Title:
Chaos Expansion for Long-Term Behavior of Carbon Fiber- Reinforced Polymer-Strengthened Reinforced Concrete Beams
Author(s):
David Micnhimer and Yail J. Kim
Publication:
Structural Journal
Volume:
117
Issue:
2
Appears on pages(s):
105-116
Keywords:
carbon fiber-reinforced polymer (CFRP); long-term; modeling; polynomial chaos expansion; rehabilitation; strengthening
DOI:
10.14359/51716805
Date:
3/1/2020
Abstract:
This paper presents a robust mathematical model to predict the long-term behavior of reinforced concrete beams strengthened with carbon fiber-reinforced polymer (CFRP) sheets. The model is constructed using the theory of Polynomial Chaos Expansion (PCE) in conjunction with the adjusted effective modulus method. The formulation of PCE is composed of quadrature rules, variable transformations, and solution algorithms, including a step-by-step implementation procedure. After verifying the modeling approach against experimental beams taken from literature, a benchmark beam is designed and used for parametric investigations in order to understand the effects of various attributes on the strengthened beam subjected to sustained loads for up to 4000 days. The creep and shrinkage of the concrete appreciably develop with time, whereas the macroscopic behavior of CFRP is relatively insusceptible. The sectional response of the beam alters owing to the
increased concrete strain and stabilizes as the amount of compression steel rises. The debonding failure of CFRP is not noticed when the beam is loaded up to 50% of its flexural capacity. The efficacy of CFRP-strengthening is substantiated through reducing steel stresses and long-term deflections, which are particularly noticeable when the beam cracks.
Related References:
1. Neville, A. M., Properties of Concrete, fourth edition, Prentice Hall, Essex, UK, 1995.
2. ACI Committee 318, “Building Code Requirements for Structural Concrete (ACI 318-14) and Commentary,” American Concrete Institute, Farmington Hills, MI, 2014, 520 pp.
3. Shahrooz, B. M.; Boy, S.; and Baseheart, T. M., “Flexural Strengthening of Four 76-Year-Old T-Beams with Various Fiber-Reinforced Polymer Systems: Testing and Analysis,” ACI Structural Journal, V. 99, No. 5, Sept.-Oct. 2002, pp. 681-691.
4. Williams, G.; Al-Mahaidi, R.; and Kalfat, R., “The West Gate Bridge: Strengthening of a 20th Century Bridge for 21st Century Loading,” Fiber-Reinforced Polymer Reinforcement for Concrete Structures, SP-275, R. Sen, R. Seracino, C. Shield, and W. Gold, eds., American Concrete Institute, Farmington Hills, MI, 2011, pp. 1-18.
5. Jung, W. T.; Keum, M. S.; Park, J. S.; Kang, J. Y.; Park, Y. H.; Chung, W.; and Kim, Y. J., “Composite Strengthening of a Bridge,” Concrete International, V. 39, No. 5, May 2017, pp. 48-53.
6. Tan, K. H., and Saha, M. K., “Long-Term Deflections of
Reinforced Concrete Beams Externally Bonded with FRP System,”
Journal of Composites for Construction, ASCE, V. 10, No. 6, 2006, pp. 474-482. doi: 10.1061/(ASCE)1090-0268(2006)10:6(474)
7. Sobuz, H. R.; Ahmed, E.; Sutan, N. M.; Hasan, N. M. S.; Uddin, H. M.; and Uddin, M. J., “Bending and Time-Dependent Responses of RC Beams Strengthened with Bonded Carbon Fiber Composite Laminates,” Construction and Building Materials, V. 29, 2012, pp. 597-611.
doi: 10.1016/j.conbuildmat.2011.11.006
8. El-Sayed, A. K.; Al-Zaid, R. A.; Al-Negheimish, A. I.; Shuraim, A. B.; and Alhozaimy, A. M., “Long-Term Behavior of Wide Shallow
RC Beams Strengthened with Externally Bonded CFRP Plates,”
Construction and Building Materials, V. 51, 2014, pp. 473-483.
doi: 10.1016/j.conbuildmat.2013.10.055
9. fib, “Externally Bonded FRP Reinforcement for RC Structures,” Bulletin 14, International Federation for Structural Concrete, Lausanne, Switzerland, 2001.
10. AASHTO, “Design of Bonded FRP Systems for Repair and Strengthening of Concrete Bridge Elements,” American Association of State Highway Transportation Officials, Washington, DC, 2012.
