Technical Papers
May 26, 2020

Closed-Form Solutions for Quantifying the Ductility of Concrete Beams with Passively Restrained Concrete

Publication: Journal of Structural Engineering
Volume 146, Issue 8

Abstract

The ductility of a beam is important in reinforced concrete member design at the ultimate limit state, especially in resisting dynamic loads such as those from earthquakes or blasts. Concrete confinement reinforcement, such as stirrups or tubes, are widely used in structures and can significantly enhance the ductility of concrete beams. However, this confinement effect is normally ignored in current design standards, limiting the ability to design specifically for ductility or to estimate the ductility of existing structures. In this paper, a novel concrete passive stress/strain relationship based on the application of partial interaction and shear friction theories is simplified to a rectangular stress block for flexural analyses. This confined concrete stress block is then applied to quantify the moment/rotation of a hinge where both the confinement of the concrete and hinge lengths are quantified through mechanics. The aim of this paper is to provide a mechanics based approach for quantifying the ductility of RC beams that can be used to develop simple design rules without the need for large amounts of member testing.

Get full access to this article

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

Data Availability Statement

All data, models, and code generated or used during the study appear in the published article.

Acknowledgments

The first author acknowledges the financial support of the China Scholarship Council.

References

ACI (American Concrete Institute). 1992. State-of-the-art report on high-strength concrete. Farmington Hills, MI: ACI.
ACI (American Concrete Institute). 2014. Building code requirements for structural concrete. ACI 318-14. Farmington Hills, MI: ACI.
Ali, M. M., D. Oehlers, and M. Griffith. 2010. “The residual strength of confined concrete.” Adv. Struct. Eng. 13 (4): 603–618. https://doi.org/10.1260/1369-4332.13.4.603.
Ali, M. M., D. Oehlers, M. Griffith, and R. Seracino. 2008. “Interfacial stress transfer of near surface-mounted FRP-to-concrete joints.” Eng. Struct. 30 (7): 1861–1868. https://doi.org/10.1016/j.engstruct.2007.12.006.
Attard, M. M., and M. G. Stewart. 1998. “A two parameter stress block for high-strength concrete.” Struct. J. 95 (3): 305–317.
Bourke, P. 1988. “Calculating the area and centroid of a polygon.” Swinburne Univ. Technol. 7.
Du, M., L. Jin, X. Du, and D. Li. 2017. “Size effect tests of stocky reinforced concrete columns confined by stirrups.” Struct. Concr. 18 (3): 454–465. https://doi.org/10.1002/suco.201600074.
fib (International Federation for Structural Concrete). 2010. Model code 2010, final draft. Lausanne, Switzerland: Fib.
Giduquio, M. B., M.-Y. Cheng, and L. S. Wibowo. 2015. “High-strength flexural reinforcement in reinforced concrete flexural members under monotonic loading.” ACI Struct. J. 112 (6): 793–804.
Hao, X. 2017. Mechanics of extracting shear-friction properties from actively confined cylinder tests. Adelaide, Australia: Univ. of Adelaide.
Hao, X. 2018a. Generation of stress-strain relationship of passively reinforced circular concrete cylinders. Adelaide, Australia: Univ. of Adelaide.
Hao, X. 2018b. Generation of stress-strain relationship of passively reinforced rectangular concrete prisms. Adelaide, Australia: Univ. of Adelaide.
Haskett, M., D. J. Oehlers, and M. M. Ali. 2008. “Local and global bond characteristics of steel reinforcing bars.” Eng. Struct. 30 (2): 376–383. https://doi.org/10.1016/j.engstruct.2007.04.007.
Haskett, M., D. J. Oehlers, M. M. Ali, and S. Sharma. 2010a. “The shear friction aggregate interlock resistance across sliding planes in concrete.” Mag. Concr. Res. 62 (12): 907–924. https://doi.org/10.1680/macr.2010.62.12.907.
