Abstract
External confinement of reinforced concrete (RC) columns with fiber-reinforced polymer (FRP) jackets and/or wraps is a technique extensively used for strengthening and retrofit of structurally deficient columns. The confinement effect produced by the externally bonded FRP acts simultaneously with the confining mechanism of the existing internal reinforcing steel, thus increasing the vertical load capacity and ductility of the member. The transverse steel confinement contribution can be significant, although it is generally ignored in existing design guidelines for FRP wrapping, potentially leading to an overconservative retrofit design. This paper proposes a modification to the design equation of FRP-confined RC circular columns subjected to axial loading that is given in the current US standards. The proposed design equation is calibrated through a structural reliability analysis approach, in which the capacity model (corresponding to the probability distribution for the axial load capacity of the columns) is generated via Monte Carlo simulation based on advanced nonlinear finite-element response analyses for multiple realistic combinations of design parameters. Under different design conditions, the newly proposed design equation provides a significantly less variable reliability index than that obtained using the current accepted design equation, which produces increasingly overconservative retrofit designs for increasing amounts of transverse steel reinforcement. A practical design procedure based on the proposed design equation is also presented.
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Acknowledgments
The authors gratefully acknowledge partial support of this research by the Brazilian National Council for Scientific and Technological Development (CNPq-Brazil). Any opinions, findings, conclusions, or recommendations expressed in this publication are those of the writers and do not necessarily reflect the views of the sponsors.
Notation
The following symbols are used in this paper:
- Ac
- area of concrete core;
- Ag
- gross cross-sectional area;
- Asl
- total area of longitudinal reinforcing steel;
- As
- total area of either longitudinal or transverse reinforcing steel;
- b
- strain-hardening ratio of longitudinal reinforcing steel;
- c
- concrete cover;
- CE
- environmental reduction factor;
- Cs
- relative steel confinement coefficient;
- D
- diameter of column cross section;
- DL
- dead loads
- DLn
- nominal dead loads
- e/D
- eccentricity-to-diameter ratio;
- Ec
- initial concrete elastic modulus;
- Ef
- FRP elastic modulus;
- Esl
- elastic modulus of longitudinal reinforcing steel;
- Est
- elastic modulus of transverse reinforcing steel;
- unconfined concrete peak strength;
- confined concrete peak strength;
- ffu
- ultimate strength of FRP;
- flf
- lateral confining ratio of FRP wraps;
- fls
- lateral confining ratio of transverse reinforcing steel;
- fyl
- yielding strength of longitudinal reinforcing steel;
- g
- limit state function;
- I
- maximum relative increase of a column axial capacity in γf;
- Kf
- FRP confining modulus;
- LL
- live loads
- LLn
- nominal live loads
- m
- design efficiency factor;
- mv
- number of primary dimensions in dimensional analysis;
- N
- minimum number of dimensionless groups in dimensional analysis;
- n
- number of FRP plies;
- nv
- number of variables in dimensional analysis;
- pf
- probability of failure;
- Pmax,exp
- experimental ultimate strength of an FRP-confined column considering FRP and steel confinement;
- Pmax,num
- numerical ultimate strength of an FRP-confined column considering FRP and steel confinement;
- experimental strength of an FRP-confined column considering FRP and steel confinement and design strain limit;
- experimental strength of an FRP-confined column considering FRP confinement only and design strain limit;
- Pn
- nominal axial capacity;
- Pr
- design axial capacity;
- Pu
- axial demand;
- Qi
- axial load in load combination;
- Qv
- set of repeating variables in dimensional analysis;
- R
- probabilistic structural capacity;
- s
- spacing of transverse reinforcing steel;
- tf
- FRP ply thickness;
- VX
- coefficient of variation of random variable X;
- α
- accidental eccentricity reduction factor in ACI 318-19;
- β
- reliability index;
- γi
- partial load factor;
- γf
- strength amplification factor due to transverse steel confinement;
- unconfined concrete strain at peak strength;
- ɛccu
- maximum compressive strain in FRP-confined concrete;
- ɛc,max
- maximum allowable concrete strain;
- ɛfe
- effective strain of FRP at failure;
- ɛfu
- ultimate strain of FRP from flat coupon tensile tests;
- ɛsu
- ultimate strain of reinforcing steel;
- κa
- shape factor;
- κb
- geometry efficiency factor;
- κc
- parameter that associates the compressive strength of in-place concrete with cylinder test results;
- κɛ
- FRP strain efficiency factor;
- λX
- bias of random variable X;
- μX
- mean value of random variable X;
- ξ
- modeling error; ratio between the numerical estimates and the experimental strength;
- πi
- nondimensional group in dimensional analysis;
- ρf
- FRP volumetric reinforcement ratio;
- ρsl
- longitudinal steel ratio;
- σX
- standard deviation of random variable X;
- Φ
- standard normal cumulative distribution function;
- ϕ
- strength reduction factor in ACI 318-19; and
- ψf
- FRP reduction factor in ACI 440.2R-17.
