臺灣博碩士論文加值系統

A two-dimensional (2D) non-linear finite element analysis method was developed in this research to analyze the mechanical behavior of reinforced concrete beams with corroded steel reinforcement. The effects of corrosion were taken into consideration by: (1) modification of the constitutive law of concrete due to size effect and corrosion cracks, (2) loss of steel area, strength, and ductility, (3) hardening and buckling of steel bars, (4) modification of the bond constitutive law between corroded concrete and steel bars .The method was validated with published experimental results. A parametric study was carried out to examine the influences of concrete compressive strength corrosion level, reinforcement ratio, and shear span-to-depth ratios on the plastic hinge length of corroded beams. The plastic hinge length of a beam was obtained by using the tip displacement extracted from the beam finite element model combined with the yield and ultimate curvature derived from the sectional analysis of the beam. A smeared bond model was proposed to modify longitudinal rebar stress-strain relationship due to bond reduction the sectional analysis. Results of the study showed that, concrete compressive strengths as well as tensile reinforcement ratios did not show sound relations to plastic hinge length of corroded concrete beams. Besides, with a given a concrete strength, a corrosion level, a tensile reinforcement ratio, the plastic hinge length enlarged with an increase in span-to-depth ratio. Furthermore, corrosion level affected plastic hinge length. The effect of corrosion levels on the plastic hinge length was observed following two phases. First phase, low corrosion levels in range of 0% to 10%, 10% percent corrosion decreased the plastic hinge length by approximately 3.48 percent. Additionally, as to second phase, more severe corrosion levels in range of 10% to 25%, 10% corrosion resulted in about 21.67% reduction of the plastic hinge. Finally, simplified expressions were proposed to modify plastic hinge length owning to corrosion levels.

A two-dimensional (2D) non-linear finite element analysis method was developed in this research to analyze the mechanical behavior of reinforced concrete beams with corroded steel reinforcement. The effects of corrosion were taken into consideration by: (1) modification of the constitutive law of concrete due to size effect and corrosion cracks, (2) loss of steel area, strength, and ductility, (3) hardening and buckling of steel bars, (4) modification of the bond constitutive law between corroded concrete and steel bars .The method was validated with published experimental results. A parametric study was carried out to examine the influences of concrete compressive strength corrosion level, reinforcement ratio, and shear span-to-depth ratios on the plastic hinge length of corroded beams. The plastic hinge length of a beam was obtained by using the tip displacement extracted from the beam finite element model combined with the yield and ultimate curvature derived from the sectional analysis of the beam. A smeared bond model was proposed to modify longitudinal rebar stress-strain relationship due to bond reduction the sectional analysis. Results of the study showed that, concrete compressive strengths as well as tensile reinforcement ratios did not show sound relations to plastic hinge length of corroded concrete beams. Besides, with a given a concrete strength, a corrosion level, a tensile reinforcement ratio, the plastic hinge length enlarged with an increase in span-to-depth ratio. Furthermore, corrosion level affected plastic hinge length. The effect of corrosion levels on the plastic hinge length was observed following two phases. First phase, low corrosion levels in range of 0% to 10%, 10% percent corrosion decreased the plastic hinge length by approximately 3.48 percent. Additionally, as to second phase, more severe corrosion levels in range of 10% to 25%, 10% corrosion resulted in about 21.67% reduction of the plastic hinge. Finally, simplified expressions were proposed to modify plastic hinge length owning to corrosion levels.