Haskett, M., D. J. Oehlers, M. M. Ali, and S. K. Sharma. 2011. “Evaluating the shear-friction resistance across sliding planes in concrete.” Eng. Struct. 33 (4): 1357–1364. https://doi.org/10.1016/j.engstruct.2011.01.013.
Haskett, M., D. J. Oehlers, M. M. Ali, and C. Wu. 2009. “Rigid body moment–rotation mechanism for reinforced concrete beam hinges.” Eng. Struct. 31 (5): 1032–1041. https://doi.org/10.1016/j.engstruct.2008.12.016.
Haskett, M., D. J. Oehlers, M. M. Ali, and C. Wu. 2010b. “Analysis of moment redistribution in fiber-reinforced polymer plated RC beams.” J. Compos. Constr. 14 (4): 424–433. https://doi.org/10.1061/(ASCE)CC.1943-5614.0000098.
Hognestad, E. 1951. Study of combined bending and axial load in reinforced concrete members. Bulletin No. 399. Champaign, IL: Univ. of Illinois.
Iravani, S. 1996. “Mechanical properties of high-performance concrete.” Mater. J. 93 (5): 416–426.
Jensen, B. C. 1975. “Lines of discontinuity for displacements in the theory of plasticity of plain and reinforced concrete.” Mag. Concr. Res. 27 (92): 143–150. https://doi.org/10.1680/macr.1975.27.92.143.
Jensen, V. P. 1943. “The plasticity ratio of concrete and it’s effect on the ultimate strength of beams.” ACI J. Proc. 39: 555–584.
Jin, L., M. Du, D. Li, X. Du, and H. Xu. 2017. “Effects of cross section size and transverse rebar on the behavior of short squared RC columns under axial compression.” Eng. Struct. 142 (Jul): 223–239. https://doi.org/10.1016/j.engstruct.2017.04.002.
Kaar, P. H., N. W. Hanson, and H. Capell. 1978. “Stress-strain characteristics of high-strength concrete.” Spec. Publ. 55: 161–186.
Li, B., R. Park, and H. Tanaka. 2001. “Stress-strain behavior of high-strength concrete confined by ultra-high-and normal-strength transverse reinforcements.” ACI Struct. J. 98 (3): 395–406.
Lopes, A. V., S. M. Lopes, and R. N. do Carmo. 2012. “Effects of the compressive reinforcement buckling on the ductility of RC beams in bending.” Eng. Struct. 37 (Apr): 14–23. https://doi.org/10.1016/j.engstruct.2011.12.038.
Mansur, M., M. Chin, and T. Wee. 1997. “Flexural behavior of high-strength concrete beams.” Struct. J. 94 (6): 663–674.
Mattock, A. H. 1974. “Shear transfer in concrete having reinforcement at an angle to the shear plane.” Spec. Publ. 42 (Jan): 17–42.
Mattock, A. H., and N. M. Hawkins. 1972. “Shear transfer in reinforced concrete—Recent research.” PCI J. 17 (2): 55–75.
Mensch, L. J. 1914. “New-old theory of reinforced concrete beams in bending.” ACI J. Proc. 10 (12): 28–41.
Oehlers, D. J., M. M. Ali, M. C. Griffith, M. Haskett, and W. Lucas. 2012. “A generic unified reinforced concrete model.” Proc. Inst. Civ. Eng. Struct. Build. 165 (1): 27–49. https://doi.org/10.1680/stbu.2012.165.1.27.
Oehlers, D. J., M. Haskett, M. Ali, W. Lucas, and R. Muhamad. 2011. “Our obsession with curvature in RC beam modelling.” Adv. Struct. Eng. 14 (3): 391–404. https://doi.org/10.1260/1369-4332.14.3.391.
Oehlers, D. J., P. Visintin, J.-F. Chen, R. Seracino, Y. Wu, and W. Lucas. 2017. “Reinforced concrete behavior, research, development, and design through partial-interaction mechanics.” J. Struct. Eng. 143 (7): 02517002. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001764.
Popovics, S. 1973. “A numerical approach to the complete stress-strain curve of concrete.” Cem. Concr. Res. 3 (5): 583–599. https://doi.org/10.1016/0008-8846(73)90096-3.
Rajagopalan, K., and N. J. Everard. 1976. “Flexural behavior of high-strength concrete beams.” J. Proc. 73 (9): 517–521.
Rashid, M., and M. Mansur. 2005. “Reinforced high-strength concrete beams in flexure.” ACI Struct. J. 102 (3): 462.
Seracino, R., M. Raizal Saifulnaz, and D. Oehlers. 2007. “Generic debonding resistance of EB and NSM plate-to-concrete joints.” J. Compos. Constr. 11 (1): 62–70. https://doi.org/10.1061/(ASCE)1090-0268(2007)11:1(62).
Silva, M. A., and C. C. Rodrigues. 2006. “Size and relative stiffness effects on compressive failure of concrete columns wrapped with glass FRP.” J. Mater. Civ. Eng. 18 (3): 334–342. https://doi.org/10.1061/(ASCE)0899-1561(2006)18:3(334).