References
ACI (American Concrete Institute). 2017. Guide for the design and construction of externally bonded FRP systems for strengthening concrete structures. ACI 440.2R-17. Farmington Hills, MI: ACI.
ACI (American Concrete Institute). 2019. Building code requirements for structural concrete. ACI 318-19. Farmington Hills, MI: ACI.
ASCE. 2017. Minimum design loads for buildings and other structures. ASCE 7-16. Reston, VA: ASCE.
Baji, H. 2017. “Calibration of the FRP resistance reduction factor for FRP-confined reinforced concrete building columns.” J. Compos. Constr. 21 (3): 04016107. https://doi.org/10.1061/(ASCE)CC.1943-5614.0000769.
Baji, H., H. R. Ronagh, and C. Q. Li. 2016. “Probabilistic assessment of FRP-confined reinforced concrete columns.” Compos. Struct. 153: 851–865. https://doi.org/10.1016/j.compstruct.2016.07.003.
Barbato, M. 2009. “Efficient finite element modelling of reinforced concrete beams retrofitted with fibre reinforced polymers.” Comput. Struct. 87 (3–4): 167–176. https://doi.org/10.1016/j.compstruc.2008.11.006.
Bartlett, F. M., and J. G. MacGregor. 1996. “Statistical analysis of the compressive strength of concrete in structures.” ACI Mater. J. 93 (2): 158–168.
Bisby, L., and M. Ranger. 2010. “Axial–flexural interaction in circular FRP-confined reinforced concrete columns.” Constr. Build. Mater. 24 (9): 1672–1681. https://doi.org/10.1016/j.conbuildmat.2010.02.024.
Breitung, K. 1984. “Asymptotic approximations for multinormal integrals.” J. Eng. Mech. 110: 357–366.
Butterfield, R. 1999. “Dimensional analysis for geotechnical engineers.” Geotechnique 49 (3): 357–366. https://doi.org/10.1680/geot.1999.49.3.357.
Casas, J. R., and J. L. Chambi. 2014. “Partial safety factors for CFRP-wrapped bridge piers: Model assessment and calibration.” Compos. Struct. 118: 267–283. https://doi.org/10.1016/j.compstruct.2014.07.032.
CNR (National Research Council). 2013. Guide for the design and construction of externally bonded FRP systems for strengthening existing structures. CNR-DT-200-R1. National Research Council—Advisory Committee on Technical Recommendations for Construction. Rome: CNR.
CSA (Canadian Standards Association). 2017. Design and construction of building structures with fibre-reinforced polymer. CSA S806-17. Rexdale, ON, Canada: CSA.
DAfStb. 2012. DAfStb-RichtIinie: Verstärken von betonbauteilen mit geklebter bewehrung. Deutscher Ausschuss für Stahlbeton [In German.] Berlin: DAfStb.
De Nicolo, B., L. Pani, and E. Pozzo. 1994. “Strain of concrete at peak compressive stress for a wide range of compressive strengths.” Mater. Struct. 27 (4): 206–210. https://doi.org/10.1007/BF02473034.
