Technical Papers
Sep 11, 2019

Rational Design Approach for the Instantaneous and Time-Dependent Serviceability Deflections and Crack Widths of FRC and UHPFRC Continuous and Simply Supported Beams

Publication: Journal of Structural Engineering
Volume 145, Issue 11

Abstract

Novel mechanics-based closed-form solutions for long- and short-term serviceability deflections and crack widths of fiber-reinforced concrete (FRC) and ultra-high-performance fiber-reinforced concrete (UHPFRC) beams are presented. These solutions incorporate the bond properties from bond tests directly and as such obviate the need for constant bond stress simplification and consequently the need for member calibration as is commonly required in code approaches. The closed-form solutions are validated on 12 simply supported and 4 continuous UHPFRC beams as well as 10 normal-strength FRC beams with good correlation. A design example is also included for a UHPFRC T-beam demonstrating application of the solutions.

Get full access to this article

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

Acknowledgments

This material is based on work supported by the Air Force Office of Scientific Research (Award No. FA2386-16-1-4098) and the Australian Research Council Discovery Project (Project No. 190102650).

References

AFGC (French Association of Civil Engineering). 2013. Betons fibres a ultra-hautes performances: Recommandations [Ultra high performance fibre reinforced-concretes: Recommendations]. Paris: AFGC.
Amin, A., S. J. Foster, and W. Kaufmann. 2017. “Instantaneous deflection calculation for steel fibre reinforced concrete one way members.” Eng. Struct. 131 (Jan): 438–445. https://doi.org/10.1016/j.engstruct.2016.10.041.
Amin, A., and R. I. Gilbert. 2018. “Instantaneous crack width calculation for steel fiber-reinforced concrete flexural members.” ACI Struct. J. 115 (2): 535–543. https://doi.org/10.14359/51701116.
Balazs, G. L. 1993. “Cracking analysis based on slip and bond stresses.” ACI Mater. J. 90 (4): 340.
Banthia, N., F. Majdzadeh, J. Wu, and V. Bindiganavile. 2014. “Fiber synergy in hybrid fiber reinforced concrete (HyFRC) in flexure and direct shear.” Cem. Concr. Compos. 48 (Apr): 91–97. https://doi.org/10.1016/j.cemconcomp.2013.10.018.
Barros, J. A., and J. A. Figueiras. 1999. “Flexural behavior of SFRC: Testing and modeling.” J. Mater. Civ. Eng. 11 (4): 331–339. https://doi.org/10.1061/(ASCE)0899-1561(1999)11:4(331).
Barros, J. A., M. Taheri, and H. Salehian. 2015. “A model to simulate the moment-rotation and crack width of FRC members reinforced with longitudinal bars.” Eng. Struct. 100 (Oct): 43–56. https://doi.org/10.1016/j.engstruct.2015.05.036.
Barros, J. A., M. Taheri, and H. Salehian. 2018. “A model to predict the crack width of FRC members reinforced with longitudinal reinforcing bars.” Spec. Publ. 319: 2. https://doi.org/10.1016/j.engstruct.2015.05.036.
Bischoff, P. H. 2003. “Tension stiffening and cracking of steel fiber-reinforced concrete.” J. Mater. Civ. Eng. 15 (2): 174–182. https://doi.org/10.1061/(ASCE)0899-1561(2003)15:2(174).
Brandt, A. M. 2008. “Fibre Reinforced Cement-Based (FRC) composites after over 40 years of development in building and civil engineering.” Compos. Struct. 86 (1–3): 3–9. https://doi.org/10.1016/j.compstruct.2008.03.006.
