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

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72.1 Use of FRP for Shear Strengthening of Concrete Girders A survey of state departments of transportation (DOTs), Washington, DC, and Puerto Rico, was conducted to deter- mine the extent of using FRP for shear strengthening. This survey included a written questionnaire (followed by either a telephone briefing or a written response) aimed at determin- ing the practices for designing concrete girders strengthened in shear using FRP and their perceived deficiencies. The responses received from 39 agencies revealed that only 7 state DOTs used FRP for shear strengthening of concrete girders and 32 DOTs have never used FRP for shear strength- ening of concrete girders. Fourteen DOTs indicated no need for shear strengthening of concrete girders, and 12 DOTs expressed a concern about the lack of proper design specifica- tions or provisions for FRP shear strengthening. Some DOTs considered the use of FRPs less efficient when compared to other strengthening techniques. The DOTs using FRP for shear strengthening follow the design methods contained in ACI 440.2R-02 (ACI 440, 2002) because it was the only design guidelines document available in the United States. Some DOTs (e.g., New York, Oregon, and Pennsylvania) have made slight modifications to ACI 440.2R-02 (ACI 440, 2002). Design guidelines and specifica- tions provided by FRP manufacturers and course notes from a workshop provided by several organizations were used by some state DOTs. Most state DOTs identified provisions regarding properties of FRP composite materials and control of failure modes as the most important issues to be addressed in future design specifications. An in-depth explanation on FRP strengthening schemes and fatigue and durability issues were also noted as major issues to be addressed. 2.2 Field Applications Although there are several field projects related to FRP strengthening systems, detailed information on these projects is not available and most of these projects were strengthened for flexural rehabilitation. The following six projects were iden- tified as directly related to FRP shear strengthening of concrete bridge girders: • A single span, reinforced concrete T-beam bridge in New York State was strengthened in flexure and shear with exter- nally bonded FRP laminates in November 1999 (Hag-Elsafi et al., 2001b). • The Gröndals Bridge in Sweden is a prestressed concrete box bridge approximately 1,300 feet in length and a free span of 394 feet. CFRP laminate strips were applied to the inside walls with steel plate anchorage system to increase the shear strength (Taljsten et al., 2007). • The Langevin Bridge in Calgary, Canada, is a six-span, four- cell, continuous box-girder bridge constructed in 1972. The internal webs were found to be deficient at the right end of span 2 where the internal prestressing tendons are horizon- tal and thus contribute nothing to the shear resistance. To correct these deficiencies, CFRP sheets were bonded to the inside face of the external webs and to both faces of the inte- rior webs. • The John Hart Bridge in Prince George, British Colum- bia and the Maryland Bridge in Winnipeg, Manitoba, are two bridges in western Canada that have been strength- ened in shear with externally bonded CFRP. The John Hart Bridge consists of seven simply supported spans with six I-shaped prestressed concrete AASHTO girders per span, and the Maryland Bridge consists of two sets of five continu- ous spans with seven I-shaped prestressed concrete AASHTO girders per span (Hutchinson et al., 2003). C H A P T E R 2 Summary of Major Findings

• The Willamette River Bridge located near Newberg, Ore- gon, was found to have significant diagonal cracking dur- ing an inspection conducted by the Oregon Department of Transportation (ODOT) in late summer of 2001. CFRP strips of 12 inch width were applied vertically in a U-shape wrapping scheme (Williams and Higgins, 2008). • The Ebay Island Viaduct Bridge is a 21⁄4 mile long section of westbound Washington State Route 2 that crosses over environmentally sensitive wetlands near the outflow of the Snohomish River into Puget Sound near Everett, Washington. The bridge was built during the late 1960s. In 1996, bridge condition inspectors noted that the bot- toms of the existing precast concrete webs exhibited con- siderable concrete spalling accompanied with primary steel reinforcement corrosion. In 1999, carbon fiber sheets were bonded to the deteriorated elements for flexural strength- ening and to compensate for steel reinforcement loss due to corrosion. In addition, carbon fiber sheets were applied with a U-wrap configuration to compensate for the shear capacity loss due to the cross-sectional loss of stirrups caused by corrosion. The carbon fiber repairs were inspected annu- ally after the completion of the repair project with no debonding or deterioration of the carbon fiber plies being reported through spring 2007 (Dornsife, 2007). 2.3 Existing Analytical Models This section summarizes the analytical models previously developed for determining the shear resistance of reinforced concrete members strengthened with externally bonded FRP. Seventeen models were found in the literature. These models have been divided into four groups based on their approaches and are presented in the same units as the original papers. The first group of models is those relying on an empirically determined value of strain/stress associated with failure of the member for which the shear contribution of the FRP is deter- mined; the principal equations of the analytical models in this group are listed in Table 2.1. The second group of models is those based on the determination of an effective FRP strain; the corresponding principal equations are listed in Table 2.2. The third group of models focuses on the non-uniformity of the strain distribution in externally bonded FRP reinforce- ments; the corresponding principal equations are listed in Table 2.3. The fourth group of models is mechanics-based theoretical approaches that do not rely on experimental results for regression or calibration; the principal equations of these models are listed in Table 2.4. 2.4 Experimental Investigations Reported in the Literature A review was conducted of experimental investigations which included studies on (1) the behavior of concrete girders strengthened in shear with externally bonded FRP, (2) bond behavior of FRP-concrete interface, and (3) anchorage systems to enhance the effectiveness of FRP strengthening systems. 2.4.1 Studies on the Behavior of Concrete Girders Strengthened in Shear with Externally Bonded FRP The review included 49 experimental studies, encompass- ing more than 500 test specimens. The review provides infor- mation on the objectives, the methodology, the experimental program, the test method, the FRP used and its orientation, as well as the strengthening scheme used (configuration). 8 Reference Author (Year) Equations Al-Sulaimani et al. (1994) 2 2 s s ave P P t h d V S τ = (for shear strips) 2 2 w P ave dhV τ= (for shear wings) 2 2 j P ult dh V τ= (for U-jackets) Chajes et al. (1995) f f f cuV A E v dε= (for FRP oriented at 0/90 degree) 2f f f cuV A E v dε= (for FRP oriented at 45/135 degree) * Terms are defined in notations section. Table 2.1. Models based on experimentally determined limiting value of FRP shear strain/stress.

9Reference Author (Year) Equations Triantafillou (1998) ( ) , , 0.9 1 cot sinfrp d frp frp frp e w frp V E b dρ ε β β γ = + ( ) ( )2 , 0.0119 0.0205 0.0104frp e frp frp frp frpE Eε ρ ρ= − + when 0 1frp frpEρ≤ ≤ GPa ( ), 0.00065 0.00245frp e frp frpEε ρ= − + when 1frp frpEρ > GPa Khalifa et al. (1998) ( )0.9 1 cot sinf frp frp fe wV E b dρ ε β β= + (Eurocode format) ( )sin cosf fe f f f A f d V s β β+ = (ACI format) fe fuRε ε= fe fuf Rf= Based on the effective FRP stress: ( ) ( )20.5622 1.2188 0.778 0.5frp frp frp frpR E Eρ ρ= − + ≤ when 1.1frp frpEρ < GPa Based on bond mechanism: ( ) ( ) 2 / 3 ' 0.58 0.0042 c fe frp f fu f f w R E t dε = Effective width: fe fw d= (complete wrapping) fe f ew d L= − (U-wrap) 2fe f ew d L= − (side bonded) ,max 4f f d s w= + '2 3 c w s f f b d V V+ ≤ Hutchinson and Rizkalla (1999) ,maxn c se fV V V V= + + ( ) ,max , cot cot sin 2 f f ff f ave f f f f d V E nt w s θ α α ε + = ( ) , max / 2 0.5 / 2f f ave f f d d d d ε ε + − = maxf feL Cε = ( )6.134 0.580ln f ft E feL e − = and 6 1 110 10C constant strain rate of mm− −= × cot se se s v dV E A s θ ε= where , sinse f ave f fs syε ε α γ ε= ≤ Table 2.2. Models based on an effective FRP strain. (continued on next page)

10 Khalifa and Nanni (2000) ( )0.9 1 cot sinf frp frp fe wV E b dρ ε β β= + (Eurocode format) ( )sin cosf fe f f f A f d V s β β+ = (ACI format) fe fuRε ε= fe fuf Rf= R is the least of : ( ) ( )20.5622 1.2188 0.778 0.5frp frp frp frpR E Eρ ρ= − + ≤ ( )2 / 3' 6738.93 4.06( ) 10c fe f frp fu f f w R t E dε − = − × 0.006 fu R ε = Triantafillou and Antonopoulos (2000) ( ),0.9 1 cot sinfk efd f f w f V E b d ε ρ β β γ = + (Eurocode format) , , max 0.005fk e f eε αε ε= ≤ = 0.8α = (recommended) ( ) , , sin cosf f f f e A f fV E bdφ φ ε ρ β β= + (ACI format) , , , max,0.9 0.006f e A f e Aε ε ε= ≤ = 0.56 2/3 3 , 0.65 10cf e f f f E ε ρ − = × (CFRP debonding failure mode) 0.30 2 / 3 , , 0.17 cf e f u f f f E ε ε ρ = (shear failure combined with or followed by CFRP fracture) 0.47 2/3 , , 0.048 cf e f u f f f E ε ε ρ = (shear failure combined with or followed by AFRP fracture) ( ) 1/ 0.563 2/3 2/3 lim max 0.65 10 0.018f f c cE f f αρ ε −× = = Chaallal et al. (2002) , f f tot f eff f f AaV f E d d s ρ ε= 5 0.65223 10eff totε ρ− −= × × , tot f snρ ρ ρ= + New deep beam coefficient: ( )1 2 /, 1000 0.6 1 12tot tot a a df d ρ ρ+= + − ≤ but greater than 1 2 / 12 a d+ Table 2.2. (Continued).

