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41 Notations a Shear span length a/d Shear span-to-depth ratio Ac Concrete area Acf Effective flange concrete area Acw Web concrete area = bwh Af Cross-sectional area of FRP Ap Cross-sectional area of strengthening material [Sim et al., 2005] Asw, Av Area of transverse steel reinforcement b, bv, bw Minimum width of cross-section over effective depth bf Width of FRP strip [Carolin and Taljsten, 2005] C Constant strain rate = 11010-6 mm-1 d, dv Effective depth of cross-section df Effective depth of FRP reinforcement Dfrp Stress distribution factor for FRP intersected by the shear crack [Chen and Teng, 2003 a and b] dFRP FRP sheet height along side of beam web [Deniaud and Cheng, 2001, 2004] Df Modified FRP strain distribution factor = Dfrp/ [Cao et al., 2005] dS Stirrup height e spacing of stirrups [Sim et al., 2005] Ef, Efrp Elastic modulus of FRP (Ef f)lim Limiting value of FRP rigidity separating debonding and FRP rupture failure modes Es Elastic modulus of steel reinforcement fc, f c Concrete compressive strength fck Concrete characteristic cubic strength fcm Mean cylindrical compressive strength of concrete fctm Concrete mean tensile strength ffd Design ultimate strength of FRP ffdd Debonding FRP strength

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42 ffe Effective tensile stress in FRP sheet/strip in the direction of the prin- cipal fibers ffed Design effective strength of the FRP shear strengthening ffrp Tensile strength of FRP in the main fiber direction [Chen and Teng, 2003 a and b] ffrp, ed Average/effective design stress of FRP intersected by shear crack at beam failure ffu FRP ultimate tensile strength fpy Yield strength of strengthening material [Sim et al., 2005] fy, fvy, Fy, fsy Yield strength of steel reinforcement h Height of RC/PC member hfrp, hfrp,e Effective FRP height hj Depth of U-jacket strengthening [Al-Sulaimani et al., 1994] hs Depth of each FRP strip [Al-Sulaimani et al., 1994] hv Effective depth of the concrete beam [Malek and Saadatmanesh, 1998] hw Height of web [Monti and Liotta, 2005] hw Height of shear wing strengthening [Al-Sulaimani et al., 1994] k Experimentally determined factor [Deniaud and Cheng, 2001, 2004] ka Coefficient describing anchorage considerations [Deniaud and Cheng, 2001, 2004] kb Covering/scale coefficient ke Integer describing number of debonding ends L Girder span length lb Available bond length of FRP Le, Leff, Lfe, le Effective bond length leq Bonded length projected vertically that would be necessary if the fabric strain was uniform Lmax Maximum bond length n Number of FRP plies n Ratio of elastic modulus of FRP to elastic modulus of transverse steel (Ef /Es) [Chaallal et al., 2002] n Number of spaces between stirrups [Deniaud and Cheng, 2001, 2004] ns Total number of stirrups crossing concrete shear plane pf FRP spacing measured orthogonal to the FRP orientation [Monti and Liotta, 2005] _ _ _ _ _ _ _ _ Q12, Q13, Q22, Q23 Stiffness elements of FRP R Ratio of effective stress/strain in the FRP sheet to its ultimate strength/ strain R* Additional reduction factor for debonding failures of beams with steel web reinforcement [Pellegrino and Modena, 2002] rc Corner rounding radius of concrete section for which FRP is wrapped Rck Concrete characteristic cubic strength RL Remaining bonded width over initial width ratio [Deniaud and Cheng, 2001, 2004]

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43 S Girder spacing s Spacing of stirrups sf, sfrp Spacing of FRP strips sf FRP slip at debonding [Monti and Liotta, 2005] sf,max Maximum spacing limitation for FRP strips sxe Crack spacing parameter t, tf, tfrp FRP thickness t Spacing of strengthening material [Sim et al., 2005] TFRP Tension force in FRP tp Nominal thickness of FRP sheet or bonded plate ts Width of each FRP strip Tv Tension force in stirrups V Shear force Vc Shear contribution of concrete Vcy Concrete contribution to shear resistance corresponding with yield- ing of the stirrups along the primary shear crack Vcu Concrete contribution to shear resistance corresponding with the ultimate (maximum) load carried by the girder Vexp Experimentally measured ultimate shear strength Vf, Vfd, Vf,max, Vf,max, Vfrp Shear contribution of FRP VFE Analytically (Finite Element) predicted ultimate shear strength Vf,model FRP contribution to shear resistance predicted by analytical models vfnr Relationship developed for the case of less than full anchorage such that debonding or other non-rupture failures are expected vfr Relationship developed for the case of full anchorage such that FRP rupture failure is expected Vfrp,d Contribution of external FRP reinforcement (design value) [Triantafillou, 1998] Vf,test Experimentally measured shear strength of a test beam with FRP re- inforcement minus the experimentally measured shear strength of the corresponding control beam without FRP reinforcement Vfy FRP contribution to shear resistance corresponding with yielding of the stirrups along the primary shear crack Vfu FRP contribution to shear resistance corresponding with the ultimate (maximum) load carried by the girder Vn Total shear capacity Vn,norm Normalized shear strength Vn,test Experimentally measured shear strength of a beam VP Fiber glass plate component of shear capacity [Al-Sulaimani et al., 1994] Vr Total shear resistance [Deniaud and Cheng, 2001, 2004] VRd,f Shear carried by FRP [Monti and Liotta, 2005] Vs, Vse Shear contribution of stirrups Vsy Transverse steel (stirrup) contribution to shear resistance correspon- ding with yielding of the stirrups along the primary shear crack

