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

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23 2.6.1.1 Influence of FRP Properties FRP debonding are likely to exhibit smaller effective strains than beams failing by FRP rupture or other failure modes. Table 2.5 indicates that CFRP sheets have been used in Similar results were reported by other researchers (Bousselham almost all studies addressing performance of RC beams and Chaallal, 2004; Khalifa and Nanni, 2000; and Triantafillou strengthened in shear with FRP. The effective strain concept and Antonopoulos, 2000). was used to evaluate the effectiveness of FRP shear strength- Figure 2.10 shows the variation in the ratio of the effective ening systems. Figure 2.9 shows the variation of the effec- FRP strain to the ultimate FRP strain (R = f e / f u) an indica- tive FRP strain (fe) versus (E f f /f c2/3) a function of FRP rigid- tor of the effectiveness of the FRP strengthening system ver- ity (Ef f) and the compressive strength of concrete (f c). The sus E f f /f c 2/3 . Figure 2.10 shows similar trends to those shown effective FRP strain (fe) was determined based on the tradi- in Figure 2.9. In all cases, the effective strains are a modest tional truss analogy using the following expression: fraction of the ultimate FRP strain. However, there is a high degree of scatter indicating an effect of other parameters on fe = V f (bw d f E f f (1 + cot )) (Eq. 2.1) the shear resistance mechanism of FRP shear strengthening systems. where: bw = the width of the web df = the effective depth of FRP reinforcement 2.6.1.2 Effect of Internal Transverse = the angle of inclination of the FRP with respect to Steel Reinforcement the longitudinal axis of the beam. Recent studies have shown that the contribution of exter- The term (E f f /f c2/3) was used because it includes the effects nally bonded FRP to shear resistance is less for beams con- of (1) the amount of FRP expressed in terms of the FRP ratio taining internal transverse steel than for beams without such (f = Af /(bw s f )), (2) the fiber type expressed in terms of the reinforcement (Li et al., 2002; Pellegrino and Modena, 2002; modulus of elasticity of FRP (Ef), and (3) the compressive Chaallal et al., 2002; Bousselham and Chaallal, 2004; and strength of concrete (f c) which is a major factor influenc- Czaderski, 2002). This interaction was observed in terms of ing the bond performance of FRP strengthening. The term resistance and strains (Bousselham and Chaallal, 2006a, b). (E f f /f c2/3) is particularly important for evaluating the contri- This study also showed that for a given load, the stresses in bution of FRP to shear resistance, as it was established in the transverse steel reinforcement of FRP-retrofitted beams were European design guidelines (fib-TG 9.3, 2001). It includes less than in beams that were not retrofitted. all the factors affecting the behavior of the materials at the FRP-concrete interface. This term is also used in many design 2.6.1.3 Scale Effect methods to calculate the contribution of FRP to shear resist- ance (ACI 440.2R-08, 2008; Chen and Teng, 2001; Khalifa and Although a T-section is generally used in practice, the Nanni, 2000; and Deniaud and Cheng, 2004). majority of the experimental data were obtained for rectan- Figure 2.9 shows that the effective FRP strain decreases as gular beams, and most tests were performed on small-scale FRP stiffness increases. It also shows that beams failing by specimens. Also, studies on the influence of the depth of an fe Ef f f c2 3 (Ef in ksi and f 'c in psi) Figure 2.9. Effective strain of FRP versus Ef f /fc2/3.

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24 1.00 FRP Debonding FRP Rupture 0.80 Other Failure Modes 0.60 R = fe / fu 0.40 0.20 0.00 0.000 0.200 0.400 0.600 0.800 1.000 1.200 Ef f f c2 3 (Ef in ksi and f ' c in psi) Figure 2.10. fe/fu versus Ef f /f c 2/3. RC beam on its shear behavior have shown that for beams beams, probably because of the arch action exhibited by deep without shear reinforcement the shear resistance decreases as beams. Thus, the shear contribution of externally bonded FRP the beam size increases (ACI-ASCE, 1998). This scale effect is is less for deep beams than for slender beams. considered one of the major factors affecting shear data. For this reason, most concrete standards (except those in North 2.6.1.5 Influence of FRP Configuration America) have introduced correction factors for size to adjust and Anchorage for the contribution of the concrete to shear resistance. It is also desirable to determine if there is a scale effect on the The frequency of each mode of failure occurrence for dif- results of tests on RC beams strengthened in shear with ferent FRP configurations (side bonding, U-wrap, or com- externally bonded FRP as shown in a preliminary investi- plete wrap), as determined from examination of the database gation (Bousselham and Chaallal, 2004). Analysis of the information, is illustrated in Figure 2.11. The figure indicates test results reported in the literature on shear strengthen- that (a) debonding is the dominant mode of failure for beams ing showed a tendency for a decrease in the gain of shear strengthened with FRP and bonded on the sides only, (b) FRP resistance due to FRP as the height of the specimen increased debonding almost never occurs in beams retrofitted with (Bousselham and Chaallal, 2004; Leung et al., 2007). The pre- complete FRP wrap and U-wraps with anchorage systems, dictive models for the contribution of FRP to shear strength and (c) failure of beams retrofitted with U-wraps occurs by proposed in the literature are largely based on test results from debonding (65%) or by other failure modes (35%), such as small-scale testing and, therefore, may yield higher than actual diagonal tension failure in the web, shear compression failure strength values. in the compression zone, and flexural failure. 2.6.1.4 Effect of Shear Span-to-Depth Ratio 2.6.1.6 Influence of Concrete Strength (Slender versus Deep Beam) Concrete strength influences the performance of shear The majority of the available experimental data were derived strengthening with FRP because it influences the bonding from tests on slender beams. However, the shear behavior of performance at the FRP-concrete interface and the failure RC beams depends largely on the shear span-to-depth ratio mode. A higher concrete strength will delay, or even inhibit, [defined as the shear length (a) divided by the effective beam failure by debonding. A low concrete strength will inhibit depth (d)]. This ratio (a/d) is used to distinguish between early crushing of concrete in the compression zone or in the slender and deep beams. It is important to determine whether diagonal struts (Bousselham and Chaallal, 2006a) but it will slender and deep beams strengthened in sheer with externally decrease the bond strength at the FRP-concrete interface. The applied FRP exhibits the same shear behavior. Bousselham guidelines for the design of RC structures strengthened with and Chaallal (2006b) studied the influence of the a/d ratio by externally applied FRP take into account the concrete strength considering both slender beams (a/d = 3.0) and deep beams when calculating the contribution of FRP to shear resistance (a/d = 1.5). The results of this study indicated a larger gain in (ACI 440.2R, 2008; and fib-TG 9.3, 2001), either for the deter- shear resistance due to FRP for slender beams than for deep mination of the effective FRP strain or to prevent premature

