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33 Figure 2.16. Strain variations along principal direction of critical FRP sheet. ments) for calculating Vf based on the comparisons of the FRP ance. Models 3, 9, 13, and 14 also demonstrated similar per- contributions predicted by each model to the experimentally formance across a broad range in categories. measured FRP contributions as reported in the database. Table 2.10 presents the average ratio of the shear strength pro- 2.8 Suggestions for Improved vided by FRP reinforcement (Vf,test/Vf), the COV, and the num- Design Methods ber of beams used in calculating this average for 13 segments of the experimental dataset. Vf,test is the experimentally mea- The statistical assessment of the performance of models sured strength of a test beam with FRP reinforcement minus the for Vf determined that the following five models provide experimentally measured strength of the corresponding (con- the lowest COV across a wide range of segments of the trol) beam without FRP reinforcement, and Vf is the strength database: calculated from each model. The first segment is the entire dataset of "all beams;" the second set contains only those test Model 3 (Triantafillou and Antonopoulos, 2000) results considered appropriate for calibrating provisions to be Model 9 (Chen and Teng, 2003a and 2003b) used in codes of practice including the AASHTO LRFD Bridge Model 13, (Cao et al., 2005) Design Specifications (AASHTO, 2008). This action reduced Model 14, (Zhang and Hsu, 2005) the potential number of available test results from 324 to 251. Model 18 (fib-TG 9.3, 2001 and Triantafillou and Antono- These results were further separated into segments according poulos, 2000) to the Mode of Failure (MoF), the use of steel shear reinforce- ment (No Av or With Av), and by combinations of these two. Based on the review of these models, a Vf model that includes It was apparent that within each segment, there was a large the following features would be appropriate for incorporation variation in the average strength ratio, and generally, the into the LRFD specifications (AASHTO, 2008): COVs are large because the models were derived to provide a best fit with a relatively small number of tests, and there is a axial stiffness of FRP reinforcement (f Ef) very wide range in types and effectiveness of FRP including compressive strength of concrete (fc) stiffness (Ef), ultimate strength (ffu), means of application, mode of failure (debonding or rupture) anchorage, orientation, and other factors. Therefore, the type of FRP application (full wrap, side bonding, or individual models would perform better (reasonable strength U-wrap) ratio and lower COV) for some segments of the test data than development length available for FRP (Le) others. For example, the model by Khalifa et al., (1998) shows bond strength between FRP and concrete (max) COV of 1.47 and 0.48 for members with observed rupture failures without and with steel shear reinforcement, respec- For use in design the Vf model must also consider the tively. Relationships for Vf in codes and guidelines are expected following: to consider a wide range of test results with a uniform average strength ratio and COV across all segments of the test data. 1. Complexity of Relationship for Evaluation. The major- Model (fib-TG9.3, 2001) exhibited the most uniform perform- ity of available models for Vf are much more complex than

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34 Table 2.10. Statistical evaluation of strength ratios Vf,test/Vf,model by test beam type. Khalifa and Nanni Monti and Liotta Hutchinson and Triantafillou and Chen and Teng Al-Sulaimani et Zhang and Hsu Saadatmanesh Pellegrino and Pellegrino and Antonopoulos Chaallal et al. Deniaud and Khalifa et al. Chajes et al. Carolin and CSA S806 Malek and fib-TG9.3 Cao et al. Hsu et al. Affiliation ACI 440 Modena Modena Rizkalla Taljsten Cheng Model JSCE al. Year 1994 1995 2000 1998 1998 2000 1999 2002 2003a,b 2002 2003 2001 2005 2005 2005b 2005 2006 2001 2001 2002 2008 Model # 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 1.) All Beams Mean 0.23 1.10 0.84 0.34 1.46 1.49 1.90 1.16 1.68 3.56 1.30 8.39 0.75 