Design of FRP Systems for Strengthening Concrete Girders in Shear (2011)

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37 3.1 Approaches for Relevant Changes to AASHTO LRFD Bridge Design Specifications The models for Vf were selected to provide best fit empiri- cal expressions incorporating the variables that were found to influence Vf. These models were formulated and calibrated to achieve a βr value around 3.5 as characterized by the AASHTO LRFD Bridge Design Specifications (AASHTO, 2008). For the evaluation of the bias and COV of strength ratios Vtest/Vn, it was necessary to evaluate Vc + Vs. The AASHTO LRFD Bridge Design Specifications (AASHTO, 2008) provide six different means of evaluating shear resistance, however, only the sim- plified procedure was selected to calibrate the model for Vf to achieve the target reliability of, βr, 3.5. The simplified procedure for evaluating Vc and Vs is given by the following equations: While this method is not applicable to members greater than 16 inches in depth that do not contain shear reinforce- ment, the relationship provided for Vc is identical to that in the General Procedure (AASHTO, 2008) which is applicable to such members when distributed horizontal reinforcement is placed on 12-in. centers, and the strain in the longitudinal reinforcement (εs) is less than 0.00187. For εs = 0.00187: The contribution of the steel reinforcement is given by: where: θ = the angle of diagonal compression and α = the angle of the transverse reinforcement relative to the longitudinal axis of the member V A f d s s v y v = +(cot cot )sin ( . . . ) θ α α 5 8 3 3 4- β ε = +( ) +( ) = + ( )( 4 8 1 750 51 39 4 8 1 750 0 00187 . . .s xes ) +( ) = 51 39 12 2 00. V f b d V c c v v c = ′ = = 0 0316 5 8 3 3 1 2 0 06 . ( . . . ) . β β - For: 32 2 ′ ′ = ′ ′ f b d f V f b d f c v v c c c v v c ( ) ( in ksi or in psi) The contribution of the FRP reinforcement can be evalu- ated using the truss model used for evaluating the contribu- tion of the steel shear reinforcement. In this case: Since ffe = Efεfe, the contribution of the FRP to shear resistance may be controlled by εfe as done in most existing models for Vf. Based on the results of statistical assessments (including the reliability study) and for simplicity, the following expres- sions are proposed for determining the effective strain (εfe) and use in the AASHTO LRFD Bridge Design Specifications (AASHTO, 2008). When “full-anchorage” is provided such that the shear resistance at shear failure is controlled by FRP rupture: where ρfEf is in ksi units and limited to 300 ksi. Comparison of this expression with the test data yields an average strength ratio (bias) of 1.68 and a corresponding COV of 0.33. When “full-anchorage” is not provided, it is likely that the shear capacity will be controlled by FRP debonding or another mode of failure before FRP rupture can be achieved: where ρf Ef is in ksi units and limited to 300 ksi. ε ε ε ρ fe fu fu fu f f f R f E R E = ≤ = = ( )− 0 012 3 6 . . where and 7 1 0≤ . ε ε ε ρ fe fu fu fu f f f R where f E and R E = = = ( ) ≤−4 1 067. . If and then:θ α= ° = ° =45 90 V A f d s f f fe f f V A f d s f f fe f f = +( )cot cot sinθ α α If and then:θ α= ° = ° =45 90 V A f d s s v y v C H A P T E R 3 Application and Implementation

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