ABSTRACT i
ACKNOWLEDGEMENTS ii
LIST OF TABLES v
LIST OF FIGURES vi
CHAPTER 1 INTRODUCTION 1
1.1 Background 1
1.2 Statement of problems 2
1.3 Objectives and Scope of the study 3
1.4 Outline 3
CHAPTER 2 PLASTIC HINGE LENGTH REVIEW 5
2.1 Previous research on Plastic hinge length 6
2.1.1 Barker (1956) 6
2.1.2 Mattock (1964, 1967) 8
2.1.3 Corley (1966) 9
2.1.4 Park, Priestley and Gill (1982) 10
2.1.5 Sakai and Sheikh (1989) 11
2.1.6 Mendis (2001) 11
2.1.7 Bae and Bayrak (2008) 11
2.1.8 Michael et al. (2008) 11
2.1.9 Ou et al. (2011) 12
2.2 Basic Knowledge of Plastic Hinge Length 13
CHAPTER 3 MATERIAL CONSTITUTIVE LAWS 15
3.1 Mechanical behavior of corroded reinforcement concrete structures 15
3.2 Corroded material model 17
3.2.1 Concrete 18
3.2.2 Tensile envelope curve 18
3.2.3 Compressive envelope curve 24
3.3 Steel reinforcing bar 33
3.3.1 Residual cross-section of corrosion damaged steel 33
3.3.2 Residual strength of corrosion damaged steel 36
3.3.3 Residual ductility of corrosion damaged steel 37
3.3.4 Tensile envelop curve of steel 39
3.3.5 Compression envelop curve of steel 42
3.4 Bond between reinforcement and concrete 45
3.4.1 Bond strength of corroded rebars. 45
3.4.2 Local bond stress-slip law 47
CHAPTER 4 FINITE ELEMENT VALIDATION 49
4.1 Finite element method modeling 49
4.2 Analysis of a plain concrete beam 49
4.3 Analysis of a reinforced concrete beam 53
4.4 Conclusions 76
CHAPTER 5 PARAMETRIC STUDY 77
5.1 Material properties 77
5.1.1 Concrete compressive strength (fc') 77
5.1.2 Steel strength 77
5.2 Design beam cross-section 78
5.2.1 Flexural members of special moment frame 78
5.2.2 Longitudinal reinforcement 79
5.2.3 Transverse reinforcement 80
5.3 Aspect ratio (L/h) 81
5.4 Corrosion level (X) 81
5.5 Check the specimens for shear strength requirement 82
5.6 Sectional analysis 89
5.6.1 Un-confined and confined concrete 89
5.6.2 Reinforcing bars 93
5.6.3 Ultimate condition 96
5.7 Results and discussion 96
5.7.1 Obtaining Plastic hinge length 97
5.7.2 Plastic hinge length result 98
5.7.3 Effect of corrosion level on plastic hinge length 102
5.7.4 Effect of compressive strength on plastic hinge length 105
5.7.5 Effect of reinforcement ratio on plastic hinge length 107
5.7.6 Effect of span-to-depth ratio on the plastic hinge length 109
CHAPTER 6 CONCLUSIONS 110
REFERENCES 112

1.Rodriguez J., Ortega L. M., Casal J., "Load carrying capacity of concrete structures with corroded reinforcement," Construction and Building Materials, V. 11, No. 4. 1997, pp. 239-248.
2.Pritpal S. Mangat, Mahmoud S. Elgarf, "Flexural strength of concrete beams with corroding reinforcement," ACI Structural Journal, V. 96, No. 1. January 1, 1999, pp. 149-158.
3.Mangat P. S., Elgarf M. S., "Strength and serviceability of repaired reinforced concrete beams undergoing reinforcement corrosion," Magazine of Concrete Research, V. 51, No. 2. April 1999, pp. 97-112.
4.Almusallam Abdullah A., Al-Gahtani Ahmad S., Aziz Abdur Rauf, Dakhil Fahd H., Rasheeduzzafar, "Effect of reinforcement corrosion on flexural behavior of concrete slabs," Journal of Materials in Civil Engineering, V. 8, No. 3. 1996, pp. 123-127.
5.Du Yingang, Clark Leslie A., Chan Andrew H. C., "Impact of renforcement corrosion on ductile behavior of reinforced concrete beams," ACI Structural Journal, V. 104, No. 3. May 2007, pp. 285-293.
6.Baker A. L. L., "Ultimate load theory applied to the design of reinforced and prestressed concrete frames," Concrete Publication Ltd, London, Uk. 1956, pp. 91.
7.Barker, A.L.L, Amarakone A.M.N, "Inelastic hyperstatic frame analysis," Flexural Mechanics of Reinforced Concrete, V. 12, American Concrete Institute, Farmington Hill. 1964, pp. 85-142.
8.Mattock A.H., "Rotational capacity of hinging regions in reinforced concrete beams," Flexural Mechanics of Reinforced Concrete, V. 12, American Concrete Institute, Farmington Hill, MI. 1964, pp. 143-181.
9.Mattock, A.H., "Discussion of Rotational Capacity of Hinging Regions In Reinforced Concrete Beams," Journal of structural Engineering, ASCE, V. 93, No. 2. 1967, pp. 519-522.
10.Corley W.G, "Rotational capacity of reinforced concrete beams," Journal of Structural Division, ASCE, V. 91, No. 5. 1966, pp. 121-146.
11.Park R., Paulay T., "Reinforced concrete structures," John Wiley and Sons, New York. 1975, pp. 769.
12.Park R., Priestley M.J.N., Gill W.D., "Ductility of square-confined soncrete columns," Journal of Structural Division, ASCE, V. 108, No. 4. 1982, pp. 929-950.