Campione, G., C. Cucchiara, L. La Mendola, and M. Papia. 2005. “Steel-concrete bond in lightweight fiber reinforced concrete under monotonic and cyclic actions.” Eng. Struct. 27 (6): 881–890. https://doi.org/10.1016/j.engstruct.2005.01.010.
Chao, S. H., A. E. Naaman, and G. J. Parra-Montesinos. 2009. “Bond behavior of reinforcing bars in tensile strain-hardening fiber-reinforced cement composites.” ACI Struct. J. 106 (6): 897.
Choi, C. K., and S. H. Cheung. 1996. “Tension stiffening model for planar reinforced concrete members.” Comput. Struct. 59 (1): 179–190. https://doi.org/10.1016/0045-7949(95)00146-8.
Conforti, A., F. Minelli, and G. A. Plizzari. 2013. “Wide-shallow beams with and without steel fibres: A peculiar behaviour in shear and flexure.” Composites Part B 51 (Aug): 282–290. https://doi.org/10.1016/j.compositesb.2013.03.033.
Deluce, J. R., S. C. Lee, and F. J. Vecchio. 2014. “Crack model for steel fiber-reinforced concrete members containing conventional reinforcement.” ACI Struct. J. 111 (1): 93 https://doi.org/10.14359/51686433.
Fantilli, A. P., and B. Chiaia. 2018. “Conventional and unconventional approaches for evaluating the crack width in FRC structures.” Spec. Publ. 319: 4.1–4.12.
Fantilli, A. P., S. Kwon, H. Mihashi, and T. Nishiwaki. 2018. “Synergy assessment in hybrid ultra-high performance fiber-reinforced concrete (UHP-FRC).” Cem. Concr. Compos. 86 (Feb): 19–29. https://doi.org/10.1016/j.cemconcomp.2017.10.012.
fib (International Federation for Structural Concrete). 2013. CEB-FIP model code 2010. Lausanne, Switzerland: fib.
Gilbert, R. I., and G. Ranzi. 2010. Time-dependent behaviour of concrete structures. Boca Raton, FL: CRC Press.
Graybeal, B. A. 2006. Material property characterization of ultra-high performance concrete. McLean, VA: Federal Highways Administration.
Gupta, A. K., and S. R. Maestrini. 1990. “Tension-stiffness model for reinforced concrete bars.” J. Struct. Eng. 116 (3): 769–790. https://doi.org/10.1061/(ASCE)0733-9445(1990)116:3(769).
Harajli, M. H. 2009. “Bond stress–slip model for steel bars in unconfined or steel, FRC, or FRP confined concrete under cyclic loading.” J. Struct. Eng. 135 (5): 509–518. https://doi.org/10.1061/(ASCE)0733-9445(2009)135:5(509).
Harajli, M. H., M. Hout, and W. Jalkh. 1995. “Local bond stress-slip behavior of reinforcing bars embedded in plain and fiber concrete.” ACI Mater. J. 92 (4): 343–353.
Hillerborg, A. 1978. A model for fracture analysis. Lund, Sweden: Division of Building Materials, Lund Institute of Technology.
Hota, S., and A. E. Naaman. 1997. “Bond stress-slip response of reinforcing bars embedded in FRC matrices under monotonic and cyclic loading.” ACI Struct. J. 94 (5): 525–537.
Jungwirth, J., and A. Muttoni. 2004. “Structural behavior of tension members in ultra high performance concrete.” In Proc. Int. Symp. on Ultra High Performance Concrete. Kassel, Germany: Univ. of Kassel.
Knight, D., P. Visintin, and D. J. Oehlers. 2015. “Displacement-based simulation of time-dependent behaviour of RC beams with prestressed FRP or steel tendons.” Struct. Concr. 16 (3): 406–417. https://doi.org/10.1002/suco.201400039.
Knight, D., P. Visintin, D. J. Oehlers, and M. S. Mohamed Ali. 2014. “Short-term partial-interaction behavior of RC beams with prestressed FRP and steel.” J. Compos. Constr. 18 (1): 04013029. https://doi.org/10.1061/(ASCE)CC.1943-5614.0000408.
Lee, S. C., J. Y. Cho, and F. J. Vecchio. 2013. “Tension-stiffening model for steel fiber-reinforced concrete containing conventional reinforcement.” ACI Struct. J. 110 (4): 639–648.