Der Kiureghian, A., H. Z. Lin, and S. J. Hwang. 1987. “Second-order reliability approximations.” J. Eng. Mech. 113 (8): 1208–1225. https://doi.org/10.1061/(ASCE)0733-9399(1987)113:8(1208).
Diniz, S. M. C., and D. M. Frangopol. 1997. “Reliability bases for high-strength concrete columns.” J. Struct. Eng. 123 (10): 1375–1381. https://doi.org/10.1061/(ASCE)0733-9445(1997)123:10(1375).
Ditlevsen, O., and H. O. Madsen. 2005. Structural reliability methods. Chichester, UK: Wiley.
Eid, R., and P. Paultre. 2008. “Analytical model for FRP-confined circular reinforced concrete columns.” J. Compos. Constr. 12 (5): 541–552. https://doi.org/10.1061/(ASCE)1090-0268(2008)12:5(541).
Ellingwood, B., T. V. Galambos, J. G. MacGregor, and C. A. Cornell. 1980. Development of a probability based load criterion for American national standard A58. NBS Special Publication SP577. Washington, DC: National Bureau of Standards.
Fardis, M. N., and H. H. Khalili. 1982. “FRP-encased concrete as a structural material.” Mag. Concr. Res 34 (121): 191–202. https://doi.org/10.1680/macr.1982.34.121.191.
Filippou, F. C., E. P. Popov, and V. V. Bertero. 1983. Effects of bond deterioration on hysteretic behaviour of reinforced concrete joints. Earthquake Engineering Research Center. Rep. UCB/EERC-83/19, Berkeley, CA: Univ. of California.
GB (Guobiao Standard). 2010. Technical code for infrastructure application of FRP composites. [In Chinese.] GB50608. Beijing: Ministry of Housing and Urban-Rural Development, General Administration of Quality Supervision, Inspection and Quarantine.
Hasofer, A. M., and M. C. Lind. 1974. “An exact and invariant first order reliability format.” J. Eng. Mech. 100: 111–121.
Hu, D., and M. Barbato. 2014. “Simple and efficient finite element modeling of reinforced concrete columns confined with fiber-reinforced polymers.” Eng. Struct. 72: 113–122. https://doi.org/10.1016/j.engstruct.2014.04.033.
Israel, M., B. Ellingwood, and R. Corotis. 1987. “Reliability-based code formulations for reinforced concrete buildings.” J. Struct. Eng. 113 (10): 2235–2252. https://doi.org/10.1061/(ASCE)0733-9445(1987)113:10(2235).
Kaeseberg, S., D. Messerer, and K. Holschemacher. 2019. “Assessment of standards and codes dedicated to CFRP confinement of RC columns.” Materials (Basel) 12 (15): 1–15. https://doi.org/10.3390/ma12152390.
Lam, L., and J. G. Teng. 2003. “Design-oriented stress–strain model for FRP-confined concrete.” Constr. Build. Mater. 17 (6–7): 471–489. https://doi.org/10.1016/S0950-0618(03)00045-X.
Li, J., and M. N. S. Hadi. 2003. “Behaviour of externally confined high-strength concrete columns under eccentric loading.” Compos. Struct. 62 (2): 145–153. https://doi.org/10.1016/S0263-8223(03)00109-0.
Liu, P. L., and A. Der Kiureghian. 1991. “Optimization algorithms for structural reliability.” Struct. Saf. 9 (3): 161–177. https://doi.org/10.1016/0167-4730(91)90041-7.
Mander, J. B, M. J. N. Priestley, and R. Park. 1988. “Theoretical stress–strain model for confined concrete.” J. Struct. Eng. 114 (8): 1804–1826. https://doi.org/10.1061/(ASCE)0733-9445(1988)114:8(1804).
Mazzoni, S., F. McKenna, M. H. Scott, and G. L. Fenves. 2006. “OpenSees command language manual.” Berkeley, CA: Pacific Earthquake Engineering Research Center.