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

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

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27 A B Loading Reaction Frame Frame External Load Test Shear Cell Region Strengthening Temporary Support Roller A B 9 ft 15 ft 11 ft Figure 2.13. Details of test set-up. those with no anchorage systems. The fibers oriented at 45 cracks yielded at a lower shear force than those in the beams with respect to the longitudinal axis of the beams appeared to without pre-existing cracks. However, the presence of pre- be more effective than those oriented at 90. However, such existing cracks did not influence the ultimate failure modes of orientation is less practical because of the difficulty of instal- the beams. Thus, pre-existing cracks do not seem to have a neg- lation. Specimens tested under negative moment condition ative impact on the effectiveness of FRP shear strengthening. exhibited similar behavior to that of the specimens tested The fatigue test performed in this study and other tests under positive moment conditions. Test results showed that reported in the literature indicate that (a) if stresses in the beams with slight corrosion damage can be effectively repaired shear stirrups are below the yield strength, the FRP strength- in shear by externally bonded FRP sheets since cracks due ening can help delay the yielding and prevent fatigue failure to corrosion do not influence the effectiveness of FRP shear of the girder in shear; and (b) if the stirrups have already strengthening. The stirrups in the beams with pre-existing yielded under existing service loads, it is unlikely that adding Table 2.7. Nominal shear strength and shear gain calculations based on normalized concrete strength. Actual Shear Vn,test Vc Vs Vf Vn,norm Shear Specimen Designation f'c (psi) Gain (kips) (kips) (kips) (kips) (kips) Gain (%) (kips) 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

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

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

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

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31 Table 2.9. Summary of shear contributions. Shear At Yielding of Steel Stirrups At Ultimate Load Cross f'c Crack Test I.D. Section Vcy Vsy Vfy Vcu Vsu Vfu (psi) Angle Failure Mode Type (kips) (kips) (kips) (kips) (kips) (kips) (deg.) 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 considered in the experimental test program, and (3) identify tion was given to concrete and interface models because of their the global and local behaviors of girders that were not moni- inherent complex properties and effects on the shear behavior). tored in the tests such as the interface behavior between con- The results obtained from the FE models were compared crete and FRP sheets. DIANA is a program with its own library to the experimental results with respect to global behavior of structural elements and constitutive material models and (i.e., shear force-displacement relationships and final failure includes a user-defined option for adding specific elements modes) and local behavior (i.e., stress and strain variations and constitutive models to provide flexibility for FE modeling. for each component). The shear force-displacement relation- Subsequently, an FE model capable of simulating the global and ships obtained from the FE model showed somewhat stiffer local behavior of the RC and PC girders strengthened with FRP behavior than that obtained from the tests on RC and PC in shear was developed. The progression of the FE model devel- girders regardless of FRP strengthening (see Figure 2.15). This opment was as follows: (i) Preliminary analyses, focused on the phenomenon is attributed to the configuration considered in modeling aspects of the FE model, were carried out at the ini- the FE model that differed from the test. For example, the FE tial state of the FE analysis using two- and three-dimensional FE simulation did not consider external configurations such as models. Another finite element program, FEAP, was used to strengthening of the specimens with the Dywidag bars. Also, confirm the results of DIANA; (ii) The results of the two- the smeared crack model used for concrete in the FE simulation dimensional FE analysis were used to refine the input param- does not precisely replicate the behavior of the test specimens eters of the three-dimensional model and improve accuracy; that were mostly governed by a few primary discrete diagonal (iii) Other modeling techniques (e.g., phase analysis, modeling cracks. However, accurate prediction of cracking and ultimate of the interface region between concrete and FRP, use of differ- loads, similar crack patterns, consistent ductility, and similar ent elements, and refinement of mesh size) were introduced strain/stress variations in each component are indications of in the developed FE models to better reflect the processes the developed FE model's efficiency. observed in the experimental girders; (iv) Because results of FE In terms of failure strength, the average ratio of experimen- models are strongly dependent on the material models chosen tal shear strength to analytically evaluated shear strength for each material, several material models for concrete, steel, of the PC girders (Vexp /VFE) was 1.04 with a maximum ratio FRP, and interface were examined, and optimized material of 1.22 and a minimum ratio of 0.95. The variance (VAR), models were incorporated in the FE model (special considera- standard deviation (STDEV), and coefficient of variance