015.11465185

31. Kim, C. S., and Gong, Y., “Numerical Investigation of Creep and Shrinkage Effects on Minimum Reinforcement of Concentrically and Eccentrically Loaded RC Columns,” Engineering Structures, V. 174, 2018, pp. 509-525. doi: 10.1016/j.engstruct.2018.07.032

32. Eom, T. S.; Kim, C. S.; Zhang, X.; and Kim, J. Y., “Time-Dependent Deformations of Eccentrically Loaded Reinforced Concrete Columns,” International Journal of Concrete Structures and Materials, V. 12, No. 1, 2018, pp. 1-12. doi: 10.1186/s40069-018-0312-1

33. An, G. H.; Seo, J. K.; Cha, S. L.; and Kim, J. K., “An Experimental and Numerical Study on Long-Term Deformation of SRC Columns,” Computers and Concrete, V. 22, No. 3, 2018, pp. 261-267. doi: 10.12989/cac.2018.22.3.261

33. Huang, Y. Q.; Fu, J. Y.; Liu, A. R.; Pi, Y. L.; Wu, D.; and Gao, W., “Effect of Concrete Creep on Dynamic Stability Behavior of Slender Concrete-Filled Steel Tubular Column,” Composites Part B: Engineering, V. 157, 2019, pp. 173-181. doi: 10.1016/j.compositesb.2018.08.117

35. Ribeiro, K.; Loriggio, D. D.; and Real, M. D. V., “Reliability Analysis of Very Slender Columns Subjected to Creep,” Latin American Journal of Solids and Structures, V. 18, No. 7, 2021, pp. 1-25. doi: 10.1590/1679-78256569

36. Huang, Y.; Fu, J.; Wang, R.; Rao, R.; and Ma, N., “Experimental Study on Creep Behavior of High-Strength Concrete Filled Steel Tubular (HSCFST) Columns,” Case Studies in Construction Materials, V. 20, 2024, p. e02690. doi: 10.1016/j.cscm.2023.e02690

37. Madureira, E. L.; Siqueira, T. M.; and Rodrigues, E. C., “Creep Strains on Reinforced Concrete Columns,” Revista IBRACON de Estruturas e Materiais, V. 6, No. 4, 2013, pp. 537-560. doi: 10.1590/S1983-41952013000400003

38. Kataoka, L. T., and Bittencourt, T. N., “Numerical and Experimental Analysis of Time-Dependent Load Transfer in Reinforced Concrete Columns,” Revista IBRACON de Estrutruas e Materias, V. 7, No. 5, 2014, pp. 747-774. doi: 10.1590/S1983-41952014000500003

39. Wahrhaftig, A. D. M., and Eisenberger, M., “Buckling Load of Heavy Columns with Variable Cross Section and Flexible End Restraints,” Zeitschrift für Angewandte Mathematik und Mechanik, V. 104, No. 12, 2024, p. e202400626. doi: 10.1002/zamm.202400626

40. Márquez, M. A. R., “Buckling in Columns. Solution of the Indeterminations of Euler’s Theory and Derivation of an Equation for Inelastic Buckling,” Results in Engineering, V. 19, 2023, p. 101262. doi: 10.1016/j.rineng.2023.101262

41. Espí, M. V.; Bravo, J. C.; and Rojas, C. O., “On Galileo’s Tallest Column,” Mathematical Problems in Engineering, V. 2015, No. 1, 2015, p. 649341. doi: 10.1155/2015/649341

42. Kara, I. F., and Dundar, C., “Three-Dimensional Analysis of Tall Reinforced Concrete Buildings with Nonlinear Cracking Effects,” Mechanics Based Design of Structures and Machines, V. 38, No. 3, 2010, pp. 388-402. doi: 10.1080/15397734.2010.483551

43. Timoshenko, S. P., and Gere, J. M., Theory of Elastic Stability, second edition, McGraw-Hill Book Company, New York, 1961.

44. Wahrhaftig, A. M.; Magalhães, K. M. M.; da Silva, M. A.; Brasil, R. M. L. R. F.; and Banerjee, J. R., “Buckling and Free Vibration Analysis of Non-Prismatic Columns Using Optimized Shape Functions and Rayleigh Method,” European Journal of Mechanics-A/Solids, V. 94, 2022, p. 104543. doi: 10.1016/j.euromechsol.2022.104543

45. Abdel-Jaber, M., and El-Nimri, R., “Comparative Investigation, Numerical Modeling, and Buckling Analysis of One-Way Reinforced Concrete Wall Panels,” Results in Engineering, V. 14, 2022, p. 100459. doi: 10.1016/j.rineng.2022.100459

46. de Macêdo Wahrhaftig, A.; Eisenberger, M.; and Borges, A. P. F., “Closed-Form Approximate Buckling Analysis of Prismatic Columns with Combined Top and Distributed Loading,” Journal of the Brazilian Society of Mechanical Sciences and Engineering, V. 47, No. 4, 2025, p. 202. doi: 10.1007/s40430-025-05480-6

47. Wahrhaftig, A. M., “Analysis of the First Modal Shape Using Two Case Studies,” International Journal of Computational Methods, V. 16, No. 6, 2019, p. 1840019. doi: 10.1142/S0219876218400194

48. Eisenberger, M., and Wahrhaftig, A. M., “Buckling Loads of Variable Stiffness Columns Loaded by Top Load and Linearly and Parabolically Distributed Loading,” International Journal of Structural Stability and Dynamics, V. 26, No. 3, 2026, p. 2650001. doi: 10.1142/S021945542650001X

49. Wahrhaftig, A. M., and Brasil, R. M. L. R. F., “Vibration Analysis of Mobile Phone Mast System by Rayleigh Method,” Applied Mathematical Modelling, V. 42, 2017, pp. 330-345. doi: 10.1016/j.apm.2016.10.020

50. Wahrhaftig, A. M., and Brasil, R. M. L. R. F., “Initial Undamped Resonant Frequency of Slender Structures Considering Nonlinear Geometric Effects: The Case of a 60.8 m-High Mobile Phone Mast,” Journal of the Brazilian Society of Mechanical Sciences and Engineering, V. 39, 2017, pp. 725-735. doi: 10.1007/s40430-016-0547-1

51. Wahrhaftig, A. M.; Brasil, R. M. L. R. F.; and Balthazar, J. M., “The First Frequency of Cantilevered Bars with Geometric Effect: A Mathematical and Experimental Evaluation,” Journal of the Brazilian Society of Mechanical Sciences and Engineering, V. 35, 2013, pp. 457-467. doi: 10.1007/s40430-013-0043-9

52. Colunga, A. T.; Arizmendi, H. C.; Arroyo, J. L. L.; and Avilés, G. G., “Seismic Behavior of Code-Designed Medium Rise Special Moment-Resisting Frame RC Buildings in Soft Soils of Mexico City,” Engineering Structures, V. 30, No. 12, 2008, pp. 3681-3707. doi: 10.1016/j.engstruct.2008.05.026

53. CSI, “SAP2000. Analysis Reference Manual. Integrated Software for Structural Analysis and Design,” Computers and Structures, Inc., Berkeley, CA, 2024.

54. Lou, T.; Wu, S.; Karavasilis, T. L.; and Chen, B., “Long-Term Deflection Prediction in Steel-Concrete Composite Beams,” Steel and Composite Structures, V. 39, No. 1, 2021, pp. 21-33. doi: 10.12989/scs.2021.39.1.021


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