Melchers, R. E. 1989. “Importance sampling in structural systems.” Struct. Saf. 6 (1): 3–10. https://doi.org/10.1016/0167-4730(89)90003-9.
Menegotto, M., and P. E. Pinto. 1973. “Method of analysis for cyclically loaded reinforced concrete plane frames including changes in geometry and nonelastic behavior of elements under combined normal force and bending.” In IABSE Symp. Resistance and Ultimate Deformability of Structures Acted on by Well-Defined Repeated Loads, 15–22. Zurich, Switzerland: International Association for Bridge and Structural Engineering.
Micelli, F., R. Mazzotta, M. Leone, and M. A. Aiello. 2015. “Review study on the durability of FRP-confined concrete.” J. Compos. Constr. 19 (3): 04014056. https://doi.org/10.1061/(ASCE)CC.1943-5614.0000520.
Mirza, S. A., and J. G. MacGregor. 1982. “Probabilistic study of strength of reinforced concrete members.” Can. J. Civ. Eng. 9 (3): 431–448. https://doi.org/10.1139/l82-053.
Nowak, A. S., and K. R. Collins. 2000. Reliability of structures. New York: McGraw Hill.
Nowak, A. S., A. M. Rakoczy, and E. K. Szeliga. 2012. “Revised statistical resistance models for RC structural components.” Spec. Publ. 284: 1–16.
Nowak, A., E. Szeliga, M. Szerszen, A. Szwed, and P. J. Podhorecki. 2008. “Reliability-Based Calibration for Structural Concrete, Phase 3.” Portland Cement Association, Research and Development Serial No. 2849, pp. 1–110.
Nowak, A. S., and M. M. Szerszen. 2003. “Calibration of design code for buildings (ACI 318): Part 1—Statistical models for resistance.” ACI Struct. J. 100 (3): 377–382.
Okeil, A. M., A. Belarbi, and D. A. Kuchma. 2013. “Reliability assessment of FRP-strengthened concrete bridge girders in shear.” J. Compos. Constr. 17 (1): 91–100. https://doi.org/10.1061/(ASCE)CC.1943-5614.0000315.
Parvin, A., and D. Brighton. 2014. “FRP composites strengthening of concrete columns under various loading conditions.” Polymers (Basel) 6: 1040–1056. https://doi.org/10.3390/polym6041040.
Peng, J., J. C. M. Ho, H. J. Pam, and Y. L. Wong. 2012. “Equivalent stress block for normal-strength concrete incorporating strain gradient effect.” Mag. Concr. Res. 64 (1): 1–19. https://doi.org/10.1680/macr.2012.64.1.1.
Petersons, N. 1968. “Should standard cube test specimens be replaced by test specimens taken from structures?” Matériaux Constr. 1 (5): 425–435. https://doi.org/10.1007/BF02473740.
Pipa, M. J. 1995. “Ductilidade de elementos de betão armado sujeitos a ações cíclicas. Influência das características mecânicas das armaduras.” [In Portuguese.] Ph.D. thesis, Dept. of Civil Engineering, Technical Univ. of Lisbon.
Rackwitz, R., and B. Fiessler. 1978. “Structural reliability under combined random load sequences.” Comput. Struct. 9 (5): 489–494. https://doi.org/10.1016/0045-7949(78)90046-9.
Realfonzo, R., and A. Napoli. 2011. “Concrete confined by FRP systems: Confinement efficiency and design strength models.” Composites, Part B 42 (4): 736–755. https://doi.org/10.1016/j.compositesb.2011.01.028.
Richart, F. E., A. Brandtzaeg, and R. L. Brown. 1929. The failure of plain and spirally bound concrete in compression. Bulletin No. 190. Champaign, IL: Univ. of Illinois, Engineering Experiment Station.
Richart, F. E., and R. L. Brown. 1934. An investigation of reinforced concrete columns. Bulletin No. 267, Champaign, IL: Univ. of Illinois, Engineering Experiment Station.