Whenever necessary, the review provides comments or com- parisons with other studies. The numerical data extracted from the experimental studies were assembled in a database. The test parameters considered in these studies are listed in Table 2.5. The major test parameters are (a) the geometry of the beam used in the experiments, (b) beam type, (c) proper- ties of concrete and steel reinforcement, (d) types of FRP, and (e) strengthening schemes. As seen from Table 2.5, most of these studies have focused on rectangular beams, although most RC bridge girders have a T-section with integrated deck slabs. The shape of the cross section is related also to the strengthening scheme. For example, rectangular beams are commonly strengthened by fully wrapping the member, an impractical solution for T-beams due to the presence of the flange. Therefore, more focus should be placed on T-beams with U-wrap and side-bonding configurations as well as on the use of mechanical anchorage systems to address the issue of debonding. Also, few tests have been conducted on mem- bers with spans comparable to those used for bridges, and fewer tests have investigated the influence of scale (i.e., model- scale versus large-scale) on the shear behavior of members strengthened with FRPs. Furthermore, because FRP is gener- ally used to strengthen damaged structures, attention needs to be given to the effects of existing cracks on the behavior of the strengthened member. The previously developed analytical models were based on the studies listed in Table 2.5, the majority of which con- sidered only small-scale testing. Therefore, this research aimed at expanding the experimental database with results from tests on full-scale T-beams, which are more representative 11 Pellegrino and Modena (2002) ( )0.9 1 cot sinf frp frp fe wV E b dρ ε β β= + (Eurocode format) ( )sin cosf fe f f f A f d V s β β+ = (ACI format) fe fuRε ε= fe fuf Rf= R is the least of : ( ) ( )20.5622 1.2188 0.778 0.5frp frp frp frpR E Eρ ρ= − + ≤ 0.006 fu R ε = ( ) ( ){ }0.582 / 3* 0.0042 /cm fe frp f fuR R f w E t dε= * , 0 0.53ln 0.29 1s fR ρ≤ = − + ≤ ,s f s sw f fE A E Aρ = Hsu et al. (2003) for continuous fiber sheet: 2sinf fe f feV w t f β= for FRP strips: ( )sin cosf fe f f f A f d V s β β+ = fe fuf Rf= , fe fuRε ε= Based on model calibration: ( ) 0.7488'1.4871 /f f cR E fρ −= Based on bonding mechanism: max 1 2 e fu f L R f t τ = ≤ ( ) ( ) ( )6 '2 2 'max 5 10 2.73 10 925.3 c cf f Englishτ − −= × × − × × + ( ) ( ) ( )4 '2 2 'max 7.64 10 2.73 10 6.38 c cf f Metricτ − −= × × − × × + * Terms are defined in notations section. Table 2.2. (Continued).

12 Reference Author (Year) Equations Chen and Teng (2003a and 2003b) ( ) , , sin cos 2 frp ed frp efrp frp frp frp frp f h V t w s β β γ + = , ,maxfrp ed frp frpf D σ= Debonding model: , , ,max 1 cos2 2 1 sin 2 21 1 zb frp zzt frp frp e frp d ifdz D h if π λ λσ ππλ λ σ π λ πλ − ≤ = = − − > ' ,max, 0.315 frp frp d w L c frp frp E f f t σ β β= ≤ Rupture model: ,max , 1 2 b t z z z frp zfrp e dz D h ε ζ ε + = = max ,max max max 0.8 if 0.8 if frp frp frp frp frp frp frp ff E f E E ε σ ε ε ≤ = > Strip spacing limitation: ( ) , 1 cot min 2 sin 300 frp e frp frp h w s mm β β + − ≤ Carolin and Taljsten (2005b) for complete wrap: α θηε sin cos ztEV ffcrf = for composite strips: cos sin sin f f cr f f f b V E t z s θηε β α= h/2 -h/2 max (y) h f dyε η ε = = θε θε ε ε 2 max 2 cos cosmin c bond fu cr Table 2.3. Models that account for non-uniform strain distribution in FRP.

13 Reference Author (Year) Equations Malek and Saadatmanesh (1998) ( ) ( ) 12 2 22 1 13 2 23 1 tanf p c Q Q V ht Q Q ε ε ε ε θ + = + + ( ) ( ) tan tan yv s s y v y c s yv s y v y c s FhV E A for s E FhV F A for s E ε ε θ ε θ = < = ≥ Deniaud and Cheng (2001, 2004) Discrete formulation: ( )2 '0.25 tan tanr c cf f cw w v s FRPV k f A A T n Tθ θ= + + + Continuous formulation: ( )' sr c c v FRP vdV k f A T T T s = + − ( ) 0.4'2.1 ck f −= v v vyT A f= ( ) 2 max sin 1 cos sin tan frp FRP FRP frp L s frp w w T d tE R n s α ε α α θ = + + 2 max sin cos sin frp FRP FRP frp L frp s w sT d tE R s d ε α α α= + Maximum allowable strain in FRP: ( ) ' 0.16 max 0.67 0.1 3 (%) ( sin ) c FRP ultFRP frp a f d tE k ε ε α = ≤ Remaining bonded width over initial width ratio: 0.4 1 1.2 exp sin FRP L e eff dR k L α = − − Table 2.4. Models derived from mechanics-based approaches. Cao et al. (2005) ,max2 frp frp f frp frp frp f frp h V D t w E s θ ε= ( )2 1 1.4 2 11 1.4< 3 1 0.2 1.4 2.05 3 f frp for D for for θ λ π λλ π λ λ ≤ − = − × < − − ≥ '4 ,max 0.427 w c f frp frp f E t β ε = * Terms are defined in notations section. Table 2.3. (Continued). (continued on next page)

14 Monti and Liotta (2005) Side bonding: { } , 1 sin min 0.9 , 2 sin f Rd f w fed f Rd f w V d h f t p β γ θ = ⋅ ⋅ ⋅ ⋅ ⋅ design effective stress for side bonding: { } 2 601 90 −⋅⋅= eq,rid eq w eq,rid fddfed z l . h,d.min zff { } , min 0.9 , sin / f rid eq w e fdd f s z d h l f E β= − − U-wrap or complete wrapping: ( ) , 1 0.9 2 cot cot fRd f fed f Rd f w V d f t p θ β γ = ⋅ ⋅ ⋅ ⋅ + ⋅ design effective stress for U-wrapping: { }−⋅= w e fddfed h,d.min sinlff 903 11 β design effective stress for complete wrapping: { } { }−⋅−+−⋅= w e fddfdR w e fddfed h,d.min sinl)ff( h,d.min sinlff 90 1 2 1 906 11 βφβ 2 f f e ctm E t l f= where: 2 /3 0.27ctm ckf R= , 20.80 f Fk fdd f d f Ef tγ Γ = where: 0.03Fk b ck ctmk f fΓ = 2 1 1 400 f f b f w p k w − = ≥ + ( ) ( )min 0.9 , sin sinf ww d h θ β θ≤ + ( ) 2b bfdd b fdd e e l lf l f l l = − (for lb < le) 0.2 1.6 where 0 0.5c cR w w r r b b φ = + ≤ ≤ Sim et al. (2005) ( ) ( ) ( ) ( ) ( )( ) 2 22 2 2 2 2 2 2 2 1 2 2 2 11 22 1 1 2 2 cu cu cu a d aa d a if d a d a d a if a d if φτ φ νσ τ φ φ φ νσ τ φ νσ + −+ − − = < + + − = − ≤ ≤ + = > V b h τ = ⋅ and ( )sin cosv sy p py cu cu A f A f b e b t φ α β β νσ νσ ⋅ ⋅ = + + ⋅ ⋅ ⋅ ⋅ * Terms are defined in notations section. Table 2.4. (Continued).

15 Properties and Parameters Concrete Type of Geometry Type of Beam and Steel FRP Strengthening Scheme Author Year N um be r o f T es ts R ec ta ng ul ar S ec tio n T- Se ct io n B ea m S pa nn i n g L< 7 ft B ea m S pa nn in g 7 ft <L <1 3 ft B ea m S pa nn in g L> 13 ft R eg ul ar B ea m s (a/ d> 2.5 ) D ee p Be am s Sc al e Ef fe ct Pr ec ra ck in g Co nc re te S tre ng th Lo ng itu di na l R ei nf or ce m en t Tr an sv er se R ei nf or ce m en t Ca rb on A ra m id G la ss Tw o- Si de B on di ng U -W ra p Co m pl et e W ra p Co nt in uo us St rip s A ng le to L on g. A xi s= 90 º A ng le to L on g. A xi s 90 º Berset 1992 2 Uji 1992 4 Al-Sulaimani et al. 1994 4 Ohuchi et al. 1994 13 Chajes et al. 1995 5 Sato et al. 1996 3 Araki et al. 1997 8 Funakawa et al. 1997 3 Kamiharako et al. 1997 1 Miyauchi et al. 1997 4 Sato et al. 1997 2 Taerwe et al. 1997 3 Taljsten 1997 3 Umezu et al. 1997 15 Chaallal et al. 1998 2 Mitsui et al. 1998 6 Triantafillou 1998 9 Khalifa et al. 1999 6 Kachlakev and Barnes 1999 3 Khalifa et al. 2000 4 Deniaud and Cheng 2001 5 Li et al. 2001a 5 Li et al. 2001b 9 Park et al. 2001 2 Chaallal et al. 2002 10 Khalifa and Nanni 2002 4 Li et al. 2002 9 Micelli et al. 2002 10 Pellegrino and Modena 2002 9 Beber 2003 28 Diagana et al. 2003 8 Hsu et al. 2003 3 Table 2.5. Summary of experimental studies. (continued on next page)

