The Proposition of an EI Equation of Square and L–Shaped Slender Reinforced Concrete Columns under Combined Loading
Published online first on April 28, 2021.
The stability and strength of slender Reinforced Concrete (RC) columns depend directly on the flexural stiffness EI, which is a major parameter in strain calculations including those with bending and axial load. Due to the non-linearity of the stress-strain curve of concrete, the effective bending stiffness EI always remains variable. Numerical simulations were performed for square and L-shaped reinforced concrete sections of slender columns subjected to an eccentric axial force to estimate the variation of El resulting from the actual behavior of the column, based on the moment-curvature relationship. Seventy thousand (70000) hypothetical slender columns, each with a different combination of variables, were used to investigate the main variables that affect the EI of RC slender columns. Using linear regression analysis, a new simple and linear expression of EI was developed. Slenderness, axial load level, and concrete strength have been identified as the most important factors affecting effective stiffness. Finally, the comparison between the results of the new equation and the methods proposed by ACI-318 and Euro Code-2 was carried out in connection with the experimental results of the literature. A good agreement of the results was found.
Keywords:flexural stiffness, reduction factor, reinforced concrete, rigidity, slender columns
ACI 318-08: Building Code Requirements for Structural Concrete and Commentary. ACI, 2008.
EN 1992-1-1:2004 - Eurocode 2: Design of concrete structures - Part 1-1: General rules and rules for. Brussels, Belgium: CEN, 2004.
C. S. Whitney and E. Cohen, "Guide for Ultimate Strength Design of Reinforced Concrete," Journal Proceedings, vol. 53, no. 11, pp. 455–490, Nov. 1956. DOI: https://doi.org/10.14359/11524
B. Bresler, "Design Criteria for Reinforced Concrete Columns under Axial Load and Biaxial Bending," ACI Journal, Proceedings, vol. 10, no. 6, pp. 481–490, Jan. 2005.
M. Khuntia and S. K. Ghosh, "Flexural Stiffness of Reinforced Concrete Columns and Beams: Experimental Verification," ACI Structural Journal, vol. 10, no. 3, May 2004.
J. L. Bonet, M. L. Romero, and P. F. Miguel, "Effective flexural stiffness of slender reinforced concrete columns under axial forces and biaxial bending," Engineering Structures, vol. 33, no. 3, pp. 881–893, Mar. 2011. DOI: https://doi.org/10.1016/j.engstruct.2010.12.009
M. Resheidat, M. Ghanma, C. Sutton, and W.-F. Chen, "Flexural rigidity of biaxially loaded reinforced concrete rectangular column sections," Computers & Structures, vol. 55, no. 4, pp. 601–614, May 1995. DOI: https://doi.org/10.1016/0045-7949(94)00493-M
S. Z. Al-Sarraf, I. A. S. Al-Shaarbaf, B. R. Al-Bakri, and K. F. Sarsam, "Flexural Rigidity of Slender RC Columns," Engineering and Technology Journal, vol. 27, no. 1, pp. 96–116, 2009.
J. Liu, Y. Zhang, and P. Luo, "Flexural Stiffness Reduction Factor of Reinforced Concrete Column with Equal L-Shaped Section," in The Twelfth COTA International Conference of Transportation Professionals, Dec. 2012, pp. 3187–3193. DOI: https://doi.org/10.1061/9780784412442.325
X. Feng, M. Shen, C. Sun, J. Chen, and P. Luo, "Research on Flexural Stiffness Reduction Factor of Reinforced Concrete Column with Equiaxial + Shaped Section," Procedia - Social and Behavioral Sciences, vol. 96, pp. 168–174, Nov. 2013. DOI: https://doi.org/10.1016/j.sbspro.2013.08.022
Ö. Avşar, B. Bayhan, and A. Yakut, "Effective flexural rigidities for ordinary reinforced concrete columns and beams," The Structural Design of Tall and Special Buildings, vol. 23, no. 6, pp. 463–482, 2014. DOI: https://doi.org/10.1002/tal.1056
N. Caglar, A. Demir, H. Ozturk, and A. Akkaya, "A simple formulation for effective flexural stiffness of circular reinforced concrete columns," Engineering Applications of Artificial Intelligence, vol. 38, pp. 79–87, Feb. 2015. DOI: https://doi.org/10.1016/j.engappai.2014.10.011
L. N. Ramamurthy and T. A. H. Khan, "L‐Shaped Column Design for Biaxial Eccentricity," Journal of Structural Engineering, vol. 109, no. 8, pp. 1903–1917, Aug. 1983. DOI: https://doi.org/10.1061/(ASCE)0733-9445(1983)109:8(1903)
Mallikarjuna and P. Mahadevappa, "Computer aided analysis of reinforced concrete columns subjected to axial compression and bending—I L-shaped sections," Computers & Structures, vol. 44, no. 5, pp. 1121–1138, Aug. 1992. DOI: https://doi.org/10.1016/0045-7949(92)90333-U
W. H. Taso and C.-T. T. Hsu, "Behaviour of biaxially loaded square and L-shaped slender reinforced concrete columns," Magazine of Concrete Research, vol. 46, no. 169, pp. 257–267, Dec. 1994. DOI: https://doi.org/10.1680/macr.1922.214.171.1247
C. Dundar, S. Tokgoz, A. K. Tanrikulu, and T. Baran, "Behaviour of reinforced and concrete-encased composite columns subjected to biaxial bending and axial load," Building and Environment, vol. 43, no. 6, pp. 1109–1120, Jun. 2008. DOI: https://doi.org/10.1016/j.buildenv.2007.02.010
D. C. Kent and R. Park, "Flexural Members with Confined Concrete," Journal of the Structural Division, vol. 97, no. 7, pp. 1969–1990, 1971. DOI: https://doi.org/10.1061/JSDEAG.0002957
H. Wang, Y. Zhang, and S. Qin, "A Study on Ductility of Prestressed Concrete Pier Based on Response Surface Methodology," Engineering, Technology & Applied Science Research, vol. 6, no. 6, pp. 1253–1257, Dec. 2016. DOI: https://doi.org/10.48084/etasr.855
A. Ali, Z. Soomro, S. Iqbal, N. Bhatti, and A. F. Abro, "Prediction of Corner Columns’ Load Capacity Using Composite Material Analogy," Engineering, Technology & Applied Science Research, vol. 8, no. 2, pp. 2745–2749, Apr. 2018. DOI: https://doi.org/10.48084/etasr.1879
How to Cite
MetricsAbstract Views: 120
PDF Downloads: 79
Copyright (c) 2021 Authors
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:
- Authors retain the copyright and grant the journal the right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) after its publication in ETASR with an acknowledgement of its initial publication in this journal.