13.Priestley M. J. N., Park R., "Strength and ductility of concrete bridge columns under seismic loading," ACI Structural Journal, V. 84, No. 1. 1987, pp. 61-67.
14.Paulay T., Priestley M. J. N., "Seismic design of reinforced concrete and mansory buildings," John Wiley and Sons, New York. 1992, pp. 767.
15.Sakai K., Sheikh S. A., "What do we know about confinement in reinforced concrete columns," ACI Structural Journal, V. 86, No. 2. Mar-Apr 1989, pp. 192-207.
16.Mendis P., "Plastic hinge lengths of normal and high-strength concrete in flexure," Advance in Structural Engineering, V. 4, No. 4. 2001, pp. 189-195.
17.Bae S., Bayrak O., "Plastic hinge length of reinforced concrete columns," ACI Structural Journal, V. 105, No. 3. 2008, pp. 290-300.
18.Michael P. Berry, Dawn E. Lehman, Lowes Laura N., "Lumped- Plasticity models for performance simulation of bridge columns," ACI Structural Journal, V. 105, No. 3. May-Jun 2008, pp. 270-279.
19.Ou Y. C., Kurniawan R. A., Kurniawan D. P., Nguyen D.N., "Plastic hinge length of circular reinforced concrete columns," Computers and Concrete. 2011, pp. (In review).
20.Rilem Report Series 14, "Durability design of concrete structures," Sarja, Asko & Vesikari, Erkki (Editors), V. 1996, E&FN Spon, Chapman & Hall.
21.Cairns John, Plizzari Giovanni A., Du Yingang, Law David W., Franzoni Chiara, "Mechanical properties of corrosion-damaged reinforcement," ACI Material Journal, V. 102, No. 4. July 1, 2005, pp. 256-264.
22.Du Y. G., Clark L. A., Chan A. H. C., "Residual capacity of corroded reinforcing bars," Magazine of Concrete Research, V. 57, No. 3. 2005, pp. 135-147.
23.Bažant Zdeněk, Oh B., "Crack band theory for fracture of concrete," Materials and Structures, V. 16, No. 3. 1983, pp. 155-177.
24.Horijk D. A., Cornelissen H. A. W., Reinhardt H. W., "Experimental determination of crack softening characteristics of normal-weight and lightweight concrete," Heron, V. 31, No. 2. 1986, pp. 45-56.
25.Diana, "DIANA Finite Element Analysis," User's Manual, V. Release 9.4., TNO Building and Construction Research, Delft, the Netherlands.
26.Ceb-Fib, "CEB-FIB Model Code 1990," Bulletin d'Information 213/214, V. Lausanne, Switzerland, 1993, 437 pp.
27.Hanjari Kamyab Zandi, Kettil Per, Lundgren Karin, "Analysis of mechanical behavior of corroded reinforced concrete structures," ACI Structural Journal, V. 108, No. 5. Sep-Oct, 2011, pp. 532-541.
28.Van Mier Jan, "Multiaxial strain-softening of concrete," Materials and Structures, V. 19, No. 3. 1986, pp. 179-190.
29.Jansen Daniel C., Surendra P. Shah, "Effect of length on compressive strain softening of concrete," Journal of Engineering Mechanics, V. 123, No. 1. 1997, pp. 25-35.
30.Powanusorn Suraphong, "Effect of confinement on shear dominated reindorced concrete element," PhD thesis, V. Texas A&M University. 2003.
31.Alca N., Alexander S. D.B., Macgregor J. G., "Effect of size on flexural behavior of high-strength concrete beams," ACI Structural Journal, V. 94, No. 1. 1997, pp. 59-67.
32.Belgin ağatay M., Şener Sıddık, "Size effect on failure of overreinforced concrete beams," Engineering Fracture Mechanics, V. 75, No. 8. 2008, pp. 2308-2319.
33.Kim Jin-Keun, Yi Seong-Tae, Park Chan-Kyu, Eo Seok-Hong, "Size effect on compressive strength of plain and spirally reinforced concrete cylinders," ACI Structural Journal, V. 96, No. 1. Jan 1999, pp. 88-94.
34.Yi Seong-Tae, Kim Min-Su, Kim Jin-Keun, Kim Jang-Ho Jay, "Effect of specimen size on flexural compressive strength of reinforced concrete members," Cement and Concrete Composites, V. 29, No. 3. 2007, pp. 230-240.
35.Hillerborg Arne, "Fracture mechanics concepts applied to moment capacity and rotational capacity of reinforced concrete beams," EngineeringFracture Mechanics, V. 35, No. 1. 1990, pp. 233-240.