of bridge girders and consider the effects of other param- eters such as pre-cracking and the amount of transverse reinforcement. 2.4.2 Bond Behavior of FRP-Concrete Interface The performance of shear strengthening of concrete gird- ers by using externally bonded FRP sheets depends on the interface bond behavior between the FRP sheets and the con- crete substrates. Many analytical models attempted to con- sider the bond characteristics at the interface between FRP and concrete substrate to predict the shear contribution of FRP when the expected failure is caused by debonding of FRP. Consideration of the bond mechanism, the intermedi- ate crack (IC) debonding, the bond stress-slip relationship, the effective bond length, and the bond strength is required for the development of improved shear design equations. The most important role of the interface bond between the FRP sheets and concrete is to transfer shear stresses from exist- ing concrete structures to externally bonded FRP sheets for both shear and flexural strengthening. The bond properties 16 Properties and Parameters Concrete Type of Geometry Type of Beam and Steel FRP Strengthening Scheme Author Year N um be r o f T es ts R ec ta ng ul ar S ec tio n T- Se ct io n B ea m S pa nn i n g L< 7 ft B ea m S pa nn in g 7 ft <L <1 3 ft B ea m S pa nn in g L> 13 ft R eg ul ar B ea m s (a/ d> 2.5 ) D ee p Be am s Sc al e Ef fe ct Pr ec ra ck in g Co nc re te S tre ng th Lo ng itu di na l R ei nf or ce m en t Tr an sv er se R ei nf or ce m en t Ca rb on A ra m id G la ss Tw o- Si de B on di ng U -W ra p Co m pl et e W ra p Co nt in uo us St rip s A ng le to L on g. A xi s= 90 º A ng le to L on g. A xi s 90 º Taljsten 2003 6 Adhikary et al. 2004 8 Xue Song et al. 2004 12 Cao et al. 2005 10 Carolin and Taljsten 2005a 18 Miyajima et al. 2005 4 Monti and Liotta 2005 16 Sim et al. 2005 9 Zhang and Hsu 2005 10 Barros and Dias 2006 5 Bousselham and Chaallal 2006a 20 Pellegrino and Modena 2006 8 Lees and Kesse 2007 8 Leung et al. 2007 12 Alrousan et al. 2009 4 Arteaga et al. 2009 15 Gamino et al. 2009 7 Rizzo and De Lorenzis 2009 1 Note: (1) Shaded cells denote considered parameters. (2) Control specimens without FRP strengthening are not included in the table. Table 2.5. (Continued).

of FRP sheet-concrete interfaces have been widely studied. Various test methods have been developed to evaluate the average interfacial bond strength. These methods include single-lap-type, double-lap-type, bending-type, and inserted- type tests, as shown in Figure 2.1. Among the interface param- eters evaluated are average shear bond strength, effective bond length, maximum shear bond stress, interfacial fracture energy, and the local bond stress-slip relationship. Bond behavior is influenced by the mechanical and physical properties of the concrete, FRP composite, and adhesive; the influencing fac- tors are listed in Table 2.6. In evaluating FRP-concrete interface bond behavior, the bond stress-slip (τ-s) relationship is the most important factor. For FRP sheets bonded to concrete, this relationship 17 Concrete FRP Load Concrete Bond Length Load Load Rebar FRPNotch Bond Length FRP Notch Concrete Load Load FRP Steel Plate Load (a) Single-lap shear bond test (b) Double-lap shear bond test (c) Bending-type shear bond test (d) Inserted-type shear bond test Figure 2.1. Test methods to evaluate the bond strength.

is determined by the strain distributions in the FRP, and the local bond stresses measured in the FRP sheets. Several empirical τ-s relationships have been proposed including a elasto-plastic model (Sato et al., 1997 and De Lorenzis et al., 2001); a bilinear model based on interfacial fracture energy (Yoshizawa et al., 2000); a model based on the Popovic’s expression (Nakaba et al., 2001); and a shear softening model (Sato et al., 2000). The experimental studies have shown that the bond shear stress at the FRP-to-concrete interface increases rapidly with increases in the interfacial slip until it reaches the peak stress (bond strength) as illustrated in Figure 2.2. After this point, interfacial softening (or micro-cracking) starts, together with a decrease in the interfacial shear stress and an increase in the interfacial slip. There is no agreement among researchers on the shape of the model, however, use of fracture mechanics implicitly leads to a very simple generic expression that considers only the FRP stiffness and interfacial fracture energy (defined as the area beneath the bond stress-slip curve) for the determi- nation of bond capacity. Debonding occurs first within the effective bond length (defined as a length over which the majority of the bond stress is maintained, see Figure 2.3) as a result of debonding of a very thin layer of concrete rather than debonding at the FRP/concrete interfaces. When the bonded length of FRP along the FRP-concrete interface exceeds the effective bond length, no further increase in fail- ure load can be achieved. However, a longer bond length may delay complete debonding and thus improve the ductility. Several studies have been performed to determine effective bond length. Figure 2.4 shows the effective bond lengths cal- culated by analytical models and equations stipulated in many current code and design guidelines versus the rigidity of FRP reinforcement (Ef ρf). As shown in the figure, most studies have reported that effective bond length increases as the stiffness of FRP sheets increases. However, two studies (Maeda et al., 1997 and ACI 440.2R-08) show a different trend, probably because these models were derived using a very limited experimental database. The analytical models for effective bond length and bond strength were derived based on small-scale tests; the bond behavior of full-size beams may be different than that pre- scribed by these models. Thus, full-scale tests would provide data to calibrate/improve these models. 2.4.3 Anchorage Systems to Enhance the Effectiveness of FRP Strengthening Systems When a proper anchorage system is not provided, failure of FRP-strengthened reinforced concrete members is com- monly manifested by debonding of the FRP. Therefore, vari- 18 Elements Influencing Factor Concrete Modulus of elasticity, thickness, surface condition, strength, drying shrinkage, water content Continuous Fiber Sheet Modulus of elasticity, strength, thickness, stiffness, length/width of sheet, weave Bonding Resin Primer FRP application Putty Modulus of elasticity, strength, glass transition temperature, spread Loading condition Bending, shearing, punching, cyclic Environmental actions Ambient temperature, moisture, sun light radiation, etc. Table 2.6. Factors influencing the bond behavior at FRP-concrete interface. Bond Stress Bond Stress Bond Stress Slip Slip Slip (a) Cutoff type (b) Bilinear type (c) Tensile softening type Figure 2.2. Various bond stress-slip models.

technique requires no surface preparation work but con- siderable labor for cutting the grooves. Another system used to prevent debonding of FRP is anchor spikes (Eshwar et al., 2003; Eshwar et al., 2008; Orton, 2007; Niemitz, 2008). Each anchor spike consists of a precured fiber portion and a dry fiber portion (see Figure 2.6). The anchor spikes may be constructed in situ. First, fibers are bundled together, and half of the fiber length is covered with plastic or duct tape. The uncovered bundled fibers are then impreg- nated and thoroughly saturated with resin. Finally, the satu- rated fibers are passed through a circular hole in a steel plate, or die, to obtain the desired diameter of the anchor spikes. The dry fibers are used for bonding purposes and trimmed to the appropriate length according to specific requirements. Following surface preparation of the concrete, holes of the desired diameter and depth are drilled and partially filled with saturant. The laminate is then applied, and while it is wet, the precured portion of each spike anchor is inserted into the holes. The dry fibers are spread around the layer in a circular fashion, and a layer of saturant is then applied (see Figure 2.6). An additional horizontal FRP strip applied on top of the ver- tical FRP strips has also been used as an anchorage system (Hutchinson and Rizkalla, 1999; Schnerch, 2001). This tech- nique is very easy to install and requires no more labor than other anchorage systems. However, different levels of effective- ness have been reported. Schnerch (2001) reported that the hor- izontal strip neither delays nor prevents debonding, and it does not increase the contribution of the FRP to the shear strength of the beam at failure. Test results reported by Hutchinson 19 Ef fe ct iv e Bo nd L en gt h, L e (in .) Stiffness of FRP reinforcement, Eftf (kip/in) 0 2 4 6 8 10 12 100 150 200 250 300 350 400 450 Maeda et al. (1997) Neubauer and Rostasy (1997) Niedermeier (1996) JCI (2003) - Sato Model JCI (2003) - Iso Model Chen and Teng (2001) Niu and Wu (2000) Kanakubo et al (2003) -1 Kanakubo et al (2003) -2 Ueda and Dai (2004) Ueda and Dai (2005) Foster and Khomwan (2005) Miller and Nanni (1999) Ben Ouezdou et al. (2008) ACI 440 (2008) CSA S806 (2002) fib-TG9.3 (2001) Appendix 1 fib-TG9.3 (2001) Appendix 2 Eurocode 8-3 (2004) Concrete Society (2004) Figure 2.4. Effective bond length versus FRP rigidity. Lo ca l b on d st re ss es Free 99.99 % of Max Load 80 % of Max Load 50 % of Max Load 20 % of Max Load Le Loaded end 99.9 % of Max Load 96.0 % of Max Load Figure 2.3. Concept of effective bond length based on stress distribution (Ueda and Dai, 2005). ous types of anchorage systems, including the near surface mounted system (NSM), fiber reinforced polymer anchor spikes, additional horizontal strips, and various mechanical anchorage systems have been studied to evaluate their effect on FRP failure by debonding. Many experimental studies have demonstrated the effec- tiveness of the NSM system (Khalifa and Nanni, 2000; De Lorenzis, 2002; Micelli et al., 2002). In this system, a bent portion of the end (or a region near the end) of the FRP reinforcement is embedded into the concrete, as shown in Figure 2.5. For fiber sheets, the bend is created during wet lay-up, and in the case of laminates, it is pre-formed. This