Standards Australia. 2009. Concrete structures. AS 3600-2009. Sydney, Australia: Standards Australia.
Sturm, A. B., P. Visintin, and D. J. Oehlers. 2017. “Time-dependent serviceability behavior of reinforced concrete beams: Partial interaction tension stiffening mechanics.” Struct. Concr. 19 (2): 508–523.
Tan, T.-H., and N.-B. Nguyen. 2005. “Flexural behavior of confined high-strength concrete columns.” ACI Struct. J. 102 (2): 198.
Thériault, M., K. W. Neale, and S. Claude. 2004. “Fiber-reinforced polymer-confined circular concrete columns: Investigation of size and slenderness effects.” J. Compos. Constr. 8 (4): 323–331. https://doi.org/10.1061/(ASCE)1090-0268(2004)8:4(323).
Visintin, P., Y. Chen, and D. Oehlers. 2015. “Size dependent axial and lateral stress strain relationships for actively confined concrete.” Adv. Struct. Eng. 18 (1): 1–20. https://doi.org/10.1260/1369-4332.18.1.1.
Visintin, P., and D. J. Oehlers. 2016. “Mechanics-based closed-form solutions for moment redistribution in RC beams.” Struct. Concr. 17 (3): 377–389.
Visintin, P., D. J. Oehlers, M. Haskett, and C. Wu. 2012a. “Mechanics-based hinge analysis for reinforced concrete columns.” J. Struct. Eng. 139 (11): 1973–1980. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000761.
Visintin, P., D. J. Oehlers, R. Muhamad, and C. Wu. 2013. “Partial-interaction short term serviceability deflection of RC beams.” Eng. Struct. 56 (Nov): 993–1006. https://doi.org/10.1016/j.engstruct.2013.06.021.
Visintin, P., D. J. Oehlers, C. Wu, and M. Haskett. 2012b. “A mechanics solution for hinges in RC beams with multiple cracks.” Eng. Struct. 36 (Mar): 61–69. https://doi.org/10.1016/j.engstruct.2011.11.028.
Warner, R., B. Rangan, A. Hall, and K. Faulkes. 1998. Concrete structures. Boston: Addison Wesley.
Whitney, C. S. 1937. “Design of reinforced concrete members under flexure or combined flexure and direct compression.” J. Proc. 33 (3): 483–498.
Yi, S.-T., J.-H. J. Kim, and J.-K. Kim. 2002. “Effect of specimen sizes on ACI rectangular stress block for concrete flexural members.” ACI Struct. J. 99 (5): 701–708.
Yuan, H., J. Teng, R. Seracino, Z. Wu, and J. Yao. 2004. “Full-range behavior of FRP-to-concrete bonded joints.” Eng. Struct. 26 (5): 553–565. https://doi.org/10.1016/j.engstruct.2003.11.006.
Yuan, H., Z. Wu, and H. Yoshizawa. 2001. “Theoretical solutions on interfacial stress transfer of externally bonded steel/composite laminates.” Doboku Gakkai Ronbunshu 2001 (675): 27–39.
Zhang, T., P. Visintin, and D. Oehlers. 2014. A semi-mechanical model for tension-stiffening. Adelaide, Australia: School of Civil, Environmental, and Mining Engineering, Univ. of Adelaide.
Zhang, T., P. Visintin, and D. J. Oehlers. 2017. “Partial-interaction tension-stiffening properties for numerical simulations.” Adv. Struct. Eng. 20 (5): 812–821. https://doi.org/10.1177/1369433216660654.

Information & Authors

Information

Published In

Go to Journal of Structural Engineering
Journal of Structural Engineering
Volume 146Issue 8August 2020

History

Received: Oct 21, 2019
Accepted: Mar 2, 2020
Published online: May 26, 2020
Published in print: Aug 1, 2020
Discussion open until: Oct 26, 2020

Permissions

Request permissions for this article.

Authors

Affiliations

Ph.D. Candidate, School of Civil, Environmental and Mining Engineering, Univ. of Adelaide, Adelaide, SA 5005, Australia. ORCID: https://orcid.org/0000-0002-5096-5447
Associate Professor, School of Civil, Environmental and Mining Engineering, Univ. of Adelaide, Adelaide, SA 5005, Australia (corresponding author). ORCID: https://orcid.org/0000-0002-4544-2043. Email: [email protected]
Deric. J. Oehlers
Emeritus Professor, School of Civil, Environmental and Mining Engineering, Univ. of Adelaide, Adelaide, SA 5005, Australia.

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