36.Hillerborg A., "The compression stress-strain curve for design of reinforced concrete beams," Fracture Mechanics: Application to concrete, Sp-118, American Institute, V. Detroit. 1989, pp. 281-294.
37.Bažant Zdeněk P., "Identification of strain-softening constitutive relation from uniaxial tests by series coupling model for localization," Cement and Concrete Research, V. 19, No. 6. 1989, pp. 973-977.
38.Feenstra P. H., "Computational aspects of biaxial stress in plain and reinforced concrete," PhD thesis, V. Delft University, the Netherlands. 1993.
39.Thorenfeldt E., Tomaszewicz A., Jensen J. J., "Mechanical properties of high-strength concrete and applications in design," Conference on the Utilization of High-Strength Conrete, Stavanger, Norway. 1987, pp. 149-159.
40.Vecchio F. J., Collins M. P., "The modified compression-field theory for reinforced concrete elements subjected to shear," Journal Proceedings, V. 83, No. 2. March 1, 1986, pp. 219-231.
41.He Wei, Wu Y. F., Liew K. M., Wu Zhishen, "A 2D total strain based constitutive model for predicting the behaviors of concrete structures," International Journal of Engineering Science, V. 44, No. 18-19. 2006, pp. 1280-1303.
42.Cervenka Vladimir, Cervenka Jan, "Computer simulation as a design tool for concrete structures," ICCE-96, The Second International Conference in Civil Engineering on Computer Applications, Research and Practice, V. Bahrain. 6-8 April 1996.
43.Vonk R., "Softening of concrete loaded in compression," PhD thesis, V. Eindhoven Univ. of Technol., Eindhoven, The Netherlands. 1992.
44.Torsak L., Ken W., Maki M., Junichiro N., "Localization effects and fracture mechanics of concrete in compression," Proceedings of the Japan Concrete Institute, V. 22, No. 3. 2000, pp. 145-150.
45.Nakamura H., Higai T., "Compressive fracture energy and fracture zone length of concrete," Modeling of Inelastic Behavior of RC Structures under Seismic Loads. 2001, pp. 471-487.
46.Vecchio F. J., Collins M. P., "Compression response of cracked reinforced concrete," Journal of Structural Engineering, V. 119, No. 12. 1993, pp. 3590-3610.
47.Coronelli D., Gambarova P., "Structural assessment of corroded reinforced concrete beams: Modeling guidelines," Journal of Structural Engineering, V. 130, No. 8. 2004, pp. 1214-1224.
48.Cape M., "Residual service-life assessment of existing R/C structures," MSc thesis, V. Chalmers University of Technology, Gothenburg, Sweden, and Milan University of Technology, Milan, Italy. 1999, pp. 133.
49.Pantazopoulou S. J., Papoulia K. D., "Modeling cover-cracking due to reinforcement corrosion in RC structures," Journal of Engineering Mechanics, V. 127, No. 4. 2001, pp. 342-351.
50.Youping Liu, Richard E. Weyers, "Modeling the time-to-corrosion cracking in chloride contaminated reinforced concrete structures," ACI Materials Journal, V. 95, No. 6. November 1, 1998, pp. 675-680.
51.Molina F., Alonso C., Andrade C., "Cover cracking as a function of rebar corrosion: Part 2—Numerical model," Materials and Structures, V. 26, No. 9. 1993, pp. 532-548.
52.Alexandros N. Kallias, Rafiq M. Imran "Finite element investigation of the structural response of corroded RC beams," Engineering Structures, V. 32, No. 9. 2010, pp. 2984-2994.
53.Bhargava Kapilesh, Ghosh A. K., Mori Yasuhiro, Ramanujam S., "Model for cover cracking due to rebar corrosion in RC structures," Engineering Structures, V. 28, No. 8. 2006, pp. 1093-1109.
54.Dimitri Val V., Robert Melchers E., "Reliability of deteriorating RC slab bridges," Journal of Structural Engineering, V. 123, No. 12. 1997, pp. 1638-1644.
55.Gonzalez J. A., Andrade C., Alonso C., Feliu S., "Comparison of rates of general corrosion and maximum pitting penetration on concrete embedded steel reinforcement," Cement and Concrete Research, V. 25, No. 2. 1995, pp. 257-264.
56.Almusallam A. A., "Effect of degree of corrosion on the properties of reinforcing steel bars," Construction and Building Materials, V. 15, No. 8. 2001, pp. 361-368.
57.Lee Han-Seung, Cho Young-Sang, "Evaluation of the mechanical properties of steel reinforcement embedded in concrete specimen as a function of the degree of reinforcement corrosion," International Journal of Fracture, V. 157, No. 1. 2009, pp. 81-88.