The four methods used to anchor the FRP sheets as shown in Figure 2.7 are (a) nail type, (b) semi-closed type, (c) sub- variation of semi-closed type, and (d) closed type. Sato et al. (1997) concluded that the shear strength of beams can be improved by transverse wrapping of FRP sheets if adequate anchoring is provided by steel plates and bolts and recommended the use of long anchor bolts that penetrate the full web. This anchorage system, however, creates stress con- centrations where the anchors are placed, and the bolts lead to discontinuity of the FRP system. Matthys (2000) conducted a project to strengthen four continuous reinforced concrete beams in shear and flexure, by supporting them with masonry columns. Bond/anchorage tests indicated a 44% increase in anchorage capacity with the use of steel bolted connections. Mechanical anchorage resulted in a less brittle failure mode due to the transition to an external tensioning system after debonding and to increased displacements resulting from CFRP slip. Schuman (2004) conducted a comprehensive study on anchorage systems for shear strengthening of reinforced concrete (RC) beams. A mechanical anchorage system was applied to increase the shear contribution of CFRP systems by embedding anchor rods into the cross section with various bearing plates, (e.g., GFRP plate). The anchorage systems are possible, the four methods described by Schuman (2004) can be summarized as (1) complete wrapping through the flange (called complete wrap), (2) FRP laminate extended into the flange, (3) bonded steel anchors with bearing plates (called two-side bonding), and (4) GFRP plate anchors. The two particularly important conclusions from Schuman’s (2004) research are (1) the FRP composite alone provides the T-beam with little additional ultimate load and displacement capacity and creates a more brittle failure mode and (2) the use of properly embedded and sized anchors allows the vertical ties to remain intact during failure. These anchors then force a more ductile compression zone and ensure a shear/flexural failure mode. Schuman (2004) also concluded that short anchors (Fig- ure 2.8) lead to an increase in load carrying and displacement capacity and cause the CFRP reinforcement to be activated before the steel reinforcement yields but deeper anchors (Fig- ure 2.8) allow the CFRP reinforcement to be activated earlier, thus delaying yielding in the steel stirrups. For all mechanical anchorage systems configurations, the embedment length, diameter of the anchor, and the bearing strength of the plate are primary considerations. Regarding embedment length, longer anchors are more effective, but they increase the amount of labor required and present the risk of damaging the concrete and steel reinforcement. The diameter of the anchor must be chosen based on the failure modes of the connection (e.g., bearing of the plate, spalling of concrete, and yielding or rupture of the anchor). 20 Figure 2.5. Construction of a NSM Anchorage System. Figure 2.6. Anchor spikes. and Rizkalla (1999) indicated that using the horizontal strip increased the shear contribution of FRP by 16 percent. Mechanical anchorage systems have been used widely to prevent premature FRP debonding. Steel angles, steel or FRP composite plates, and anchor bolts are examples of most commonly used mechanical anchorage systems. Sato et al. (1997) conducted a series of tests using various anchoring methods to develop a shear strengthening tech- nique for beams and a method of estimating their effective- ness. The test results showed that sufficient strength can be achieved only if the CFRP sheets are mechanically anchored.

2.5 Current Codes/Guidelines/ Specifications Design procedures for shear strengthening of concrete structures with externally bonded FRP are available in various forms (e.g., codes, guidelines, and specifications). The Guide for the Design and Construction of Externally Bonded FRP Systems for Strengthening Concrete Structures (ACI 440, 2008) was developed based on ACI 318-08 (ACI 318, 2008). This guide determines the shear contribution of exter- 21 (b) Deep embedment depth (a) Shallow embedment depth Figure 2.8. Specimen details (Schuman 2004). Nail Thin Plate Bolt (50 mm) Bolt (130 mm) Lateral Plate Upper Plate Bolt Welding Angled Plate CFRP Sheet Type 1 Nail type Type 2 Sub-version of type 3 Type 3 Semi-closed type Type 4 Closed type Figure 2.7. Anchoring methods of CFRP sheets. nally bonded FRP based on failure modes. FRP rupture is the likely mode of failure for complete wrapping applications and the ultimate strain of the FRP can be used for calculation of the shear contribution of FRP, with the use of a strength reduction factor of 0.75. However, the ultimate strain is lim- ited to 0.004 in order to maintain aggregate interlock. For U-wrap and side bonding applications, both FRP debonding and rupture are potential failure modes, and the shear con- tribution of the FRP should be investigated for each failure mode with the lesser value used for design. The analytical

model proposed by Khalifa et al. (1998) is adopted to predict the shear contribution of FRP for debonding of FRP. The Canadian Design and Construction of Building Com- posites with Fiber Reinforced Polymers (CAN/CSA S806, 2002) is a design code that addresses externally bonded FRP rein- forcement for concrete. The equations in this code are based on the simplified method for shear design used in the con- crete design code (CAN/CSA A23.3, 1994), which is limited to the usual cases of shear reinforcement (including FRP) perpendicular to the longitudinal axis of beams. The shear con- tribution of the FRP is determined based on failure modes. The ultimate strain is limited to 0.004 for failure due to FRP rupture and 0.002 for bond critical applications. The Canadian Highway Bridge Design Code (CAN/CSA S6-06, 2006) deals with the shear strengthening of concrete with externally-bonded FRPs. This code specifies that the FRP shear strengthening system should consist of U-wraps anchored in the compression zone or complete wrapping of the cross-section. This code specifies the same equations con- tained in ACI 440 (2002). European fib bulletin 14 Design and Use of Externally Bonded Fiber Polymer Reinforcements (FRP EBR) for Rein- forced Concrete Structures, (fib-TG9.3 2001) is a combination of guidelines and state-of-the-art reports and calculates the FRP contribution to shear capacity (Vfd) according to a model proposed by Triantafillou and Antonopoulos (2000), and the bulletin recognizes the difference in expected performance between FRP material types as well as between preformed and wet lay-up FRP systems, which is expressed in the form of various material safety factors. Delamination and debond- ing are addressed using a simplified bilinear bond model and by considering the effects of the loss of composite action between the FRP and concrete substrate. Durability is dis- cussed but no design guidelines are provided. Japan Society of Civil Engineering Recommendations for Upgrading of Concrete Structures with Use of Continuous Fiber Sheets (JSCE, 2001) employs a performance-based approach to the design of externally bonded FRP materials. In addition to verifying flexural and shear capacity, flexural crack width and protection of the concrete substrate from chloride ion penetration are also considered. The Manual for Strengthening Reinforced Concrete Struc- tures with Externally-Bonded Fiber Reinforced Polymers, prepared by the Canadian Intelligent Society of Innovative Structures (ISIS, 2001), provides guidance and design exam- ples for the use of externally bonded FRP based on Canadian Codes (CAN/CSA S6-06, 2006 and CAN/CSA S806-02, 2002). The British Concrete Society Technical Report 55, Design Guidelines on Strengthening Concrete Structures Using Fiber Composite Materials (Concrete Society, 2004) is similar to fib- Bulletin 14 (fib-TG9.3, 2001) in approach and scope; how- ever, it addresses construction issues associated with the use of externally bonded FRP materials. Externally bonded FRP strips are treated using a 45-degree truss analogy. The strain in the FRP is limited to one half of the ultimate design strain for FRP rupture failure. For debonding failure, this report adopts an equation proposed by Neubauer and Rostasy (1997); the strain is limited to 0.004 for all cases. 2.6 Factors Affecting the Design of FRP Shear Strengthening The factors affecting the design of FRP shear strengthening systems was investigated by (1) reviewing existing experi- mental databases, (2) conducting an experimental program to investigate the factors that had not been considered in prior research, and (3) performing an analysis using finite element method (FEM) to verify the experimental results. 2.6.1 Investigation on the Existing Experimental Database A total of 49 published experimental studies containing more than 500 test results were reviewed. These studies cov- ered all relevant, detailed and specific data from tests related to FRP shear strengthening (see Table 2.5). These data were examined for appropriateness and validity by reviewing the test set-up, failure modes reported, and material properties. The data was then compiled into a tabular format to facili- tate identification of the parameters that influence design of externally bonded FRP systems. These data were also used to (1) develop an experimental program to be carried out as part of this project and (2) develop and calibrate shear design pro- visions for concrete girders retrofitted with externally bonded FRP. The following parameters and criteria were successively subjected to qualitative and quantitative analysis: (a) mechan- ical and geometric properties of the FRP, (b) transverse steel ratio, (c) longitudinal steel ratio, (d) shear span-to-depth ratio or type of beams (slender versus deep), and (e) scale factor or size effect of the specimens. Other parameters and crite- ria that were also qualitatively examined included the effects of (a) concrete strength, (b) fatigue, (c) anchorage details, (d) pre-cracking, and (e) prestress. The effects of failure modes were also considered because the analysis was performed by discretization of the various fail- ure modes. The failure modes considered were (a) shear fail- ure due to debonding, including delamination and (b) shear failure due to rupture of the FRP. Other shear failure modes (due to diagonal concrete crushing or concrete splitting) were not considered in the analyses. Results of tests in which test beams failed in flexure were disregarded. 22

2.6.1.1 Influence of FRP Properties Table 2.5 indicates that CFRP sheets have been used in almost all studies addressing performance of RC beams strengthened in shear with FRP. The effective strain concept was used to evaluate the effectiveness of FRP shear strength- ening systems. Figure 2.9 shows the variation of the effec- tive FRP strain (εfe) versus (E f ρf /f ′2/3c ) a function of FRP rigid- ity (Ef ρf) and the compressive strength of concrete (f c′). The effective FRP strain (εfe) was determined based on the tradi- tional truss analogy using the following expression: where: bw = the width of the web df = the effective depth of FRP reinforcement β = the angle of inclination of the FRP with respect to the longitudinal axis of the beam. The term (Ef ρf /f ′2/3c ) was used because it includes the effects of (1) the amount of FRP expressed in terms of the FRP ratio (ρf = Af /(bwsf)), (2) the fiber type expressed in terms of the modulus of elasticity of FRP (Ef), and (3) the compressive strength of concrete (f c′) which is a major factor influenc- ing the bond performance of FRP strengthening. The term (E f ρf /f ′2/3c ) is particularly important for evaluating the contri- bution of FRP to shear resistance, as it was established in the European design guidelines (fib-TG 9.3, 2001). It includes all the factors affecting the behavior of the materials at the FRP-concrete interface. This term is also used in many design methods to calculate the contribution of FRP to shear resist- ance (ACI 440.2R-08, 2008; Chen and Teng, 2001; Khalifa and Nanni, 2000; and Deniaud and Cheng, 2004). Figure 2.9 shows that the effective FRP strain decreases as FRP stiffness increases. It also shows that beams failing by ε ρ βfe f w f f fV b d E= +( )( )1 cot ( )Eq. 2.1 FRP debonding are likely to exhibit smaller effective strains than beams failing by FRP rupture or other failure modes. Similar results were reported by other researchers (Bousselham and Chaallal, 2004; Khalifa and Nanni, 2000; and Triantafillou and Antonopoulos, 2000). Figure 2.10 shows the variation in the ratio of the effective FRP strain to the ultimate FRP strain (R = εf e/ε fu) an indica- tor of the effectiveness of the FRP strengthening system ver- sus E f ρf /f ′2/3c . Figure 2.10 shows similar trends to those shown in Figure 2.9. In all cases, the effective strains are a modest fraction of the ultimate FRP strain. However, there is a high degree of scatter indicating an effect of other parameters on the shear resistance mechanism of FRP shear strengthening systems. 2.6.1.2 Effect of Internal Transverse Steel Reinforcement Recent studies have shown that the contribution of exter- nally bonded FRP to shear resistance is less for beams con- taining internal transverse steel than for beams without such reinforcement (Li et al., 2002; Pellegrino and Modena, 2002; Chaallal et al., 2002; Bousselham and Chaallal, 2004; and Czaderski, 2002). This interaction was observed in terms of resistance and strains (Bousselham and Chaallal, 2006a, b). This study also showed that for a given load, the stresses in transverse steel reinforcement of FRP-retrofitted beams were less than in beams that were not retrofitted. 2.6.1.3 Scale Effect Although a T-section is generally used in practice, the majority of the experimental data were obtained for rectan- gular beams, and most tests were performed on small-scale specimens. Also, studies on the influence of the depth of an 23 2 3 f f cE fρ ′ feε (Ef in ksi and f ’c in psi) Figure 2.9. Effective strain of FRP versus Eff /f 2/3c .

