Technical Papers
Oct 18, 2011

Finite-Element Modeling to Calculate the Overall Stiffness of Cracked Reinforced Concrete Beams

Publication: Journal of Structural Engineering
Volume 138, Issue 7

Abstract

The macro-finite-element (MFE) modeling proposed in this paper is dedicated to the calculation of the deflection of already cracked reinforced concrete beams under service loading at the stabilized cracking stage. MFEs are beam finite elements, characterized by their average moment of inertia, calculated using nonlinear assumed distributions of steel strain, concrete strain, and neutral axis between two consecutive bending cracks. The results of the MFE model are successfully compared with experiments performed on five RC beams, including square- and T-section beams and two concretes (grades 30 and 40 MPa). A successful application of the MFE method to a statically indeterminate beam is also presented. The MFE modeling is appealing for use in practice because of its computational simplicity.

Get full access to this article

View all available purchase options and get full access to this article.

References

Alwis, W. A. M. (1990). “Trilinear moment-curvature relationship for reinforced concrete beams.” ACI Struct. J., 87(3), 276–283.ASTJEG
Batoz, J.-L., and Dhatt, G. (1990). Modélisation des structures par éléments finis, poutres et plaques, vol. 2, Presses Université Laval, Sainte-Foy, Québec, Canada.
Bazant, Z. P., and Gambarova, P. (1980). “Rough cracks in reinforced concrete.” J. Struct. Div.JSDEAG, 106(ST4), 819–842.
Bischoff, P. H. (2005). “Reevaluation of deflection prediction for concrete beams reinforced with steel and fiber-reinforced polymer bars.” J. Struct. Eng.JSENDH, 131(5), 752–767.
Bouazaoui, L., and Li, A. (2008). “Analysis of steel/concrete interfacial shear stress by means of pull out test.” Int. J. Adhes. Adhes., 28(3), 101–108.IJAADK
Carreira, J. D., and Chu, K. (1986). “The moment-curvature relationship of reinforced concrete members.” ACI Struct. J., 83(2), 191–198.ASTJEG
Castel, A., Vidal, T., and François, R. (2006). “Effective tension active cross-section of reinforced concrete beams after cracking.” Mater. Struct., 39(1), 103–113.MASTED
Castel, A., Vidal, T., and François, R. (2010). “Bond and cracking properties of self-consolidating concrete.” Constr. Build. Mater.CBUMEZ, 24(7), 1222–1231.
CEB-FIP. (1999). “Model code structural concrete. volume 1.” Updated knowledge of the CEB-FIP model code 1990, Comité Euro-International du Béton (CEB), Paris.
Cedolin, L., and Dei Poli, S. (1977). “Finite element studies of shear-critical R/C beams.” J. Eng. Mech. Div., 103(n.EM3), 395–410.JMCEA3
Chan, H. C., Cheung, Y. K., and Huang, Y. P. (1992). “Crack analysis of reinforced concrete tension members.” J. Struct. Eng.JSENDH, 118(8), 2118–2132.
Chan, H. C., Cheung, Y. K., and Huang, Y. P. (1993). “Analytical crack model for reinforced-concrete structures.” J. Struct. Eng.JSENDH, 119(5), 1339–1359.
Choi, C. K., and Cheung, S. H. (1996). “Tension stiffening model for planar reinforce concrete members.” Comput. Struct., 59(1), 179–190.CMSTCJ
Floegl, H., Herbert, H., and Mang, A. (1982). “Tension stiffening concept on bond slip.” J. Struct. Eng.JSENEI, 108(12), 2681–2701.
François, R., Castel, A., and Vidal, T. (2006). “A finite element for corroded reinforced concrete.” Mater. Struct.MASTED, 39(5), 569–582.
Gilbert, R. I. (2008). “Control of flexural cracking in reinforced concrete.” ACI Struct. J., 105(3), 301–307.ASTJEG
Gupta, A. K., and Maestrini, S. R. (1989). “Post-cracking behavior of membrane reinforced concrete elements including tension-stiffening.” J. Struct. Eng.JSENDH, 115(4), 957–976.
Kwak, H. G., and Song, J. Y. (2002). “Cracking analysis of RC members using polynomial strain distribution function.” Eng. Struct.ENSTDF, 24(4), 455–468.
Manfredi, G., and Pecce, M. (1998). “A refined R.C. beam element including bond-slip relationship for the analysis of continuous beams.” Comput. Struc., 69(1), 53–61.
Prakhya, G. K. V., and Morley, C. T. (1990). “Tension stiffening and moment-curvature relations of reinforced concrete elements.” ACI Struct. J.ASTJEG, 87(5), 597–605.
Somayaji, S., and Shah, S. P. (1981). “Bond stress versus slip relationship and cracking response of tension members.” J. Am. Concr. Inst.JACIAX, 78(3), 217–225.
Vecchio, F. (2000). “Disturbed stress field model for reinforced concrete: formulation.” J. Struct. Eng.JSENDH, 126(9), 1070–1077.
Wu, H. Q., and Gilbert, R. I. (2009). “Modeling short-term tension stiffening in reinforced concrete prisms using a continuum-based finite element model.” Eng. Struct.ENSTDF, 31(10), 2380–2391.
Yankelevsky, D. Z., Jabareen, M., and Abutbul, A. D. (2008). “One-dimensional analysis of tension stiffening in reinforced concrete with discrete cracks.” Eng. Struct.ENSTDF, 30, 206–217.
Zhang, R., Castel, A., and François, R. (2009). “Serviceability limit state criteria based on steel-concrete bond loss for corroded reinforced concrete in chloride environment.” Mater. Struct., 42(10), 1407–1421.MASTED

Information & Authors

Information

Published In

Go to Journal of Structural Engineering
Journal of Structural Engineering
Volume 138Issue 7July 2012
Pages: 889 - 898

History

Received: Jan 13, 2011
Accepted: Oct 14, 2011
Published online: Oct 18, 2011
Published in print: Jul 1, 2012

Permissions

Request permissions for this article.

Authors

Affiliations

Arnaud Castel [email protected]
Professor, Université de Nice-Sophia Antipolis, Laboratoire J.A. Dieudonné, UMR CNRS 6621, 06108 Nice Cedex 2, France (corresponding author). E-mail: [email protected]
Thierry Vidal
Assistant Professor, Université de Toulouse, UPS, INSA, LMDC (Laboratoire Matériaux et Durabilité des Constructions), Toulouse 31077, France.
Raoul François
Professor, Université de Toulouse, UPS, INSA, LMDC (Laboratoire Matériaux et Durabilité des Constructions), Toulouse 31077, France.

Metrics & Citations

Metrics

Citations

Download citation

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.

Cited by

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share