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37 CHAPTER 3 Application and Implementation 3.1 Approaches for Relevant Av f y dv Changes to AASHTO LRFD If = 45 and = 90 then: Vs = s Bridge Design Specifications The contribution of the FRP reinforcement can be evalu- The models for Vf were selected to provide best fit empiri- ated using the truss model used for evaluating the contribu- cal expressions incorporating the variables that were found to tion of the steel shear reinforcement. In this case: influence Vf. These models were formulated and calibrated to achieve a r value around 3.5 as characterized by the AASHTO A f f fe d f LRFD Bridge Design Specifications (AASHTO, 2008). For the Vf = (cot + cot ) sin sf evaluation of the bias and COV of strength ratios Vtest/Vn, it was necessary to evaluate Vc + Vs. The AASHTO LRFD Bridge A f f fe d f If = 45 and = 90 then: V f = Design Specifications (AASHTO, 2008) provide six different sf means of evaluating shear resistance, however, only the sim- Since ffe = Ef fe, the contribution of the FRP to shear plified procedure was selected to calibrate the model for Vf to resistance may be controlled by fe as done in most existing achieve the target reliability of, r, 3.5. The simplified procedure models for Vf. for evaluating Vc and Vs is given by the following equations: Based on the results of statistical assessments (including Vc = 0.0316 fc bv dv (5.8.3.3-1) the reliability study) and for simplicity, the following expres- For: = 2 Vc = 0.0632 fc bv dv ( fc in ksi) sions are proposed for determining the effective strain (fe) or Vc = 2 fc bv dv ( fc in ps si) and use in the AASHTO LRFD Bridge Design Specifications (AASHTO, 2008). While this method is not applicable to members greater When "full-anchorage" is provided such that the shear than 16 inches in depth that do not contain shear reinforce- resistance at shear failure is controlled by FRP rupture: ment, the relationship provided for Vc is identical to that in the General Procedure (AASHTO, 2008) which is applicable fe = R fu where fu = f fu E f and R = 4 ( f E f ) -.67 to such members when distributed horizontal reinforcement 1.0 is placed on 12-in. centers, and the strain in the longitudinal reinforcement (s) is less than 0.00187. For s = 0.00187: where fEf is in ksi units and limited to 300 ksi. Comparison of this expression with the test data yields an 4.8 51 4.8 51 average strength ratio (bias) of 1.68 and a corresponding = = = 2.00 (1 + 750 s ) (39 + sxe ) (1 + 750(0.00187 )) (39 + 12) COV of 0.33. The contribution of the steel reinforcement is given by: When "full-anchorage" is not provided, it is likely that the shear capacity will be controlled by FRP debonding or another Av f y dv (cot + cot )sin mode of failure before FRP rupture can be achieved: Vs = (5.8.3.3-4) s fe = R fu 0.012 where fu = f fu E f and where: = the angle of diagonal compression and = the angle R = 3( f E f ) -.67 1.0 of the transverse reinforcement relative to the longitudinal axis of the member where f Ef is in ksi units and limited to 300 ksi.