Rocca, S. 2007. “Experimental and analytical evaluation of FRP-confined large size reinforced concrete columns.” Ph.D. thesis, Dept. of Civil, Architectural and Environmental Engineering, Univ. of Missouri.
Roy, N., P. Paultre, and J. Proulx. 2010. “Performance-based seismic retrofit of a bridge bent: Design and experimental validation.” Can. J. Civ. Eng. 37 (3): 367–379. https://doi.org/10.1139/L09-138.
Scanlon, A. 1995. “Applications in concrete structures.” In Probabilistic structural mechanics handbook: Theory and industrial applications, edited by C. Sundararajan, 663–683. London: Chapman and Hall.
Slater, W. A., and I. Lyse. 1931. “First progress report on column tests at Lehigh University.” Proc. ACI 27 (2): 677–730
Spoelstra, M. R., and G. Monti. 1999. “FRP-confined concrete model.” J. Compos. Constr. 3 (3): 143–150. https://doi.org/10.1061/(ASCE)1090-0268(1999)3:3(143).
Szerszen, M. M., and A. S. Nowak. 2003. “Calibration of design code for buildings (ACI 318): Part 2—Reliability analysis and resistance factors.” ACI Struct. J. 100 (3): 383–391.
Teng, J. G., G. Lin, and T. Yu. 2015. “Analysis-oriented stress–strain model for concrete under combined FRP-steel confinement.” J. Compos. Constr. 19 (5): 04014084. https://doi.org/10.1061/(ASCE)CC.1943-5614.0000549.
Val, D. V. 2003. “Reliability of fiber-reinforced polymer-confined reinforced concrete columns.” J. Struct. Eng. 129 (8): 1122–1130. https://doi.org/10.1061/(ASCE)0733-9445(2003)129:8(1122).
Wang, N., and B. R. Ellingwood. 2015. “Limit state design criteria for FRP strengthening of RC bridge components.” Struct. Saf. 56: 1–8. https://doi.org/10.1016/j.strusafe.2015.03.004.
Wang, Y. C., and J. I. Restrepo. 2001. “Investigation of concentrically loaded reinforced concrete columns confined with glass fiber-reinforced polymer jackets.” ACI Struct. J. 98 (3): 377–385.
Wiśniewski, D. F., P. J. S. Cruz, A. A. R. Henriques, and R. A. D. Simões. 2012. “Probabilistic models for mechanical properties of concrete, reinforcing steel and pre-stressing steel.” Struct. Infrastruct. Eng. 8 (2): 111–123. https://doi.org/10.1080/15732470903363164.
Wu, H. C., and C. D. Eamon. 2017. Strengthening of concrete structures using fiber reinforced polymers (FRP): Design, construction and practical applications. Sawston, UK: Woodhead Publishing.
Zignago, D., and M. Barbato. 2021. “Effects of transverse steel on the axial-compression strength of FRP-confined reinforced concrete columns based on a numerical parametric study.” J. Compos. Constr. 25 (4): 04021024. https://doi.org/10.1061/(ASCE)CC.1943-5614.0001135.
Zignago, D., M. Barbato, and D. Hu. 2018. “Constitutive model of concrete simultaneously confined by FRP and steel for finite-element analysis of FRP-confined RC columns.” J. Compos. Constr. 22 (6): 04018064. https://doi.org/10.1061/(ASCE)CC.1943-5614.0000902.
Zou, Y., and H. P. Hong. 2011. “Reliability assessment of FRP-confined concrete columns designed for buildings.” Struct. Infrastruct. Eng. 7 (3): 243–258. https://doi.org/10.1080/15732470802416998.
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Published In
Journal of Composites for Construction
Volume 26 • Issue 3 • June 2022
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Aug 31, 2021
Accepted: Dec 12, 2021
Published online: Feb 24, 2022
Published in print: Jun 1, 2022
Discussion open until: Jul 24, 2022
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