Marchand, P., et al. 2016. “Bond behaviour of reinforcing bars in UHPFRC.” Mater. Struct. 49 (5): 1979–1995. https://doi.org/10.1617/s11527-015-0628-0.
Meda, A., F. Minelli, and G. A. Plizzari. 2012. “Flexural behaviour of RC beams in fibre reinforced concrete.” Composites Part B 43 (8): 2930–2937. https://doi.org/10.1016/j.compositesb.2012.06.003.
Mobasher, B., Y. Yao, and C. Soranakom. 2015. “Analytical solutions for flexural design of hybrid steel fiber reinforced concrete beams.” Eng. Struct. 100 (Oct): 164–177. https://doi.org/10.1016/j.engstruct.2015.06.006.
Muhamad, R., M. M. Ali, D. J. Oehlers, and M. Griffith. 2012. “The tension stiffening mechanism in reinforced concrete prisms.” Adv. Struct. Eng. 15 (12): 2053–2069. https://doi.org/10.1260/1369-4332.15.12.2053.
Ning, X., Y. Ding, F. Zhang, and Y. Zhang. 2015. “Experimental study and prediction model for flexural behavior of reinforced SCC beam containing steel fibers.” Constr. Build. Mater. 93 (Sep): 644–653. https://doi.org/10.1016/j.conbuildmat.2015.06.024.
Oesterlee, C. 2010. “Structural response of reinforced UHPFRC and RC composite members.” Ph.D. thesis, School of Architecture, Civil, and Environmental Engineering, Ecole Polytechnique Federale de Lausanne.
Park, S. H., D. J. Kim, G. S. Ryu, and K. T. Koh. 2012. “Tensile behavior of ultra high performance hybrid fiber reinforced concrete.” Cem. Concr. Compos. 34 (2): 172–184. https://doi.org/10.1016/j.cemconcomp.2011.09.009.
RILEM. 1994. “RILEM recommendations for the testing and use of constructions materials.” In RC 6 bond test for reinforcement steel. 2. Pull-out test, 1983. New York: E & FN SPON.
Schumacher, P. 2006 “Rotation capacity of self-compacting steel fibre reinforced concrete.” Ph.D. thesis, Faculty of Civil Engineering and Geosciences, Delft Univ.
Singh, M., A. H. Sheikh, M. M. Ali, P. Visintin, and M. C. Griffith. 2017. “Experimental and numerical study of the flexural behaviour of ultra-high performance fibre reinforced concrete beams.” Constr. Build. Mater. 138 (May): 12–25. https://doi.org/10.1016/j.conbuildmat.2017.02.002.
Sobuz, H. R., P. Visintin, M. M. Ali, M. Singh, M. C. Griffith, and A. H. Sheikh. 2016. “Manufacturing ultra-high performance concrete utilising conventional materials and production methods.” Constr. Build. Mater. 111 (May): 251–261. https://doi.org/10.1016/j.conbuildmat.2016.02.102.
Standards Australia. 2014. Concrete structures—Commentary (supplement to AS3600-2009). AS 3600 Supplement 1:2014. Sydney: Standards Australia.
Standards Australia. 2018. Concrete structures. AS 3600. Sydney: Standards Australia.
Stang, H., and T. Aarre. 1992. “Evaluation of crack width in FRC with conventional reinforcement.” Cem. Concr. Compos. 14 (2): 143–154. https://doi.org/10.1016/0958-9465(92)90007-I.
Sturm, A. B., and P. Visintin. 2019. “Local bond slip behaviour of steel reinforcing bars embedded in UHPFRC.” Struct. Concr. 20 (1): 108–122. https://doi.org/10.1002/suco.201700149.
Sturm, A. B., P. Visintin, and D. J. Oehlers. 2018a. Mechanics of the flexural behaviour of UHPFFRC beams under instantaneous and sustained loading. Adelaide, Australia: School of Civil, Environmental & Mining Engineering, Univ. of Adelaide.