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44 Vsu Transverse steel (stirrup) contribution to shear resistance correspon- ding with the ultimate (maximum) load carried by the girder wf, wfrp Width of FRP strip wfe Effective width of FRP strip Z Limit state function z Length of a vertical tension tie zb Co-ordinate of lower edge of effective FRP bonded to the sides of a beam zrid,eq Vertically projected length of the FRP strip, minus the effective bond length where bond is building up, plus a bonded length that would be necessary if the FRP stress was uniform under the debonding slip zt Co-ordinate of upper edge of effective FRP bonded to the sides of a beam Angle of inclination of transverse steel reinforcement to longitudi- nal axis of beam Reduction factor [Triantafillou and Antonopoulos, 2000] Crack inclination angle [Carolin and Taljsten, 2005] Angle between principal direction of FRP sheets and the longitudinal axis of the beam [Deniaud and Cheng, 2001, 2004] Strength efficiency factor [Sim et al., 2005] f Angle between principal direction of FRP sheets and the longitudinal axis of the beam [Hutchinson and Rizkalla, 1999] MF Random variable for uncertainties in material and fabrication tolerances Angle of inclination of FRP fibers to longitudinal axis of member Factor relating effect of longitudinal strain on the shear capacity of concrete, as indicated by the ability of diagonally cracked concrete to transmit tension [AASHTO LRFD, 2008] L Bond length coefficient r Reliability index r,target Reliability index targeted by most AASHTO calibration studies w FRP strip width coefficient 1, 2 Strains in the principal 12 directions bond Maximum allowable strain without achieving anchor failure [Car- olin and Taljsten, 2005] c max Maximum allowable strain to achieve concrete contribution cr Critical FRP strain f,ave Average strain in FRP at failure [Hutchinson and Rizkalla, 1999] fe, f,e, frp,e, eff Effective tensile strain of FRP fk,e Characteristic effective FRP strain in principal fiber direction [Triantafillou and Antonopoulos, 2000] f,e,A Effective FRP strain in principal fiber direction--ACI code format [Triantafillou and Antonopoulos, 2000] f max, f, max Maximum strain in FRP sheet fu Ultimate tensile strain of FRP f (y) Strain in FRP fibers at height y [Carolin and Taljsten, 2005]

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45 max Maximum or limiting value of FRP strain max Maximum FRP strain over remaining bonded width [Deniaud and Cheng, 2001, 2004] max,A Limiting value of effective FRP strain--ACI code format [Triantafillou and Antonopoulos, 2000] s Tensile strain in cracked concrete in direction of tension tie se Effective stirrup strain at failure [Hutchinson and Rizkalla, 1999] sy, y Yield strain of steel stirrups ultFRP Ultimate FRP strain [Deniaud and Cheng, 2001, 2004] vcu Ultimate vertical tensile strain of the concrete taken as 0.005 [Chajes et al., 1995] _ z Normalized strain in FRP [Chen and Teng, 2003b] _ z,max Maximum normalized strain in FRP [Chen and Teng, 2003 b] f Shear strength reduction factor for FRP R Coefficient accounting for the effects of sheets wrapped around a corner f, frp, Rd Partial safety factor for FRP fs The ratio of the vertical component of average strain in the FRP sheets to the average strain in the steel stirrups f,d Partial safety factor depending on the FRP application accuracy Fk Specific fracture energy of the FRP-concrete bond interface Average fiber utilization (effectiveness) factor GDF Random variable for girder distribution factor Shear span-to-effective depth ratio Normalized maximum bond length of FRP = Lmax /Le [Chen and Teng, 2003a] frp Normalized FRP bond length = Lmax /Le [Cao et al., 2005] Constant that represents the contribution of compressive strength of concrete , c Shear crack angle or angle of diagonal compression Angle between the principal tensile stress and the fiber direction [Carolin and Taljsten, 2005] f Shear plane angle in flange w Shear plane angle in web P Random variable for analysis model accuracy Af 2n f t f w f f, frp FRP reinforcement ratio = = (wf = sf = 1.0 for continu- bv s f bv s f ous wraps) f FRP reinforcement ratio = (Af per unit length/bd) = 2tf /bd [Chaallal et al., 2002] s Shear steel reinforcement ratio = (Av per unit length/bd) = Av /sbd [Chaallal et al., 2002] s,f Stiffness ratio between the transverse steel shear reinforcement and FRP shear reinforcement [Pellegrino and Modena, 2002]

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46 tot Total shear reinforcement ratio [Chaallal et al., 2002] Av v Transverse steel reinforcement ratio = bv s cu Concrete compressive strength frp,max Maximum stress in FRP intersected by shear crack [Chen and Teng, 2003b] frp,max,d Maximum stress in FRP intersected by shear crack for design [Chen and Teng, 2003a] frp,z Stress in the FRP at the ultimate limit state at the location where the intersecting critical shear crack is at a coordinate z [Chen and Teng, 2003a] Shear stress ave Average shear stress max Ultimate direct bond shear strength between FRP and concrete ult Interface shear strength between concrete and fiberglass plates [Al-Sulaimani et al., 1994] Coordinate ratio of the upper edge to the lower edge of the effective FRP = zt /zb DC Random variable for component dead load LL+IM Random variable for highway live load including impact loads WS Random variable for wearing surface dead load