58.Andrade C., Alonso C., Garcia D., Rodriguez J., "Remaining lifetime of reinforced concrete structures: Effect of corrosion in the mechanical properties of the steel, Life predication of corrodible structures," Proceedings of the International Symposium of the National Assiciation of Corrosion Engineers, Cambridge, UK. 23-26 September1991, pp. 12/11-12/11.
59.Palsson Ragnar, Mirza Saeed M., "Mechanical response of corroded steel reinforcement of abandoned concrete bridge," ACI Structural Journal, V. 99, No. 2. March 1, 2002, pp. 157-162.
60.Apostolopoulos Ch. Alk, Michalopoulos D., Dimitrov L., "The impact of corrosion on the mechanical behavior of welded splices of reinforcing steel S400 and B500," Journal of Materials Engineering and Performance, V. 17, No. 1. 2008, pp. 70-79.
61.Du Y. G., Clark L. A., Chan A. H. C., "Effect of corrosion on ductility of reinforcing bars," Magazine of Concrete Research, V. 57, No. 7. 2005, pp. 407-419.
62.Rodriguez Mario E., Botero Juan C., Villa Jaime, "Cyclic stress-strain behavior of reinforcing steel including effect of buckling," Journal of Structural Engineering, V. 125, No. 6. 1999, pp. 605-612.
63.Dhakal Rajesh Prasad, Maekawa Koichi, "Path-dependent cyclic stress–strain relationship of reinforcing bar including buckling," Engineering Structures, V. 24, No. 11. 2002, pp. 1383-1396.
64.Dhakal Rajesh Prasad , Maekawa Koichi "Modeling for postyield buckling of reinforcement," Journal of Structural Engineering, V. 128, No. 9. 2002, pp. 1139-1147.
65.Maaddawy Tamer El, Soudki Khaled, Topper Timothy, "Analytical model to predict nonlinear flexural behavior of corroded reinforced concrete beams," ACI Structural Journal, V. 102, No. 4. July 1, 2005, pp. 550-559.
66.Lundgren K., "Effect of corrosion on the bond between steel and concrete: an overview," Magazine of Concrete Research, V. 59, No. 6. 2007, pp. 447-461.
67.Bhargava Kapilesh, Ghosh A. K., Mori Yasuhiro, Ramanujam S., "Corrosion-induced bond strength degradation in reinforced concrete—Analytical and empirical models," Nuclear Engineering and Design, V. 237, No. 11. 2007, pp. 1140-1157.
68.Al-Sulaimani G. J., Kaleemullah M., Basunbul I. A., Rasheeduzzafar, "Influence of corrosion and cracking on bond behavior and strength of reinforced concrete members," ACI Structural Journal, V. 87, No. 2. March 1, 1990, pp. 220-231.
69.Fang Congqi, Lundgren Karin, Chen Liuguo, Zhu Chaoying, "Corrosion influence on bond in reinforced concrete," Cement and Concrete Research, V. 34, No. 11. 2004, pp. 2159-2167.
70.Lee Han-Seung, Noguchi Takafumi, Tomosawa Fuminori, "Evaluation of the bond properties between concrete and reinforcement as a function of the degree of reinforcement corrosion," Cement and Concrete Research, V. 32, No. 8. 2002, pp. 1313-1318.
71.Azad A.K., Ahmad S., Azher S.A., "Residual strength of corrosion-damaged reinforced concrete beams," ACI Material Journal, V. 104, No. 1. 2006, pp. 40-47.
72.Torres-Acosta Andres A., Navarro-Gutierrez Sergio, Teran-Guillen Jorge, "Residual flexure capacity of corroded reinforced concrete beams," Engineering Structures, V. 29, No. 6. 2007, pp. 1145-1152.
73.Aci Committee 318 "Building code requirements for structural concrete (ACI 318-08) and Commentary (ACI 318R-08)," American Concrete Institute, V. Farmington Hills, MI, U.S.A, 2008.
74.Mander J. B., Priestley M. J. N., Park R., "Theoretical stress-strain model for confined concrete," Journal of Structural Engineering, V. 114, No. 8. 1988, pp. 1804-1826.
75.Bhargava Kapilesh, Ghosh A. K., Mori Yasuhiro, Ramanujam S., "Suggested Empirical Models for Corrosion-Induced Bond Degradation in Reinforced Concrete," Journal of Structural Engineering, V. 134, No. 2. 2008, pp. 221-230.
76.Xtract/Ucfyber, "Xtract/UCFyber: Cross-sectional analysis of structural components," User's Manual, V. 3.0.8 , UC Berkeley. 2007.