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38 2.0 1.8 JSCE, 2001 Carolin and U-Wrapping Taljsten, 2005b 1.6 Khalifa et al., 1998 1.4 CSA S806, 2002 Chajes et al., 1995 Vf / (bw df) (ksi) 1.2 Hutchinson and Rizkalla, 1999 1.0 ACI 440, 2008 0.8 Cao et al., 2005 Zhang Pellegrino and 0.6 and Hsu, Modena, 2002 2005 vfr Chaallal et al., 0.4 2002 fib-TG9.3, 2001 0.2 Monti and Liotta, 2005 Triantafillou and vfnr Antonopoulos, 2000 Chen & Teng, 2003a,b 0.0 0 25 50 75 100 125 150 175 200 225 250 275 f E f (ksi) Figure 3.1. Influence of FRP axial rigidity on FRP shear stress resistance. Comparison of this expression with the test data yields an (Chen and Teng, 2003a,b; Zhang and Hsu, 2005) provide average strength ratio (bias) of 1.44, and a corresponding values similar to those obtained from the models that provide COV of 0.25. the best estimates of FRP shear contribution (i.e., Triantafil- These expressions are only applicable for RC and PC mem- lou and Antonopoulos, 2000; and fib-TG9.3, 2001). bers in which dv /bv < 4.0, and the calculated R value should not be taken greater than one (i.e., R 1.0). Figure 3.1 shows the calculated shear stress capacity pro- 3.2 Design Guidelines vided by the FRP reinforcement (Vf /bw df) as a function of the Recommended design guidelines for concrete girders axial rigidity of the FRP reinforcement (f Ef) for 15 models and strengthened in shear with FRP were developed based on the the two relationships identified in this study for a member findings of this research. The guidelines, provided as Attach- having a rectangular cross-section and the following properties: ment B, were drafted in LRFD format to facilitate incorpo- ration into the AASHTO LRFD Bridge Design Specifications Dimensions: 7.09 inches wide, 19.69 inches high, and a (AASHTO, 2008). shear span-to-depth ratio of 3.5 FRP reinforcement: CFRP sheets externally bonded with fibers oriented at 90 in a U-wrap configuration over a 3.3 Design Examples height of 17.32 inches Concrete compressive strength: 8,557 psi Six design examples were prepared to illustrate the use of Modulus of elasticity of the CFRP sheets: 33,939 ksi the proposed design. Four of the design examples consider RC Ultimate tensile strength of the CFRP sheet: 653 ksi T-beams (i.e., two with transverse steel reinforcement and two without transverse steel reinforcement) with a U-wrap FRP The case of full anchorage for which FRP rupture failure is strengthening scheme with and without anchorage (i.e., two expected is labeled by vfr, and the case of less than full anchor- with mechanical anchorage and two without any anchorage). age for which debonding or other non-rupture failure modes The other two design examples consider PC I-girders with are expected is labeled vfnr. Figure 3.1 shows that the strength transverse steel reinforcement and U-wrap FRP strengthening when full anchorage is not provided is less than when full scheme with and without anchorage (i.e., one with mechanical anchorage is provided. In addition, the two relationships anchorage and one without any anchorage).