1.19 1.15 1.67 0.41 1.24 0.52 1.46 1.65 COV 0.67 1.05 1.10 0.81 1.05 1.03 1.01 0.77 0.64 2.29 0.89 1.71 0.71 0.59 0.81 0.75 0.73 0.60 0.76 0.99 0.96 Num 324 324 324 324 315 317 324 324 324 244 244 324 324 324 324 324 324 317 324 324 317 2.) All "Valid" Beams (those used in LRFD Vf Model Calibration) Mean 0.25 1.23 0.98 0.38 1.53 1.57 2.10 1.18 1.83 3.24 1.39 9.30 0.78 1.30 1.25 1.84 0.44 1.35 0.57 1.61 1.78 COV 0.62 0.94 0.56 0.73 0.97 0.95 0.91 0.60 7.57 1.34 0.89 1.71 0.57 0.53 0.73 0.66 0.67 0.50 0.66 0.89 0.88 Num 251 251 251 251 244 244 251 251 251 187 187 251 251 251 251 251 251 244 251 251 244 3.) "Valid" Beams: MoF = Rupture Mean 0.24 0.88 0.81 0.32 1.25 1.32 1.53 1.07 1.48 2.73 1.35 8.85 0.62 1.22 1.08 1.58 0.38 1.17 0.48 1.18 1.35 COV 0.69 0.70 0.38 0.69 0.57 0.69 0.68 0.62 0.45 1.16 0.79 1.33 0.52 0.44 0.69 0.51 0.63 0.43 0.59 0.67 0.61 Num 126 126 126 126 125 125 126 126 126 94 94 126 126 126 126 126 126 125 126 126 125 4.) "Valid" Beams: MoF = Debonding Mean 0.22 1.60 1.19 0.49 2.14 2.07 2.73 1.43 2.23 4.85 1.92 15.70 1.01 1.64 1.65 2.31 0.56 1.58 0.73 2.09 2.36 COV 0.45 1.00 0.62 0.77 1.18 1.18 0.96 0.67 0.57 1.31 1.03 1.63 0.49 0.56 0.77 0.73 0.73 0.48 0.72 0.94 1.00 Num 61 61 61 61 58 58 61 61 61 40 40 61 61 61 61 61 61 58 61 61 58 5.) "Valid" Beams: MoF = Other Mean 0.30 1.55 1.12 0.37 1.51 1.62 2.63 1.18 2.12 2.91 1.05 4.08 0.89 1.15 1.23 1.89 0.42 1.52 0.58 2.00 2.10 COV 0.53 0.82 0.53 0.56 0.72 0.66 0.80 0.66 0.54 1.35 0.35 1.29 0.53 0.52 0.56 0.64 0.50 0.50 0.55 0.78 0.73 Num 64 64 64 64 61 61 64 64 64 53 53 64 64 64 64 64 64 61 64 64 61 6.) "Valid" Beams: No Av Mean 0.30 1.48 1.14 0.41 1.74 1.92 2.54 1.01 2.06 1.89 1.22 4.31 0.83 1.23 1.36 1.89 0.47 1.49 0.62 1.94 2.15 COV 0.61 1.00 0.59 0.77 1.16 1.04 0.97 0.53 0.58 1.08 0.76 1.21 0.56 0.41 0.77 0.68 0.70 0.44 0.69 0.95 0.96 Num 114 114 114 114 108 108 114 114 114 108 108 114 114 114 114 114 114 108 114 114 108 7.) "Valid" Beam: With Av Mean 0.21 1.01 0.85 0.35 1.36 1.30 1.74 1.33 1.63 5.08 1.62 13.45 0.74 1.37 1.16 1.80 0.41 1.25 0.52 1.33 1.48 COV 0.54 0.71 0.44 0.67 0.58 0.62 0.68 0.70 0.51 1.13 0.96 1.49 0.56 0.59 0.67 0.64 0.63 0.53 0.61 0.67 0.62 Num 137 137 137 137 136 136 137 137 137 79 79 137 137 137 137 137 137 136 137 137 136 8.) "Valid" Beams: MoF = Debonding: No Av Mean 0.31 0.82 0.87 0.30 1.38 1.62 1.43 0.91 1.53 1.42 1.18 5.21 0.63 1.22 1.00 1.62 0.39 1.27 0.47 1.10 1.42 COV 0.71 0.77 0.40 0.73 0.65 0.74 0.75 0.47 0.49 0.65 0.52 0.77 0.57 0.40 0.73 0.55 0.71 0.42 0.60 0.75 0.67 Num 47 47 47 47 46 46 47 47 47 46 46 47 47 47 47 47 47 46 47 47 46 9.) "Valid" Beams: MoF = Rupture: No Av Mean 0.22 1.95 1.36 0.57 2.45 2.55 3.33 1.10 2.37 2.67 1.53 5.62 0.94 1.34 1.90 2.08 0.62 1.61 0.79 2.55 2.88 COV 0.39 1.09 0.73 0.86 1.47 1.35 1.05 0.61 0.67 1.34 1.06 1.50 0.60 0.43 0.86 0.90 0.78 0.54 0.84 1.03 1.13 Num 29 29 29 29 26 26 29 29 29 26 26 29 29 29 29 29 29 26 29 29 26 10.) "Valid" Beams: MoF = Other: No Av Mean 0.33 1.96 1.30 0.42 1.68 1.84 3.31 1.05 2.48 1.93 1.05 2.20 1.01 1.16 1.40 2.07 0.45 1.69 0.66 2.51 2.56 COV 0.50 0.67 0.43 0.33 0.69 0.60 0.65 0.48 0.42 0.64 0.30 0.48 0.41 0.38 0.33 0.51 0.36 0.32 0.37 0.64 0.64 Num 38 38 38 38 36 36 38 38 38 36 36 38 38 38 38 38 38 36 38 38 36 11.) "Valid" Beams: MoF = Debonding: With Av Mean 0.19 0.92 0.77 0.34 1.17 1.14 1.59 1.16 1.44 3.99 1.52 11.02 0.61 1.22 1.12 1.56 0.38 1.11 0.48 1.22 1.31 COV 0.50 0.65 0.36 0.66 0.49 0.55 0.64 0.65 0.42 0.99 0.89 1.28 0.48 0.46 0.66 0.48 0.57 0.43 0.58 0.63 0.55 Num 79 79 79 79 79 79 79 79 79 48 48 79 79 79 79 79 79 79 79 79 79 12.) "Valid" Beams: MoF = Rupture: With Av Mean 0.22 1.28 1.03 0.43 1.89 1.68 2.19 1.72 2.11 8.91 2.64 24.84 1.07 1.91 1.42 2.51 0.51 1.56 0.66 1.68 1.94 COV 0.50 0.57 0.32 0.53 0.48 0.57 0.54 0.62 0.42 0.92 0.89 1.27 0.39 0.56 0.53 0.59 0.62 0.43 0.48 0.52 0.53 Num 32 32 32 32 32 32 32 32 32 14 14 32 32 32 32 32 32 32 32 32 32 13.) "Valid" Beams: MoF = Other: With Av Mean 0.27 0.96 0.86 0.29 1.26 1.30 1.63 1.36 1.60 5.00 1.07 6.82 0.72 1.13 0.97 1.63 0.38 1.28 0.47 1.25 1.44 COV 0.56 0.97 0.64 0.89 0.73 0.73 0.93 0.76 0.69 1.24 0.44 1.07 0.69 0.69 0.89 0.83 0.67 0.74 0.80 0.90 0.77 Num 26 26 26 26 25 25 26 26 26 17 17 26 26 26 26 26 26 25 26 26 25