11. ACI Committee 440, “Guide for the Design and Construction of Externally Bonded FRP Systems for Strengthening Concrete Structures (ACI 440.2R-17),” American Concrete Institute, Farmington Hills, MI, 2017, 112 pp.
12. Plevris, N., and Triantafillou, T. C., “Time-Dependent Behavior of RC Members Strengthened with FRP Laminates,” Journal of
Structural Engineering, ASCE, V. 120, No. 3, 1994, pp. 1016-1042.
doi: 10.1061/(ASCE)0733-9445(1994)120:3(1016)
13. Arockiasamy, M.; Chidambaram, S.; Amer, A.; and Shahawy, M., “Time-Dependent Deformations of Concrete Beams Reinforced with CFRP Bars,” Composites. Part B, Engineering, V. 31, No. 6-7, 2000, pp. 577-592. doi: 10.1016/S1359-8368(99)00045-1
14. Sudret, B.; Blatman, G.; and Berveiller, M., “Chapter 8: Response Surfaces Based on Polynomial Chaos Expansions,” Construction Reliability: Safety, Variability and Sustainability, Wiley, Hoboken, NJ, 2011.
15. McClarren, R. G., “Polynomial Chaos Expansions for Uncertainty Quantification,” AICES EU Regional School, Aachen Institute for Advanced Study in Computational Engineering, Aachen, Germany, 2016.
16. Baudin, M., and Martinez, J.-M., “Introduction to Polynomials Chaos with NISP,” Scilab Enterprises, Rungis Complexe, France, 2013.
17. CEB-FIP, “Model Code for Concrete Structures,” Comite Euro-international du Beton, Federation Internationale de la Precontrainte, Thomas Telford, London, UK, 1990.
18. ACI Committee 435, “Control of Deflection in Concrete Structures (ACI 435R-95(00)),” American Concrete Institute, Farmington Hills, MI, 2003, 89 pp.
19. CEN, “Eurocode 2: Design of Concrete Structures (EN 1992-1-1: 2004),” Comite Europeen de Normalisation, Brussels, Belgium, 2004.
20. ACI Committee 209, “Guide for Modeling and Calculating Shrinkage and Creep in Hardened Concrete (ACI 209.2R-08),” American Concrete Institute, Farmington Hills, MI, 2008, 45 pp.
21. Gilbert, R. I., “Deflection Calculation for Reinforced Concrete Structures—Why We Sometimes Get It Wrong,” ACI Structural Journal, V. 96, No. 6, Nov.-Dec. 1999, pp. 1027-1032.
22. Bischoff, P. H., and Scanlon, A., “Effective Moment of Inertia for Calculating Deflections of Concrete Members Containing Steel Reinforcement and Fiber-Reinforced Polymer Reinforcement,” ACI Structural Journal, V. 104, No. 1, Jan.-Feb. 2007, pp. 68-75.
23. Giussani, F., “The Effects of Temperature Variations on the Long-Term Behaviour of Composite Steel-Concrete Beams,” Engineering Structures, V. 31, No. 10, 2009, pp. 2392-2406. doi: 10.1016/j.engstruct.2009.05.014
24. Shimizu, Y.; Hirosawa, M.; and Zhou, J., “Statistical Analysis of Concrete Strength in Existing Reinforced Concrete Buildings in Japan,” Proceedings of 12th World Conference on Earthquake Engineering, New Zealand Society for Earthquake Engineering, Paper No. 1499, 2000,
pp. 1-8.
25. Okeil, A.; El-Tawil, S.; and Shahawy, M., “Flexural Reliability of Reinforced Concrete Bridge Girders Strengthened with Carbon Fiber-Reinforced Polymer Laminates,” Journal of Bridge Engineering, ASCE, V. 7, No. 5, 2002, pp. 290-299. doi: 10.1061/(ASCE)1084-0702(2002)7:5(290)
26. Nowak, A. S., and Collins, K. R., Reliability of Structures, second edition, CRC Press, Boca Raton, FL, 2013.
27. Atadero, R. A., and Karbhari, V. M., “Calibration Of Resistance Factors for Reliability Based Design of Externally-Bonded FRP Composites,” Composites. Part B, Engineering, V. 39, No. 4, 2008, pp. 665-679. doi: 10.1016/j.compositesb.2007.06.004
28. Sánchez-Heres, L.; Ringsberg, J. W.; and Johnson, E., “Influence of Mechanical and Probabilistic Models on the Reliability Estimates of Fibre-Reinforced Cross-Ply Laminates,” Structural Safety, V. 51, 2014,
pp. 35-46. doi: 10.1016/j.strusafe.2014.06.001