RC beam on its shear behavior have shown that for beams without shear reinforcement the shear resistance decreases as the beam size increases (ACI-ASCE, 1998). This scale effect is considered one of the major factors affecting shear data. For this reason, most concrete standards (except those in North America) have introduced correction factors for size to adjust for the contribution of the concrete to shear resistance. It is also desirable to determine if there is a scale effect on the results of tests on RC beams strengthened in shear with externally bonded FRP as shown in a preliminary investi- gation (Bousselham and Chaallal, 2004). Analysis of the test results reported in the literature on shear strengthen- ing showed a tendency for a decrease in the gain of shear resistance due to FRP as the height of the specimen increased (Bousselham and Chaallal, 2004; Leung et al., 2007). The pre- dictive models for the contribution of FRP to shear strength proposed in the literature are largely based on test results from small-scale testing and, therefore, may yield higher than actual strength values. 2.6.1.4 Effect of Shear Span-to-Depth Ratio (Slender versus Deep Beam) The majority of the available experimental data were derived from tests on slender beams. However, the shear behavior of RC beams depends largely on the shear span-to-depth ratio [defined as the shear length (a) divided by the effective beam depth (d)]. This ratio (a/d) is used to distinguish between slender and deep beams. It is important to determine whether slender and deep beams strengthened in sheer with externally applied FRP exhibits the same shear behavior. Bousselham and Chaallal (2006b) studied the influence of the a/d ratio by considering both slender beams (a/d = 3.0) and deep beams (a/d = 1.5). The results of this study indicated a larger gain in shear resistance due to FRP for slender beams than for deep beams, probably because of the arch action exhibited by deep beams. Thus, the shear contribution of externally bonded FRP is less for deep beams than for slender beams. 2.6.1.5 Influence of FRP Configuration and Anchorage The frequency of each mode of failure occurrence for dif- ferent FRP configurations (side bonding, U-wrap, or com- plete wrap), as determined from examination of the database information, is illustrated in Figure 2.11. The figure indicates that (a) debonding is the dominant mode of failure for beams strengthened with FRP and bonded on the sides only, (b) FRP debonding almost never occurs in beams retrofitted with complete FRP wrap and U-wraps with anchorage systems, and (c) failure of beams retrofitted with U-wraps occurs by debonding (65%) or by other failure modes (35%), such as diagonal tension failure in the web, shear compression failure in the compression zone, and flexural failure. 2.6.1.6 Influence of Concrete Strength Concrete strength influences the performance of shear strengthening with FRP because it influences the bonding performance at the FRP-concrete interface and the failure mode. A higher concrete strength will delay, or even inhibit, failure by debonding. A low concrete strength will inhibit early crushing of concrete in the compression zone or in the diagonal struts (Bousselham and Chaallal, 2006a) but it will decrease the bond strength at the FRP-concrete interface. The guidelines for the design of RC structures strengthened with externally applied FRP take into account the concrete strength when calculating the contribution of FRP to shear resistance (ACI 440.2R, 2008; and fib-TG 9.3, 2001), either for the deter- mination of the effective FRP strain or to prevent premature 24 2 3 f f cE fρ ′ /fe fuR ε ε= (Ef in ksi and f ’c in psi) 0.00 0.20 0.40 0.60 0.80 1.00 0.000 0.200 0.400 0.600 0.800 1.000 1.200 FRP Debonding FRP Rupture Other Failure Modes Figure 2.10. fe/fu versus Eff /f 2/3c .

crushing of concrete. Therefore, the range in concrete strengths used in tests should be representative of the strength prevail- ing in practice for existing bridge structures. 2.6.1.7 Influence of Fatigue Limited research has dealt with fatigue behavior of concrete structures strengthened with externally bonded FRP lami- nates; most of the research have focused on flexural strength- ening (Muszynski and Sierakowski, 1996; Papakonstantinou et al., 2001; Senthilnath et al., 2001; Lopez-Anido et al., 2003; Breña and Gussenhoven, 2005; Ekenel and Myers, 2005). Williams and Higgins (2008) reported on repeated load tests conducted on three full-size girder specimens repaired with bonded carbon fiber laminate for shear strengthening and static tests conducted on two similar specimens. The speci- mens were 1,219 mm high with a 356 mm wide stem and a deck portion 914 mm wide by 152 mm thick. The fatigue loading resulted in localized debonding along the FRP termi- nation locations at the stem-deck interface but did not signif- icantly alter the ultimate shear capacity of the specimens. Chaallal et al., (2009) tested six specimens under fatigue loading that varied between 35% and 65% of the respective static capacity of the specimen. Three of the beams had no internal shear reinforcement, and the other three had inter- nal transverse steel reinforcement. The specimens of each group were tested with none, one, and two layers of continu- ously wrapped CFRP for up to 5 million cycles at a frequency of 2 Hz. However, the predicted capacities differed by as much as 50% from the measured values. 2.6.1.8 Influence of Pre-Cracking Almost all reported experimental investigations that dealt with the shear performance of strengthened RC beams were performed on beams that had not been loaded (or cracked) prior to their retrofit. However, external strengthening with FRP is often performed on pre-cracked, or slightly-damaged, structures. The few investigations carried out on RC beams that were pre-cracked prior to strengthening indicated that pre-cracking does not affect the shear performance of retro- fitted beams (Czaderski, 2002; Carolin and Taljsten, 2005a, and Hassan Dirar et al., 2006). 2.6.1.9 Influence of Prestress According to a fib report (fib-T.G 9.3, 2001), less than 10% of the bridges that have been strengthened with FRP are prestressed. The literature review revealed only one study dealing with PC beams strengthened in shear with FRP (Hutchinson and Rizkalla, 1999). In this study, the authors proposed shear equations based on ACI 318 (ACI 318, 1999) and reported predictions in good agreement with the test results of seven prestressed concrete beams strengthened with CFRP strips. 2.6.1.10 Influence of Structural Continuity The ACI 440 Committee (ACI 440, 2008) reported that the methodology for determining the bond reduction coefficient κυ described in this guide has been validated for members in regions of high shear and low moment, such as monotonically- loaded, simply supported beams. However, no reference was made to the shear response for areas subjected to a combina- tion of high flexural and shear stresses. The literature reports on very few tests performed on continuous beams (Khalifa et al., 1999; Mitsui et al., 1998; and Miyauchi et al., 1997) but provides no information on the behavior of the web under this condition. 25 67 111 1 6 22 60 10 40 49 0 20 40 60 80 100 120 140 160 180 200 Side U-Wrap Complete Wrap N um be r of Te st Sp e c im e n s FRP Configurations Other FRP Rupture FRP Debonding Figure 2.11. Modes of failure related to strengthening scheme.