Sturm, A. B., P. Visintin, D. J. Oehlers, and R. Seracino. 2018b. “Time-dependent tension-stiffening mechanics of fiber-reinforced and ultra-high-performance fiber-reinforced concrete.” J. Struct. Eng. 144 (8): 04018122. https://doi.org/10.1061/(ASCE)ST.1943-541X.0002107.
Taheri, M., J. A. Barros, and H. Salehian. 2011. “A design model for strain-softening and strain-hardening fiber reinforced elements reinforced longitudinally with steel and FRP bars.” Composites Part B 42 (6): 1630–1640. https://doi.org/10.1016/j.compositesb.2011.04.009.
Visintin, P., M. Ali, T. Xie, and A. B. Sturm. 2018a. “Experimental investigation of moment redistribution in ultra-high performance fibre reinforced concrete beams.” Constr. Build. Mater. 166 (1): 433–444. https://doi.org/10.1016/j.conbuildmat.2018.01.156.
Visintin, P., and D. J. Oehlers. 2017. “Fundamental mechanics that govern the flexural behaviour of reinforced concrete beams with fibre-reinforced concrete.” Adv. Struct. Eng. 21 (7): 1088–1102. https://doi.org/10.1177/1369433217739705.
Visintin, P., D. J. Oehlers, and M. Haskett. 2013. “Partial-interaction time dependent behaviour of reinforced concrete beams.” Eng. Struct. 49 (Apr): 408–420. https://doi.org/10.1016/j.engstruct.2012.11.025.
Visintin, P., A. B. Sturm, M. S. Mohamed Ali, and D. J. Oehlers. 2018b. “Blending macro and micro fibres to enhance to the serviceability behaviour of UHPFRC.” Aust. J. Civ. Eng. 16 (2): 106–121. https://doi.org/10.1080/14488353.2018.1463608.
Volkersen, O. 1938. “Die Nietkrafverteilung in zugbeanspruchten Nietverbindungen mit konstanten Laschenquerschnitten.” Luftfahrtvorschung 15: 41–47.
Wille, K., S. El-Tawil, and A. E. Naaman. 2014. “Properties of strain hardening ultra high performance fiber reinforced concrete (UHP-FRC) under direct tensile loading.” Cem. Concr. Compos. 48 (Apr): 53–66. https://doi.org/10.1016/j.cemconcomp.2013.12.015.
Wu, Z., H. Yoshikawa, and T. A. Tanabe. 1991. “Tension stiffness model for cracked reinforced concrete.” J. Struct. Eng. 117 (3): 715–732. https://doi.org/10.1061/(ASCE)0733-9445(1991)117:3(715).
Yoo, D. Y., N. Banthia, and Y. S. Yoon. 2016. “Flexural behavior of ultra-high-performance fiber-reinforced concrete beams reinforced with GFRP and steel rebars.” Eng. Struct. 111 (Mar): 246–262. https://doi.org/10.1016/j.engstruct.2015.12.003.
Yoo, D. Y., K. Y. Kwon, J. J. Park, and Y. S. Yoon. 2015. “Local bond-slip response of GFRP rebar in ultra-high-performance fiber-reinforced concrete.” Compos. Struct. 120 (Feb): 53–64. https://doi.org/10.1016/j.compstruct.2014.09.055.
Yoo, D. Y., H. O. Shin, J. M. Yang, and Y. S. Yoon. 2014. “Material and bond properties of ultra high performance fiber reinforced concrete with micro steel fibers.” Composites Part B 58 (Mar): 122–133. https://doi.org/10.1016/j.compositesb.2013.10.081.
Yuguang, Y., J. C. Walraven, and J. A. den Uijl. 2009. “Combined effect of fibers and steel rebars in high performance concrete.” Heron 54 (2–3): 205–224.
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 145Issue 11November 2019

History

Received: Apr 10, 2018
Accepted: Mar 13, 2019
Published online: Sep 11, 2019
Published in print: Nov 1, 2019
Discussion open until: Feb 11, 2020

Permissions

Request permissions for this article.

Authors

Affiliations

A. B. Sturm
Ph.D. Candidate, School of Civil, Environmental and Mining Engineering, Univ. of Adelaide, Adelaide, SA 5005, Australia.
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]
D. 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