2.6.1.11 Factors Recommended for Further Investigation Based on the review of the factors affecting the design of FRP shear strengthening, the effects of (a) internal transverse steel reinforcement, (b) scale, (c) FRP configuration and anchorage, (d) fatigue (e) pre-cracking (f) prestressing, and (g) structural continuity were selected for further investigation. 2.6.2 Results of Experimental Investigation An experimental investigation was designed to address the factors and designs that affect the shear behavior of FRP strengthened girders but have not been fully investigated in earlier studies. These factors include the effects of: (1) pre- cracking, (2) negative moments, (3) long-term conditions such as fatigue loading and corrosion of internal steel rein- forcement, and (4) prestressing. The experimental program included full-scale RC T-beams and AASHTO type prestressed I-girders. The results of this experimental program, together with the existing experimental database were used to develop design equations for predicting the contribution of exter- nally bonded FRP to shear strength. 2.6.2.1 RC T-Beams The experimental program was conducted to investigate the shear performance of full-scale RC T-beams strengthened with externally bonded FRP sheets. Tests were performed on eight full-scale RC beams, seven of which were designed to pro- vide two distinct test regions and one beam was designated for fatigue testing. Thus a total of 15 tests were performed to investigate the effects of (1) transverse steel reinforcement, (2) pre-cracking, (3) mechanical anchorage systems, (4) fiber orientations (45° and 90° relative to the longitudinal axis of the beam), (5) negative moment, (6) environmental condi- tioning (corrosion damage), and (7) fatigue loading. The test beams were designed to mimic the geometry of beams used in a bridge located in Troy, New York (Hag-Elsafi et al., 2001a), that were strengthened with externally bonded FRP in 1999. This bridge is a 42-feet long by 120-feet wide RC structure consisting of 26 simply-supported T-beams spaced at 4.5 feet on center with an integral concrete deck. The bridge was built in 1932 and exhibited severe corrosion damage. The RC T-beams of the bridge have been strengthened in shear and flexure with externally bonded CFRP laminates. The cross section of the test beams is shown in Figure 2.12. The transverse reinforcement was designed to ensure shear failure prior to flexural failure and thus required the use of #3 stirrups at moderate (8 in.) and large (12 in.) spacing. Grade 40 steel (similar to that used in the Troy Bridge) was used for the transverse reinforcement. The test set-up, shown in Figure 2.13, was designed to provide a shear-span-to-depth ratio of 3.3. Table 2.3 summarizes the test results. The specimen desig- nations indicate the stirrup spacing in inches (8 or 12), the strengthening configuration (S90 = strips at 90° to the longi- tudinal axis, and S45 = strips at 45°), the presence and type of mechanical anchorage (NA = no anchorage, DMA = discon- tinuous mechanical anchorage, SDMA = sandwich discontin- uous mechanical anchorage, and HA = additional horizontal strips), the presence of pre-existing cracks (PC), testing under negative moment conditions (HM), and fatigue loading con- ditions (Ftg). The shear contributions of stirrups (Vs) and FRP (Vf) listed in Table 2.7, were determined from the measured strains in the stirrups and FRP sheets bridging the critical cracks. The shear contribution of the concrete was calculated by subtract- ing the contributions of the stirrups and FRP from the total shear resistance (Vn,test). A direct comparison of the shear strengths of the test beams could not be made because of the differences in concrete strength. Thus, the concrete strength and shear strength were normalized and listed in the table. The test results showed that the differences in the amount of internal transverse steel reinforcement (stirrups) used in the RC-8 and RC-12-Series beams did not significantly influ- ence the shear strength gain. However, a shear component analysis revealed an interaction between the contribution of FRP and the contribution of stirrups. Of the different anchor- age systems, the sandwich discontinuous mechanical anchor- age (SDMA) systems provided the best performance leading to rupture of FRP sheets. The specimens with discontinuous mechanical anchorage (DMA) systems and horizontal addi- tional (HA) FRP strips provided higher shear strength than 26 R=34" 42.0'' 30.0'' 18.0'' 1.5'' 1.5'' 32.7'' 1.5'' 7.0'' 1.5'' 12 #11 #3 8#5 Figure 2.12. Cross-section of test beams.

those with no anchorage systems. The fibers oriented at 45° with respect to the longitudinal axis of the beams appeared to be more effective than those oriented at 90°. However, such orientation is less practical because of the difficulty of instal- lation. Specimens tested under negative moment condition exhibited similar behavior to that of the specimens tested under positive moment conditions. Test results showed that beams with slight corrosion damage can be effectively repaired in shear by externally bonded FRP sheets since cracks due to corrosion do not influence the effectiveness of FRP shear strengthening. The stirrups in the beams with pre-existing cracks yielded at a lower shear force than those in the beams without pre-existing cracks. However, the presence of pre- existing cracks did not influence the ultimate failure modes of the beams. Thus, pre-existing cracks do not seem to have a neg- ative impact on the effectiveness of FRP shear strengthening. The fatigue test performed in this study and other tests reported in the literature indicate that (a) if stresses in the shear stirrups are below the yield strength, the FRP strength- ening can help delay the yielding and prevent fatigue failure of the girder in shear; and (b) if the stirrups have already yielded under existing service loads, it is unlikely that adding 27 Reaction Frame Loading Frame External Shear Strengthening Test Region Roller Temporary Support Load Cell A A B B 9 ft 15 ft 11 ft Figure 2.13. Details of test set-up. Specimen Designation f'c (psi) Vn,test(kips) Vc (kips) Vs (kips) Vf (kips) Vn,norm (kips) Actual Shear Gain (kips) Shear Gain (%) RC-8-Control 2,800 153 72 81 - 153 - - RC-12-Control 2,880 124 65 59 - 124 - - RC-8-S90-NA 3,000 191 87 64 41 189 36 23.2 RC-8-S90-DMA 3,450 212 133 56 24 199 47 30.9 RC-12-S90-NA 4,190 172 92 41 40 156 33 26.3 RC-12-S90-DMA 4,420 205 112 38 55 183 60 48.1 RC-12-S90-SDMA-PC 2,780 214 118 37 59 216 92 74.6 RC-12-S90-HA-PC 2,650 188 88 38 61 191 67 54.5 RC-12-S90-SDMA-Cor 6,180 268 98 64 106 237 113 91.1 RC-12-S45-NA 6,050 217 79 44 95 191 67 54.0 RC-12-S45-HA 3,850 181 53 41 86 174 50 40.2 RC-12-S45-SDMA 4,230 203 37 42 124 196 73 58.6 RC-12-S90-NA-HM 3,710 186 28 103 55 182 59 47.3 RC-12-S90-SDMA-HM 4,060 229 44 87 84 222 99 80.4 RC-12-S90-NA-Ftg 4,730 - - - - - - - f'c : Concrete strength at the time of testing Vn,test : Measured Shear Strength Vc: Shear contribution of concrete Vs: Shear contribution of stirrups Vf: Shear contribution of FRP Vn,norm: Normalized Shear Strength Table 2.7. Nominal shear strength and shear gain calculations based on normalized concrete strength.

an FRP strengthening system will reduce stresses consider- ably, but it would help contain the stresses and prevent cata- strophic failure of the girder. Therefore, it is important to consider shear strengthening of a concrete girder using FRP within an overall strengthening plan that also considers the flexural capacity. Strengthening a girder that is deficient in shear may be required to raise the shear resistance to an acceptable level without the need to increase flexural capacity. In addition, limiting the stress in the stirrups to the yield strength will eliminate that fatigue failure of the girder in shear. 2.6.2.2 PC Girders Tests were conducted on full-scale AASHTO type PC gird- ers to investigate the effects of FRP shear strengthening. Table 2.8 lists the test parameters for the PC girders. The param- eters investigated included (a) size of test girders (Type 4 and 28 Cross-Section Type Pre-Existing Cracks Strengthening Scheme Anchorage Type Steel Shear Reinforcement FRP Shear Reinforcement Shear Span (ft) Shear Span- to-Depth Ratio (a/d) T4-12-Control None #3 @ 12" ( v = 0.0031) f = 0 9 = 0 9 2.9 T4-18-Control None None #3 @ 18" ( v = 0.0020) f 2.9 2.9 2.9 T4-18-S90-NA I I I II No No No No II II No No Strips/90 #3 @ 18" ( v = 0.0020) f = 0.0014 9 T4-18-S90-CMA ContinuousCFRP Plates #3 @ 18" ( v = 0.0020) f = 0.0014 12 2.9 T4-18-S90-DMA DiscontinuousCFRP Plates #3 @ 18" ( v = 0.0020) f = 0.0014 12 2.9 T4-18-S45-DMA DiscontinuousCFRP Plates #3 @ 18" ( v = 0.0020) f = 0.0010 12 12 12 2.9 T4-12-Control-Deck II No None None None None None #3 @ 12" ( v = 0.0031) f = 0 T4-12-S90-SDMA II No No Strips/90 Strips/45 Strips/90 Strips/90 Strips/90 Strips/90 Strips/90 Discontinuous Sandwich CFRP Plates #3 @ 12" ( v = 0.0031) f = 0.0014 12 2.9 T3-12-Control III None None #3 @ 12" ( v = 0.0031) f = 0 T3-12-S90-NA III No Strips/90 #3 @ 12" ( v = 0.0031) f = 0.0014 12 3.4 3.4 3.4 T3-12-S90-NA-PC III Yes None #3 @ 12" ( v = 0.0031) f = 0.0014 12 3.4 T3-12-S90-DMA III No Strips/90 DiscontinuousCFRP Plates #3 @ 12" ( v = 0.0031) f = 0.0014 12 12 3.4 T3-18-Control IV IV IV No No No None None #3 @ 18" ( v = 0.0020) f = 0 T3-18-S90-NA None #3 @ 18" ( v = 0.0020) f = 0.0014 12 3.4 T3-18-S90-HS HorizontalFRP Strips #3 @ 18" ( v = 0.0020) f = 0.0014 12 3.4 T3-18-S90-SDMA IV No Strips/90 Discontinuous Sandwich CFRP Plates #3 @ 18" ( v = 0.0020) f = 0.0014 12 3.4 2 Test Parameters Type 3 Type 4 3 4 5 MoDOT Standard 6 7 8 Test I.D.Girder 1 Table 2.8. PC girder test parameters.

Type 3), (b) stiffness of top and bottom flanges (cross-sectional type), (c) effects of pre-existing damage (pre-cracking), (f) FRP strengthening scheme (fibers oriented at 90° versus 45°), (g) types of mechanical anchorage, and (h) transverse steel reinforcement (stirrups) ratio. All PC girders were designed with consideration for the AASHTO LRFD design guidelines (AASHTO, 2008). Girder geometry and strand patterns were based on standard I- girders used by the Missouri Department of Transportation (MoDOT). The girders were designed to fail in shear, with moderate and low levels of shear reinforcement, to investigate the influence of the transverse reinforcement on the shear behavior. Girders with the four cross-sectional designs shown in Figure 2.14 were constructed and tested. The PC girders were tested in a three point loading con- figuration with each girder being designed to have two test regions: one on each end of the girder. Electric resistance strain gages, confinement bars, and longitudinal reinforce- ment to monitor local strains were installed on the stirrups within the test regions. Strain gages were also installed on the mechanical anchorage systems and at various locations along the FRP strips to monitor strain variation along the width and height of the FRP strips. These gages were also used to mon- itor the progression of delamination/debonding of the FRP. A strain rosette consisting of 21 LVDTs was anchored to the web of each test girder to measure shear strains within the test region for the purpose of determining the principal strains and their orientation. A similar system consisting of Demec gages glued to the opposite side of the web was used as a sec- ondary measure for evaluating the principal strains and their orientations. Additional string transducers and LVDTs were also used to monitor deformations at critical points along the test girders. The results of the PC girder testing were inconclusive as to the effectiveness of the FRP shear strengthening because of the variety of failure modes observed during the testing. In many cases, no shear gain was observed for the FRP strengthened specimens. Failure modes included (1) horizontal failure along the top flange, (2) debonding of FRP, (3) localized rup- ture of FRP, (4) diagonal shear tension, (5) web crushing, (6) mechanical anchorage failure, and (7) failure due to high stress concentrations localized at the reaction point. Some test specimens exhibited multiple failure modes either at the same time or in a sequential manner. For the MoDOT Type 4 girders [Figures 2.14 (a) and (b)], shear cracks in the web propagated toward the top flange at which point they turned and ran horizontally along the lon- gitudinal compression reinforcement located at the interface between the web and top flange. The maximum shear force carried by all MoDOT Type 4 girders was ultimately governed by a failure plane created by the horizontal cracks along the top flange (failure mode—TF). For the MoDOT Type 4 gird- ers strengthened in shear with FRP, the horizontal top flange failure was generally preceded by debonding of the FRP (failure mode—D). In two extreme cases, ultimate failure was accom- panied by failure of the mechanical anchorage (T4-18-S90- CMA) (failure mode—MA) and localized rupture of the FRP (T4-18-S90-DMA) (failure mode—LR). For the MoDOT Type 3 girders, failure due to web crushing (failure mode— WC) or high stress concentrations near the reaction point (failure mode—SC) were observed when a moderate level of transverse steel reinforcement was provided (stirrups spaced at 12 inches). For the MoDOT Type 3 girders with low transverse steel reinforcement conditions (stirrups spaced at 18 inches), ultimate failure was always characterized by diagonal shear- tension failure (failure mode—DT) preceded by some level of debonding (failure mode—D) when FRP reinforcement was present. The diminished effectiveness of the FRP shear strength- ening is probably related to the thin web and stiff flange geom- etry of the PC girders and the adverse effect of FRP debonding when it is accompanied by peeling off of the concrete cover. In extreme cases, web crushing failure can occur, which is a failure mode that cannot benefit from FRP strengthening. The use of properly anchored FRP systems (e.g., with mechanical anchorage) will minimize the extent of debonding and improve performance. To better understand the shear resistance mechanisms and quantify the FRP contribution to the ultimate shear capacity, it is necessary to examine the effects of the individual compo- nents contributing to the total shear resistance. The primary components contributing to the shear resistance are those pro- vided by the concrete (Vc), steel stirrups (Vs), and externally bonded FRP (Vf). A shear component analysis was conducted on the experimental data to identify the contribution of each component throughout the loading history of the test girders. The three individual components (Vc, Vs, and Vf) were evalu- ated from crack-based free-body diagrams of a portion of the test girders along the critical shear cracks. Vs and Vf were deter- mined from strain gage measurements along the stirrups and FRP strips within the test regions. Only strain measurements closest to the critical shear crack were used for such analysis. Vc was estimated as the difference between the applied shear force (Vn) and the contributions of the stirrups and FRP (i.e., Vs + Vf). A shear component analysis showed that externally bonded FRP provides a significant contribution to the total shear resist- ance of a PC girder. The results of this analysis are summarized in Table 2.9 at the stages corresponding to yielding of the steel stirrups and ultimate load. 2.6.3 Results of Finite Element Method (FEM) Analysis Nonlinear finite element analyses were carried out using the commercial FE program DIANA (DIsplacement ANA- lyzer) to (1) predict the behavior of the test girders prior to testing, (2) investigate the effects of additional parameters not 29

30 #3 stirrups 13" 5" 1" 25" 6" 8" 17" (8) #8 bars 6" (20) 0.6" dia. tendons prestressed to 40% of ultimate #3 spaced as needed (long. reinf. support) #3 confinement bar 3-7/8" (8) #8 bars Deck Slab 13" 12" #3 stirrups (20) 0.6" dia. tendons prestressed to 40% of ultimate #3 confinement bar 9-7/8" 5-3/16" Horizontal Shear Studs #5 bar spaced @ 12" o.c. (a) Cross-Section Type I (b) Cross-Section Type II 8" 1'-9" 5" 1" 1'-8" 6" 7" 3/4" 1'-5" 6" (12) 0.6" dia. tendons prestressed to 70% of ultimate (11) #6 bars #3 stirrups (2) #5 bars (3) #3 bars (c) Cross-Section Type III (d) Cross-Section Type IV 3'-1" 8" #3 stirrups (3) #6 bars (10) #3 bars (24) 0.6" dia. tendons prestressed to 60% of ultimate Figure 2.14. Specimen cross sections.

considered in the experimental test program, and (3) identify the global and local behaviors of girders that were not moni- tored in the tests such as the interface behavior between con- crete and FRP sheets. DIANA is a program with its own library of structural elements and constitutive material models and includes a user-defined option for adding specific elements and constitutive models to provide flexibility for FE modeling. Subsequently, an FE model capable of simulating the global and local behavior of the RC and PC girders strengthened with FRP in shear was developed. The progression of the FE model devel- opment was as follows: (i) Preliminary analyses, focused on the modeling aspects of the FE model, were carried out at the ini- tial state of the FE analysis using two- and three-dimensional FE models. Another finite element program, FEAP, was used to confirm the results of DIANA; (ii) The results of the two- dimensional FE analysis were used to refine the input param- eters of the three-dimensional model and improve accuracy; (iii) Other modeling techniques (e.g., phase analysis, modeling of the interface region between concrete and FRP, use of differ- ent elements, and refinement of mesh size) were introduced in the developed FE models to better reflect the processes observed in the experimental girders; (iv) Because results of FE models are strongly dependent on the material models chosen for each material, several material models for concrete, steel, FRP, and interface were examined, and optimized material models were incorporated in the FE model (special considera- tion was given to concrete and interface models because of their inherent complex properties and effects on the shear behavior). The results obtained from the FE models were compared to the experimental results with respect to global behavior (i.e., shear force-displacement relationships and final failure modes) and local behavior (i.e., stress and strain variations for each component). The shear force-displacement relation- ships obtained from the FE model showed somewhat stiffer behavior than that obtained from the tests on RC and PC girders regardless of FRP strengthening (see Figure 2.15). This phenomenon is attributed to the configuration considered in the FE model that differed from the test. For example, the FE simulation did not consider external configurations such as strengthening of the specimens with the Dywidag bars. Also, the smeared crack model used for concrete in the FE simulation does not precisely replicate the behavior of the test specimens that were mostly governed by a few primary discrete diagonal cracks. However, accurate prediction of cracking and ultimate loads, similar crack patterns, consistent ductility, and similar strain/stress variations in each component are indications of the developed FE model’s efficiency. In terms of failure strength, the average ratio of experimen- tal shear strength to analytically evaluated shear strength of the PC girders (Vexp/VFE) was 1.04 with a maximum ratio of 1.22 and a minimum ratio of 0.95. The variance (VAR), standard deviation (STDEV), and coefficient of variance 31 At Yielding of Steel Stirrups At Ultimate Load Test I.D. f'c(psi) Cross Section Type Shear Crack Angle (deg.) Failure Mode Vcy (kips) Vsy (kips) Vfy (kips) Vcu (kips) Vsu (kips) Vfu (kips) T4-12-Control 9,970 I 32.0 TF N/A N/A N/A 131 71 N/A T4-18-Control 9,930 I 26.0 TF 127 57 N/A 149 57 N/A T4-18-S90-NA 10,020 I 21.0 D + TF 83 43 67 83 43 67 T4-18-S90-CMA 10,120 II 25.0 D + MA + TF N/A N/A N/A 95 47 87 T4-18-S90-DMA 10,160 II 24.0 D + LR + TF N/A N/A N/A 161 39 44 T4-18-S45-DMA 10,190 II 32.0 D + TF N/A N/A N/A 144 34 77 T4-12-Control-Deck 10,660 II 26.0 TF 142 86 N/A 159 86 N/A T4-12-S90-SDMA 10,330 II 30.0 TF 113 57 35 134 57 67 T3-12-Control 8,890 III 23.0 SC 133 100 N/A 153 100 N/A T3-12-S90-NA 8,910 III 22.0 D + WC 120 86 23 143 90 38 T3-12-S90-NA-PC 9,470 III 21.0 D + WC 110 86 41 115 86 39 T3-12-S90-DMA 10,380 III 25.0 SC N/A N/A N/A 158 60 31 T3-18-Control 9,590 IV 21.0 DT 108 59 N/A 192 60 N/A T3-18-S90-NA 10,120 IV 15.0 D + DT 52 86 26 112 86 18 T3-18-S90-HS 10,190 IV 26.0 D + DT 82 43 38 140 51 31 T3-18-S90-SDMA 10,430 IV 33.0 D + DT 48 77 110 48 77 110 Table 2.9. Summary of shear contributions.

(COV) are calculated as 0.01, 0.07, and 0.07, respectively. For RC girders, the average shear strength ratio was 0.98 with a maximum ratio of 1.11 and a minimum ratio of 0.90, and VAR, STDEV, and COV are calculated as 0.00, 0.07, and 0.07, respectively. The FE analyses showed a good agreement with test results for the ultimate strength suggesting that the devel- oped FE models appropriately predict the ultimate strength of both PC and RC girders. The FE analysis allowed investigation of local behaviors that could not be examined through experiments such as the interface behavior between concrete and FRP sheets. The FE analysis also provides the stress and strain variations for con- crete, steel, FRP, and interface regions that were used to investigate each component contribution to the shear trans- fer mechanism. In particular, strain variations along the prin- cipal direction of FRP sheets are valuable inputs for design- ing FRP strengthening for shear. Figure 2.16 illustrates the strain distribution determined from FE analysis along the principal direction of a critical FRP sheet for a series of increasing load stages. As shown in the figure, when the test beam reached the ultimate state (i.e., a loading state of 250 kips), the maximum strain in the FRP was only 0.0091 which is 54% of the rupture strain (0.017). 2.7 Performance Evaluation of Existing Design Methods This section presents a summary of the performance eval- uation conducted for existing models and relationships for Vf. Table 2.10 presents a summary of the performance of 21 different relationships (i.e., 17 models presented in research papers and four models included in code and guideline docu- 32 0 50 100 150 200 250 0 1 2 3 4 5 0 1 2 3 4 5 6 7 8 9 10 Displacement (in.) Fo rc e (ki ps ) w i thout softening w i th softening Experiment (a) PC girders 0 50 100 150 200 250 Displacement (in.) Fo rc e (ki ps ) Case 4-1_FE Case 4-2_FE 12in-S90-NoMA (b) RC girders Figure 2.15. Representative shear force-displacement relationship.

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

34 M o de l Af fili at io n Al - Su la im a n i e t al . Ch aje s et a l. Tr ia nt af illo u an d An to n o po ul os M a lek an d Sa ad at m an es h Kh al ifa et al . Kh al ifa a nd N an ni Hu tc hi ns on a n d Ri zk al la Ch aa lla l e t a l. Ch en an d Te n g Pe lle gr ino an d M o de n a Hs u et al . De n ia u d an d Ch en g Ca o et al . Zh an g an d Hs u Ca ro lin an d Ta ljst en M o n ti a n d Li o tta Pe lle gr in o an d M o de n a fib - TG 9. 3 JS CE CS A S8 06 AC I 4 40 Year 1994 1995 2000 1998 1998 2000 1999 2002 2003a,b 2002 2003 2001 2005 2005 2005b 2005 2006 2001 2001 2002 2008 Model # 2 4 7 9 6 1 3 5 8 10 11 12 13 14 15 16 17 18 19 20 21 1.) All Beams Mean 0.23 0.67 0.69 0.45 0.62 1.10 0.84 0.34 0.81 1.46 1.05 1.49 1.03 1.90 1.01 1.16 1.68 3.56 2.29 1.30 8.39 0.75 1.19 1.15 1.67 0.41 1.24 0.52 1.46 1.65 COV 1.10 0.77 0.64 0.89 1.71 0.71 0.59 0.81 0.75 0.73 0.60 0.76 0.99 0.96 Num 324 324 324 315 317 324 324 324 244 244 324 324 324 324 324 324 317 324 324 317 2.) All "Valid" Beams (those used in LRFD Vf Model Calibration) Mean 0.25 1.23 0.98 0.38 0.73 1.53 1.57 2.10 1.18 1.83 3.24 1.39 0.89 9.30 0.78 1.30 1.25 1.84 0.44 1.35 0.57 1.61 1.78 COV 0.94 0.56 0.97 0.95 0.91 0.60 7.57 1.34 1.71 1.33 0.57 0.53 0.73 0.66 0.67 0.50 0.66 0.89 0.88 Num 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 0.70 0.38 0.69 0.57 0.69 0.68 0.62 0.45 1.16 0.79 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 0.53 COV 0.61 COV 0.54 COV 0.71 COV 0.39 COV 0.50 COV 0.50 COV 0.50 COV 0.56 COV 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 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 61 61 53 53 61 61 61 61 61 61 61 61 61 61 61 61 61 61 61 61 58 58 58 58 40 40 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 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 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 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 47 29 38 79 32 26 26 26 26 25 25 26 26 26 26 26 26 26 26 26 26 26 25 25 17 17 32 32 32 32 32 32 32 32 32 32 32 32 32 32 32 32 32 32 14 14 79 79 79 79 79 79 79 79 79 79 79 79 79 79 79 79 79 79 48 48 38 38 38 36 36 38 38 38 38 38 38 38 38 38 38 38 36 36 36 36 29 29 29 29 29 29 29 29 29 29 29 29 29 29 26 26 26 26 26 26 47 47 47 47 47 47 47 47 47 47 47 47 47 47 46 46 46 46 46 46 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 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 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 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 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 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 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 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 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 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 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 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 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 324 251 1.05 Table 2.10. Statistical evaluation of strength ratios Vf,test/Vf,model by test beam type.

most formulas in codes of practice and therefore, not suit- able for use in practice. 2. Availability and Reliability of Model Parameter Data. The models proposed by most researchers require knowl- edge of the measurable features of the test beam and FRP application, such as the development length of the FRP reinforcement. While such requirements improve accu- racy, design provisions must include items that are avail- able or can be appropriately assumed. The parameters proposed in a Vf relationship for use in the LRFD specifi- cations should recognize that FRP shear reinforcement is most likely to be used for strengthening of an existing old structure for which full design details may not be available. 3. Calibration with Full Shear Strength Ratio Considering Specific Vc and Vs Relationships. A comparative evaluation of Vf models, can be conducted using the strength ratios of Vf,test/Vf. However, to include in a code of practice, the rela- tionship for Vf must be calibrated based on the bias (strength ratio) and COV of the Vn,test/Vn ratio (Vn = Vc + Vs + Vf). 2.9 Reliability Assessment A study was conducted to assess the reliability of the pro- posed design equations using procedures similar to those used in the calibration of AASHTO-LRFD specifications (AASHTO, 2008). The First Order Reliability Method (FORM) was used for calculating the reliability index (βr) of 36 bridges that were designed for such purposes. These bridges covered three span lengths, interior and exterior girders, and three shear defi- ciency levels that were strengthened with FRP shear rein- forcement (i.e., a set of 3 × 2 × 3 = 18 bridges). One set used anchored FRP reinforcement where FRP rupture is the domi- nating mode of failure, and another set used non-anchored FRP reinforcement where debonding is to be expected. Table 2.11 lists the nominal properties of these bridges, illustrating the wide range in the ratio of FRP contribution (Vf) to the nominal strength of the existing structure. The live-to-dead load shear demand ratio for these bridges ranges from 0.83 to 2.32. The nominal values of the bridge properties were used to obtain random variables for each of the main parameters in the design equation. This step required knowledge of the sta- tistical characteristics of the random variables. Some of the required information was obtained from the literature, and other information specific to this study had to be determined by estimating the random variables’ bias (ratio of random variable’s mean value to its nominal value) and COV (ratio of random variable’s standard deviation to its mean value). For example, the statistical characteristics of the analysis model uncertainty, ξP, were obtained by comparing the predicted shear strength using the proposed equations to the experi- mentally, measured values as reported in the database. The effect of material and fabrication tolerances on the resistance model was determined using Monte Carlo simulations and some recently published data (Nowak and Szerszen, 2003). The statistical characteristics of load-related random vari- ables were taken from NCHRP Report 368 (Nowak, 1999). Table 2.12 shows the bias and coefficient of variation for the main parameters used in the limit state function (Z) that 35 Bridge Case sdA vv(in2) fw (in) fs (in) ft (in) cV (kips) sV (kips) fV (kips) sc f VV V +Span Length Girder Rupture Debond 45 ft Interior L45F1I 0.847 4.0 12.0 0.00774 0.01863 73.57 50.82 33.88 0.272 L45F2I 0.730 10.0 0.01142 0.02749 43.79 40.91 0.349 L45F3I 0.613 8.0 0.01477 0.03556 36.76 47.94 0.435 Exterior L45F1E 0.697 12.0 0.01461 0.03519 41.79 41.79 0.362 L45F2E 0.532 10.0 0.02315 0.05575 31.92 51.66 0.490 L45F3E 0.368 8.0 0.03146 0.07576 22.05 61.53 0.643 60 ft Interior L60F1I 0.696 14.0 0.00644 0.01023 111.24 41.77 41.77 0.273 L60F2I 0.580 12.0 0.00644 0.01402 34.78 48.76 0.334 L60F3I 0.463 10.0 0.00728 0.01753 27.79 55.76 0.401 Exterior L60F1E 0.565 14.0 0.01461 0.01855 33.89 50.84 0.350 L60F2E 0.468 12.0 0.02315 0.02210 28.06 56.67 0.407 L60F3E 0.371 10.0 0.03146 0.02477 22.23 62.49 0.468 75 ft Interior L75F1I 0.501 16.0 0.00596 0.00596 163.81 30.06 45.09 0.233 L75F2I 0.319 14.0 0.00648 0.00776 19.12 56.03 0.306 L75F3I 0.136 12.0 0.00664 0.01142 8.18 66.97 0.389 Exterior L75F1E 0.394 16.0 0.00730 0.00849 23.67 55.23 0.295 L75F2E 0.214 14.0 0.00764 0.01277 12.86 66.04 0.374 L75F3E 0.034 12.0 0.00762 0.01734 2.05 76.85 0.463 Table 2.11. Shear resistance components.

accounts for variabilities and uncertainties in material and fabrication tolerances (αMF), analysis model accuracy (ξp), and girder distribution factors (ηGDF) as well as the different loading types (wearing surface, dead load, and live load). The simplified approximate expressions used in previous AASHTO calibration studies were not used because of the high COV for the analysis model, which exceed the limits of the applicability of the simplified approximated expressions. A detailed iterative FORM analysis was performed; the results were validated using Monte Carlo simulations for one bridge. After several trials, the proposed design expression was adjusted to achieve βr values close to the level targeted by most AASHTO calibration studies (i.e., βr,target = 3.50). The performance of the proposed expression is illustrated in Figure 2.17 for a range of girder span lengths and spacings. The figure shows that the reliability index is nearly the same for all girder spacings and is about 3.50 for shorter span lengths but decreases for longer span lengths. 36 Random Variable Bias COV Material and Fabrication Tolerances, αMF Varies (see Appendix) Analysis Model, ξP FRP Rupture 1.680 0.330Other 1.410 0.269 Wearing Surface DL, ζWS 1.000 0.250 Component DL, ζDC 1.050 0.100 Highway LL (including impact), ζLL+IM L=45 ft 1.041 0.180 L=60 ft 1.046 0.180 L=75 ft 1.071 0.180 LRFD Girder Distribution Factor, ηGDF Interior 1.134 0.157 Exterior 1.307 0.239 Table 2.12. Summary of bias and COV values used in calibration study. 2.75 3.00 3.25 3.50 3.75 20 30 40 50 60 70 80 90 Re lia bi lit y I nd ex , β r Girder Span Length, L (ft) Girder Spacing, S = 5 ft Girder Spacing, S = 7 ft Girder Spacing, S = 9 ft Figure 2.17. Reliability index (r) versus span lengths for different girder spacings.